prudent valuation
TRANSCRIPT
Prudent Valuation
Here we go
Global Derivatives Trading & Risk Management
Budapest, 10 May 2016
Marco Bianchetti
Head of Fair Value Policy, Financial and Market Risk Management, Intesa Sanpaolo
Adjunct Professor, University of Bologna
In collaboration with
Umberto Cherubini β Professor of Mathematical Finance, Bologna University
AIFIRM β Association of Italian Financial Risk Managers
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 2
Summary [1]
1. Introductiono Overviewo Prudent valuation history
2. Theoretical Backgroundo Price opacity & financial crisiso Pricing beyond Black-Scholeso Market incompleteness & illiquidity
3. Regulationo Overviewo The Capital Requirement Regulation 575/2013o The EBA Regulatory Technical Standardso AVAs vs XVAso Prudent valuation reportingo Prudent valuation data NEW
NEW
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 3
Summary [2]
4. AVA calculationo Definitions and basic assumptionso Market price uncertainty AVAo Close-out costs AVAo Model risk AVAo Unearned credit spreads AVAo Investing and funding costs AVAo Concentrated positions AVAo Future administrative costs AVAo Early termination AVAo Operational risk AVA
5. Prudent valuation frameworko Implementationo Methodological frameworko Operational frameworko IT frameworko Documentation & reportingo Example of prudent valuation framework
6. Conclusions7. References8. Glossary
NEW
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 4
1: IntroductionOverview
Traditionally, quantitative finance practitioners are divided into two populations: thosewho seek fair values, i.e. means of price distributions, and those who seek riskmeasures, i.e. quantiles of price distributions. Fair value people and risk people typicallylive in separate lands, and worship different gods: the profit and loss balance sheet, andregulatory capital, respectively.
Prudent Valuation is a rather unexplored midland which has recently emergedsomewhere in between the well known mainlands of Pricing and Risk Management. Infact, the Capital Requirements Regulation (CRR), requires financial institutions to applyprudent valuation to all fair value positions. The difference between the prudent valueand the fair value, called Additional Valuation Adjustment (AVA), is directly deductedfrom the Core Equity Tier 1 (CET1) capital. The Regulatory Technical Standards (RTS)for prudent valuation proposed by the EBA have been adopted by the EU (reg.2016/101) on 28th Jan. 2016.
The 90% confidence level required by regulators for prudent valuation links quantiles ofprice distributions (exit prices) to capital, thus bridging the gap between the Pricing andRisk Management mainlands, and forcing the crossbreeding of the fair value and riskpopulations above.
In this seminar, we will explore the Prudent Valuation land.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 5
1: IntroductionOverview
Q-LandQ-measure
Pricing: extrapolate the
presentFair value
Profit and loss
P-LandP-measure
Risk: model the future
Risk measuresCapital
Prudent LandPrudent measurePrice distribution
90% exit priceCapital
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 6
See A. Meucci, βP versus Q: Differences and Commonalities between the Two Areas of Quantitative Financeβ, GARP Risk Professional, pp. 47-50, February 2011, http://ssrn.com/abstract=1717163
1: IntroductionP vs Q and beyond
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 7
The idea of prudent valuation dates back to Basel 2 regulation (see BCBS, βInternational Convergence of Capital Measurement and Capital Standards β A revised frameworkβ, June 2004).
In particular, sec. VI (βTrading book issuesβ), ch. B (βPrudent valuation guidanceβ), par. 690-701 set the requirements for prudent valuation in terms ofo systems and controls,o valuation methodologies,o valuation adjustments or reserves, impacting regulatory capital (not P&L).
The CRR inherited most of the contents in its art. 105.
In more recent times, prudent valuation has been required by the Financial Stability Agency (FSA) to UK institutions, see refs. below.
o Financial Services Authority, βDear CEO Letter: Valuation and Product Controlβ, August 2008, http://www.fsa.gov.uk/pubs/ceo/valuation.pdf
o Financial Services Authority, βProduct Control Findings and Prudent Valuation Presentationβ, November 2010, http://www.fsa.gov.uk/pubs/other/pcfindings.pdf
o Financial Services Authority, βRegulatory Prudent Valuation Returnβ, Policy Statement 12/7, April 2012, http://www.fsa.gov.uk/library/policy/policy/2012/12-07.shtml
1: Introduction Prudent valuation history [1/3]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 8
1: Introduction Prudent valuation history [2/3]
August 2008
FSA βDear
CEO letterβ
November 2010
FSA βProduct Control
Findings and Prudent
Valuation Presentationβ
April 2012
FSA βRegulatory Prudent
Valuation Returnβ, Policy
Statement
2008 2009 2010 2011 20122006 20072004 2005
June 2004
BCBS βInternational Convergence
of Capital Measurement and
Capital Standardsβ (Basel 2)
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 9
1: Introduction Prudent valuation history [3/3]
13 November 2012
EBA Discussion
Paper
(EBA/DP/2012/03)
10 July 2013
EBA Consultation
Paper
(EBA/CP/2013/28)
1 Jan. 2014
CRR
575/2013
31 March 2014
EBA Final Draft RTS
and first application of
prudent valuation
28 Jan. 2016
EBA RTS
published on
OJEU
8 November 2013
EBA Quantitative
Impact Study
2012 2013 2014 2015
23 Jan. 2015
EBA Final Draft
RTS amended
Prudent valuation in
place
2016
28 October 2015
EU commission
adoption of EBA RTS
NEW
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 10
Elaborated by AIFIRM Market Risk Committee, working group on prudent valuation, 148 pages, publicy available at http://www.aifirm.it/position-
paper-prudent-valuation
Summary Executive summary Introduction Regulatory requirements Prudent Valuation scope General assumptions and considerations Theoretical background AVA calculation under the simplified
approach AVA calculation under the core approach Prudent valuation operating framework Prudent valuation technology Conclusions Appendixes References Glossary and notation
1: Introduction Prudent valuation guidelines and sound practices
NEW
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Summary
2. Theoretical backgroundo Price opacity & financial crisiso Pricing beyond Black-Scholeso Market incompleteness & illiquidity
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 12
o Price opacity & financial crisisthe crisis, and the Enron case before, has introduced the problem of valuation as a mean of diffusion of losses among financial institutions and assets.
o Pricing beyond Black-Scholesthe problem of getting the price wrong is linked to the fact that, already after the 19th October1987 market crash, the standard Black-Scholes assumptions of normal distribution of assets returns and perfect replication in continuous time of all financial products proved wrong.
o Market incompleteness & illiquidityother sources of risk, not traded in the market, such as volatility and correlation (smile and skew) have surfaced as key valutation elements. The hedging problem has become more complex and perfect hedging impossible (the market incompleteness problem). Moreover, if hedging can be done (volatility swaps or correlation swaps), it has to be done in highly illiquid markets, or even with OTC transactions.
o Credit risk: βunearned credit spreadsβ, that is expected loss due to default of the counterparty has become the major element in the evaluation of a financial product. This has added even more focus on hedging complexities.
2: Theoretical backgroundIntroduction
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2: Theoretical backgroundA history of financial crises
September-October, 1998LTCM, the major issue of the crisis is the impossibility to replicate financial derivatives in continuous time, and in perfectly liquid markets. It is the first case of incomplete markets.
December, 2001Enron, the issue is lack of transparency in accounting data. The impact was uncertainty of valuation of similar companies or companies with the same auditor (Arthur Andersen). It was called βfinancial contagion by incomplete informationβ.
May 2005Sudden drop in credit correlation triggered losses in financial intermediaries absorbing equity risk in securitization deals. It was a case about correlation uncertainty and hedging risk. Equity hedging strategies based on mezzanine were turned into losses by a major decrease in correlation.
2007-2008 Subprime crisis. The crisis themes were illiquidity, lack of transparency and an increase in correlation (systemic risk). On top of that, the peculiar issue of the crisis was the role played by the accounting standards in spreading contagion across intermediaries.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 14
2: Theoretical backgroundAccounting and the subprime crisis
What is the link between financial crisis and valuation?
βDefault losses on US subprime mortgages about 500 billion dollars.
But in a mark-to-market world, deadly losses are valuation losseso Valuation losses as high as 4 trillions. o Major banks failed without a single penny of default
BIS study of rescue package: 5 trillions in committed resources. β
Eli Remolona, IV Annual Risk Management Conference, Singapore, July 2010
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 15
2: Theoretical backgroundToxic assets
. βFinancial assets the value of which has fallen significantly and may fall
further, especially as the market for them has frozen. This may be due tohidden risks within the assets becoming visible or due to changes in extremalmarket environmentβ
FT Lexicon
Toxic assets are a matter of:o Liquidity (βmarket frozenβ)o Opacity and ambiguity (βhidden risks becoming visibleβ)o βExtremal market environmentβ
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 16
2: Theoretical background A simple example [1]
Take a very simple financial product, that is an equity linked note promising to pay a participation to the increase in some stock market index in five years.
The replicating portfolio of the product is made up by: o A zero coupon bond paying the Libor with five years maturity o A zero coupon bond paying the credit risk spread of the issuer with five years
maturity o An equity option with five years exercise time
The main sources of valuation uncertainty are the following. o The calibration of the five year zero coupon Libor, using fixed income market
data and bootstrapping techniques. This valuation problem is common to other fixed income products.
o The calibration of the five year zero coupon credit spread, using the issuerβs or comparable CDS and bond data, and bootstrapping techniques.
o The calibration of the five year equity volatility, using equity optionsβ market data and bootstrapping techniques. Typically, exchange traded or OTC derivatives do not have a liquid market for 5 years maturity and we must extend implied volatility beyond the traded maturities.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 17
2: Theoretical background A simple example [2]
There are actually other risk sources, mostly the correlations among the risk factors involved.
o Correlation between equity and bondsIt could seem that this should not affect the pricing problem, since it is made under the Forward Martingale Measure (FMM), but the volatility of the forward price depends on correlation.
o Correlation between underlying asset and volatilityThis is relevant in cases in which the underlying asset and its volatility co-move in directions leading to a decrease of the embedded option. This is not the case of this product, which is long both in the underlying asset and its volatility, while the equity market and volatility are known to be negatively correlated.
o Correlation between the embedded option and the credit quality of the issuerActually the embedded option is a vulnerable option whose value is affected by the positive correlation between the exposure (the exercise of the option) and the default probability of the issuer.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 18
2: Theoretical backgroundIncomplete markets: definition
Complete markets are defined by all financial products being βattainableβ. This meansthat the payoff of every financial contract or product can be exactly replicated by sometrading strategy. This implies lack of frictions and continuous rebalancing of thereplicating portfolio. Markets are assumed to be perfectly liquid and trading iscostless.
If markets are complete, there exists a unique Equivalent Martingale Measure (EMM)such that the price of each and every asset can be computed by the expected valueunder such measure, and discounted with the risk-free rate. With complete marketsthe price of each financial product would be unique, and there would be no valuationuncertainty problem.
Real world markets are incomplete and there exists a valuation uncertainty problem.The reason is that no perfect hedge exists. More precisely, the reasons for incompletemarkets are:o there are not enough assets to hedge all possible risk factors (no enough Arrow-
Debreu prices);o replicating portfolios cannot be rebalanced in continuous time in such a way as to
allow for a perfect hedge;o there is not enough liquidity in the market, particularly in stress times, to allow
rebalancing of the replicating portfolios.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 19
2: Theoretical backgroundIncomplete markets: theory
From a technical point of view, selecting a price in incomplete markets amounts tochoose a probability measure (pricing kernel) in a set of probability measures. This set contains the probabilities such that the price of each product is a martingale. Thisimplies that for each product it is not possible to find a replicating strategy that attainsthe product for sure.
ππ π‘ = πΌπ π·(π‘, π)π(π)Θπ β β
The problem is then to define: the set of probabilities including all the risk-neutral probabilities; a strategy to select a probability in the set.
Notice that the problem of selecting a probability amounts to selecting a lottery. So, apossible strategy to select a specific probability is to use expected utility or some of itsextensions.
Hedging error: every probability measure that is chosen is subjected to hedging error.Based on this, for example, one could select the probability with the lowest hedgingvariance, in the set with some expected hedging cost.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 20
2: Theoretical backgroundIncomplete markets: back to expected utility
We remind that expected utility ranks lotteries by the expected value of a function ofthe pay-off. The function weighting the pay-off is increasing and concave (for risk-averse decision makers) and is called utility function. So, lottery A is preferred tolottery B if
E(U(A)) > E(U(B))with U(x) the utility function.
Ellsberg paradox: what happens if the probability of some lottery is not known forsure? If there is a preference for the lottery whose probability is known, or for theother, the expected utility does not work.
Example: there are 90 balls in an urn, we know that 30 are Red, and the others areBlue or Green. Do you have any preference between:
A lottery paying a premium if the ball is Red A lottery paying a premium if the ball is Blue
Now consider the choice between: A lottery paying a premium if the ball is Blue or Green A lottery paying a premium if the ball is Red or Green
If you have preferences of Red over Blue, then Prob(Red) = 1/3 > Prob(Blue), byconsistently: Prob(Red Green) < Prob(Blue Green) = 2/3 and Prob(Blue) > 1/3
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 21
2: Theoretical backgroundIncomplete markets: non-additive expected utility
Notice that the problem with expected utility is additivity. In fact, since additivity meansProb(A B) = P(A) + P(B), for A and B disjoint, we have
Probl(Red) + Prob (Green) > Prob(Blue) + Prob(Green)
which implies Prob(Red) > Prob(Blue).
This implies that allowing for the preferences in the two lotteries to be represented bythe same measure one has to break down additivity.
Non additive representations of preferences are called capacities. These measuresare monotone and are not required to be additive. The expected value with respect tocapacities is represented by the Choquet integral.
There is a duality relationship between sub and super additive capacities andbetween lower and upper Choquet integrals. The duality reminds of the Dempster-Shafer theory.
We will see that this representation is important to represent the set of probabilitymeasures.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 22
2: Theoretical backgroundAlternative theories for price bounds
There are two different approaches to address valuation uncertainty. In both cases theprice bounds are obtained by assuming interval valuation.
Uncertain Volatility Model Volatility is assumed be included in a given interval This leads to two conservative pricing bounds (BSB PDE functions) Avellaneda, Levy and ParΓ s (1996), AMF
Choquet pricing Interval probabilities (MMEU, Gilboa and Schmeidler, 1989) Conservative valuation (Choquet integral) Cherubini (1997) AMF, Cherubini and Della Lunga (2001) AMF
AMF = Applied Mathematical Finance
MMEU: assume the worst possible probability scenario and select the choice that yields the maximum expected utility.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 23
2: Theoretical backgroundUncertain Volatility Model
Set the delta-neutral portfolio
Volatility choice
The Black-Scholes formula becomes non linear (Black-Scholes-Baremblatt)
where
arg minππππβ€πβ€ππππ₯
1
2π2π2
π2π
ππ2=
ππππ, πππ2π
ππ2> 0,
ππππ₯, πππ2π
ππ2< 0.
minππππβ€πβ€ππππ₯
πΞ =ππ
ππ‘+1
2π2π2
π2π
ππ2ππ‘ = πΞ = π π β π
ππ
ππ.
π2π2π
ππ2
+
: =ππππ2 , ππ
π2π
ππ2> 0,
ππππ₯2 , ππ
π2π
ππ2< 0.
ππ
ππ‘+
1
2π2
π2π
ππ2
+
π2π2π
ππ2+ ππ
ππ
ππβ ππ = 0,
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 24
2: Theoretical backgroundChoquet pricing
Long and short positions
Long and short positions are represented by Choquet integrals with respect tocapacities.
Given a function f and a non-additive measure ππ π’π, the upper and lower Choquetintegrals are defined as
ππ π‘ =
minπββ
ΰΆ±π· π‘, π π π, π ππ , long position,
maxπββ
ΰΆ±π· π‘, π π π, π ππ , short position.
ΰΆ±
ββ
0
ππ π’π π β€ π₯ ππ₯ + ΰΆ±
0
+β
1 β ππ π’π π β€ π₯ ππ₯ , lower Choquet integral,
ΰΆ±
ββ
0
1 β ππ π’π π β₯ π₯ ππ₯ + ΰΆ±
0
+β
ππ π’π π β₯ π₯ ππ₯ upper Choquet integral.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 25
2: Theoretical backgroundChoquet pricing
Assume the Breeden and Litzenberger representation of the pricing kernel and thecorresponding call and put prices. According to Breeden and Litzenberger theprobability of exercise of an option can be recovered from the derivative of the optionwith respect to the strike price.
By integrating the pricing kernel we can then recover the prices of call and put optionsas a function of the integral of cumulative distributions, that is, as Choquet integrals,
β1
π π‘, π
ππΆπππ
ππΎ= π π π > πΎ , β πΆπππ π‘ = π(π‘, π) ΰΆ±
πΎ
+β
)1 β π(π₯ ππ₯ ,
1
π π‘, π
πππ’π‘
ππΎ= π π π β€ πΎ β ππ’π‘ π‘ = π(π‘, π) ΰΆ±
ββ
πΎ
π(π₯)ππ₯ .
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 26
2: Theoretical backgroundExamples of valuation uncertainty
Derivatives with counterparty riskCVA and DVA with correlation between the underlying asset and the credit risk of the counterparty (wrong way risk)
Toxic assetsExample: a senior tranche, with high attachment, of a securitization deal traded on the market at much lower value.
Correlation productsthat is Breeden and Litzenberger representation of the pricing kernel and the corresponding call and put prices. Example: options on baskets.
Illiquid derivatives with concentration riskLarge derivative positions require large positions of the underlying asset for delta hedging. Example: large plain vanilla calls/puts on funds.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 27
2: Theoretical backgroundCVA valuation
Assume that the payment schedule of a swap be {t1, t2,β¦, tn} and that default of the
counterparty receiving fixed rate (B) occurred between tj-1 and tj. In this case the loss
suffered by the surviving counterparty A will be
where sr is the swap rate at the date of default and k is that at the origin.
By the same token, the loss suffered by B due to default of A will be
1-n
ji
1A 0,,max,Lgd nji ttsrkttP
1-n
ji
1B 0,,max,Lgd kttsrttP nji
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 28
2: Theoretical backgroundCVA valuation with copula function
Denote GB(tj) the survival probability of party B beyond time tj. Then, the default
probability between time tj - 1 and time tj is GB(tj-1) β GB(tj). Moreover, assume C(u,v)
to be a copula function, and Q(x) the pricing kernel of the swap rate
Then the CVA for counterparty A will be
1
11 ,1,n
ji K
jBjBiB dtGtGQCttPLgd
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 29
2: Theoretical backgroundCVA valuation with wrong way risk
Now assume perfect dependence between the underlying asset and default of the
counterparty. In this case, we have the FrΓ©chet bound π π₯, π¦ β€ πππ π₯; π¦ .
In this case, the CVA can be computed in closed form as
CVA = LgdBmax[k*(tj) β k,0]A(t, tj, tn) [GB(tj-1) β GB(tj)]
β LgdB PayerSwaption(.;max(k*(tj),k))
where k*(tj) is defined from Q((sr(tj,tn) > k*(tj)) = GB(tj-1) β GB(tj), and
is the swap annuity.
π΄(π‘; π‘π , π‘π) =
π=π
πβ1
π π‘, π‘πβ1 ππ
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 30
2: Theoretical backgroundCVA valuation with wrong way risk
o For the short end of the contract the worst scenario is perfect negative dependence
between the underlying asset and default of the counter party. In this case, we have
the FrΓ©chet bound π π₯, π¦ > πππ π₯ + π¦ β 1; 0 .
In this case, the CVA can be computed in closed form as
CVA = LgdA[ReceiverSwaption(.;min(k*(tj),k)) β Receiver swaption(.;k)]
+ LGDA max[k β k*(tj),0](1 β GA(tj β 1) β GA(tj))
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 31
2: Theoretical backgroundCVA valuation with wrong way risk (long party)
Vulnerable Call Swaptions: Financial Institution Paying Fixed
0
0,002
0,004
0,006
0,008
0,01
0,012
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Independence
Perfect positive dependence
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 32
2: Theoretical backgroundCVA valuation with wrong way risk (short party)
Vulnerable Put Swaptions: Financial Institution Receiving Fixed
0
0,0005
0,001
0,0015
0,002
0,0025
0,003
0,0035
0,004
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Independence
Perfect Negative Dependence
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 33
2: Theoretical backgroundTranche senior
Assume a senior tranche with attachment equal to 30%, so that it begins to absorblosses only from 30% of collateral on.
Assume a standard valuation model such as Vasicek asymptotic model, that is basedon the assumption that all exposures in the basket have the same default probabilityP and the same asset correlation with systemic risk.
Then, the expected loss of a senior tranche with attachment πΏπ is
πΈπΏ = π β π πβ1 π ,πβ1 πΏπ , 1 β π2
where π πβ1 π₯ ,πβ1 π¦ , π is the Gaussian copula function.
Now notice that by considering the two extreme values of the copula functionπ π₯, π¦ = π₯π¦ and π π₯, π¦ = min(π₯, π¦) yields extreme values for the expected losses ofthe senior tranche.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 34
2: Theoretical backgroundTranche senior: pricing bounds
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
Rho = 0
Rho = 1
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 35
2: Theoretical backgroundRainbow options
Assume a call option on the minimum of a set of assets (Everest). This can be pricedwith a Choquet integral using the copula as the Choquet integral
From the point of view of the issuer, we can compute the conservative value in closedform, for a bivariate product
dTSQTSQTSQCTtP
TKSSSCall
KN
N
))((),...)((),)((,
),),,...,(min(
21
21
)*,max(;,
;,*;,
,,
2
11*
*],max[
2
*
11* 2
KKtSC
KtSCKtSC
dSQTtPdSQTtPC
KK
KK
K
K
KK
1
1
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 36
2: Theoretical backgroundDynamic replication of illiquid derivatives
Now assume you are trading a derivative with a costumer, maybe for a large quantityof the underlying asset (concentration risk) or for an illiquid underlying. In this case,standard textbook references for the pricing of options do not apply, since theproduction process of the derivative has an impact on the underlying asset.
Here the only process is to start with a dynamics of the underlying asset and to try areplication strategy, allowing for the liquidity cost of rebalancing the portfolio, and thefunding cost of changing the leverage position. So, the market price incorporatesliquidity costs, both in the sens of market liquidity and funding liquidity. Both thesources of cost are all the more relevant the larger the size of the position.
The problem of finding an optimal trade-off between liquidity cost and liquidity risk isextremely involved. In fact, it requires to define trading strategies: how many times torebalance, when, whether at fixed intervals or contingent on some rule.
The problem is magnified by the need to specify the market impact function, thatincludes:
Which is the trade off between the market impact due to sudden rebalancetrades versus the volatility risk to which one is exposed for partitioned unwinding
How much of the market impact is temporary and how much is permanent.Permanent impacts make the problem particularly involved.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 37
Summary
3. Regulationo Overviewo The Capital Requirement Regulation 575/2013o The EBA Regulatory Technical Standardso AVAs vs XVAso Prudent valuation reportingo Prudent valuation data
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 38
3: Regulation Overview
Articles 34 and 105 of Capital Requirements Regulation (CRR, n. 575/2013), in forcesince 1 January 2014, require financial institutions to apply prudent valuation to all fairvalue positions (included positions outside the trading book), setting a new prudentialrequisite for regulatory capital including valuation uncertainty.
The difference between the prudent value and the fair value, accounted in theinstitutionβs balance sheet, is called βAdditional Valuation Adjustmentβ (AVA), and isdirectly deducted from the Core Equity Tier 1 (CET1) capital.
Following the CRR, the EBA published a Discussion Paper (EBA/DP/2012/03), aConsultation Paper (EBA/CP/2013/28), and a Final Draft (EBA/RTS/2014/06), to beapproved by the EU Commission, setting the Regulatory Technical Standards (RTS)for prudent valuation.
The EBA Final Draft defines the AVA calculation methodology using two alternativeapproaches, named Simplified Approach and Core Approach. The Final Draft setsalso the requirements on systems, controls and documentation that should supportthe prudent valuation process.
Acronyms: CRR, AVA, CET1, EBA, RTS, EU, Keywords: fair/prudent value, simplified/core approach
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 39
Market Data
Models
Estimates
Fair Value accounting AVA
(Additional Valuation
Adjustment)
IFRS 13
Prudent valuation
Prudent value
Deducted from Common
Equity Tier 1 capital
CRR article 105 requisites
Policies &
procedures
Control
systems
Prudent
valuation
principles
3: Regulation CRR 575/2013 [1/8]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 40
3: Regulation CRR 575/2013 [2/8]
Art. 34Prudent valuation
scope
Systems and
controls
Valuation
Valuation
adjustments
Art. 105
CRR
575/2013
CRR Prudent Valuation Tree
Prudent valuation
principles
Degree of certainty, art. 105.1
S&C requirements, art. 105.2
Revaluation frequency art. 105.3
Mark to market, art. 105.4-5
Mark to model, art. 105.6-7
IPV, art. 105.8
Valuation adjustments, art. 105.9-10
Illiquid positions, art. 105.11
Other valuation adj., art. 105.12
Complex products, art. 105.13
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 41
CRR art. 34: scope and target
o Scope: all assets measured at fair value
o Target: CET1 capital (not P&L)
3: Regulation CRR 575/2013 [3/8]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 42
CRR art. 105.1, scope and degree of certainty: all positions are subject to prudent
valuation, achieving an appropriate degree of certainty with regard to:
o the dynamic nature of the positions,
o the demands of prudential soundness, and
o the mode of operation and purpose of capital requirements in respect of trading book
positions.
CRR art 105.2, systems and controls: institutions establish and maintain systems and
controls to ensure prudent and reliable valuations, including at least.o Documented policies and procedures for the valuation process, including:
β’ clearly defined responsibilities of the various areas involved in the determination of the
valuation,
β’ sources of market information and review of their reliability,
β’ guidelines for the use of unobservable inputs that reflect the assumptions of authority on
the elements used by market participants to determine the price of the position,
β’ frequency of independent valuation,
β’ timing of closing prices,
β’ procedures for the correction of assessments,
β’ procedures for the reconciliation of month end and ad hoc.
o Clear and independent (of the front office) reporting lines for the department in charge of the
valuation process.
3: Regulation CRR 575/2013 [4/8]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 43
CRR art 105.3, revaluation frequency: institutions revalue trading book positions at
least daily
CRR art 105.4-5, mark to market: institutions mark their positions to market whenever
possible, using the more prudent side of bid and offer unless they can close out at mid
market.
CRR art 105.6, mark to model: where marking to market is not possible, institutions
must conservatively mark to model their positions and portfolios.
3: Regulation CRR 575/2013 [5/8]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 44
CRR art 105.7, mark to model: o senior management must be aware of the fair-valued positions marked to model and must
understand the materiality of the uncertainty of the risk/performance of the business;
o source market inputs, where possible, in line with market prices, and assess the
appropriateness of market inputs and model parameters on a frequent basis;
o use valuation methodologies which are accepted market practice;
o where the model is developed by the institution itself, it must be based on appropriate
assumptions, assessed and challenged by suitably qualified parties independent of the
development process;
o have in place formal change control procedures, hold a secure copy of the model and use
it periodically to check valuations;
o risk management must be aware of the weaknesses of the models used and how best to
reflect those in the valuation output;
o models are subject to periodic review to determine the accuracy of their performance,
including assessment of the continued appropriateness of assumptions, analysis of profit
and loss versus risk factors, and comparison of actual close out values to model outputs;
o the model must be developed or approved independently
of the trading desk and independently tested, including
validation of the mathematics, assumptions and software
implementation.
3: Regulation CRR 575/2013 [6/8]
Very detailed article
regarding valuation
in general
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 45
CRR art. 105.8, independent price verification (IPV): institutions perform independent
price verification in addition to daily marking to market/model. Verification of market
prices and model inputs must be performed by unit independent from units that benefit
from the trading book, at least monthly, or more frequently depending on the nature of
the market or trading activity. Where independent pricing sources are not available or
pricing sources are more subjective, prudent measures such as valuation adjustments
may be appropriate.
CRR art 105.9-10: valuation adjustments: institutions establish and maintain
procedures for considering valuation adjustments, and formally consider the following:
unearned credit spreads, close-out costs, operational risks, market price uncertainty,
early termination, investing and funding costs, future administrative costs and, where
relevant, model risk.
CRR art 105.11, illiquid/concentrated positions: Institutions shall establish and
maintain procedures for calculating an adjustment to the current valuation of any less
liquid positions, which can in particular arise from market events or institution-related
situations such as concentrated positions and/or positions for which the originally
intended holding period has been exceeded.
3: Regulation CRR 575/2013 [7/8]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 46
CRR art. 105.12, other valuation adjustments:
institutions must consider whether to apply a valuation adjustment also:
o when using third party valuations,
o when marking to model,
o for less liquid positions, including an ongoing basis review their continued suitability,
o for uncertainty of parameter inputs used by models.
CRR art. 105.13, complex products: institutions must explicitly assess the need for
valuation adjustments to reflect the model risk associated with using:
o a possibly incorrect valuation methodology
o unobservable (and possibly incorrect) calibration parameters in the valuation model.
3: Regulation CRR 575/2013 [8/8]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 47
3: Regulation Fair Value Vs Prudent Value [1]
Fair Value
o Regulation: IFRS13
o Application: balance sheet
o Percentile: 50% (expected
value)
o The price that would be received
to sell an asset or paid to
transfer a liability in an orderly
transaction between market
participants at the measurement
date
o Must include all the factors that
a market participants would use,
acting in their economic best
interest.
o Atoms: single trades.
o Fair value adjustments
o Non-entity specific
Prudent value
o Regulation: CRR/EBA
o Application: CET1
o Percentile: 90%
o Must reflect the exit price at which
the institution can trade within the
capital calculation time horizon.
o Atoms: valuation positions subject
to a specific source of price
unertainty
o Entity specific
o Subject to diversification benefit
(50% weight for MPU, CoCo, MoRi
AVAs)
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 48
3: Regulation Fair Value Vs Prudent Value [2]
Why capital and not P&L ?
P&L is accounted under accounting standards
o EU listed companies: use IFRS (International Financial Reporting Standards),
established and maintained by the IASB (International Accounting Standards
Board) see www.ifrs.org
o US listed companies: use GAAP (Generally Accepted Accounting Standards),
established and maintained by the FASB (Financial Accounting Standards Board),
see www.fasb.org
o Convergence towards IFRS is in progress
Both IFRS and GAAP define the fair value as an exit price, not as a prudent price. Fair
value must be fair, not prudent.
Thus, regulators have decided to account for prudent price through capital, instead of
altering the accounting standards.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 49
3: RegulationOverlaps and possible offsets
AVAs have to be deducted by CET1. Hence, possible double counting w.r.t. other capital deductions should be considered.
AVA UCS vs Expected Loss AmountsCRR article 159 states that βInstitutions shall subtract the expected loss amounts calculated in accordance with Article 158 (5), (6) and (10) from the general and specific credit risk adjustments and additional value adjustments in accordance with Articles 34 and 110 and other own funds reductions related to these exposuresβ¦β. The Credit Risk capital requirements, including the expected loss (EL) amount, are calculated using the higher accounting values, not the AVA adjusted values. As a result, without an adjustment to the capital requirements on those assets, there is a double hit to capital. The AVA UCS offset against EL, in Article 159, is a mitigation that prevents from double hit.
Day One Profit & Loss deductionsSince these are deductions from profit and loss to account for fair value uncertainty, it seems that there exist a double counting with AVAs, and AVAs can be reduced accordingly. See survey.
OthersTo be understood and clarified, possibly with regulators.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 50
3: RegulationEBA RTS: overview
The EBA RTS issued on 23rd Jan. 2015 have been adopted by the EU with Commission
delegated regulation (EU) 2016/101, published on the OJEU on
The RTS set the detailed regulatory technical standards on prudent valuation under
articles 34 and 105 of CRR
The most important feature of the EBA RTS is the distinction between two different
approaches for the implementation of the prudent valuation methodology: the simplified
approach and the core approach.
The choice between the two approaches depends on a threshold on the sum of the
absolute values of fair-valued assets and liabilities. The EBA sets the threshold at EUR
15 billion.
The EBA RTS sets further requirements in terms of documentation (art. 18), systems
and controls (art. 19). These provisions essentially require Institutions to have in place a
two-level internal policy for fair value (Fair Value Policy) and for prudent value (Prudent
Valuation Policy).
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 51
3: RegulationEBA RTS: overview
General
provisions
Sec. 1
Core
approach
Sec.3
EBA RTS
Final draft
EBA RTS Prudent Valuation Tree
Simplified
approach
Sec.2
Documentation
systems &
controls
Sec.4
Methodology for AVA, art. 1
Definitions, art. 2
Sources of market data, art. 3
Conditions of application, art. 4
AVA calculation, art. 5
AVA aggregation, art. 6
Overview, fall back, art. 7
General provisions, art. 8
AVA calculation, art. 9-17
Documentation, art. 18
Systems & controls, art. 19
Entry into force, art. 20 AVA OpR, art. 17
AVA EaT, art. 16
AVA FAC, art. 15
AVA CoPo, art. 14
AVA IFC, art. 13
AVA UCS, art. 12
AVA MoRi, art. 11
AVA CoCo, art. 10
AVA MPU, art. 9
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 52
3: RegulationEBA RTS: prudent valuation scope [1/9]
General rules
Region of application: since the CRR is an EU directive, prudent valuation applies to
all institutions within EU countries. In case of institution made of a central holding and
one or more subsidiaries, prudent valuation applies to those individual subsidiaries
included in EU countries.
Scope of application: the CRR art. 5, defines the prudent valuation scope as including
all trading book positions. However, the CRR art. 34 requires that institutions apply the
standards of art. 105 to all assets measured at fair value. The combination of the above
CRR articles 34 and 105 implies that the prudent valuation scope includes all fair-valued
positions, regardless of whether they are held in the trading book or banking book.
The positions at fair value held in both trading and banking books are the following:
Assets Liabilities
Financial assets held for trading (HFT) Financial liabilities held for trading (HFT)
Financial assets at fair value Financial liabilities at fair value
Financial assets available for sale (AFS) (for
the portion not subject to prudential filters)
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 53
3: RegulationEBA RTS: prudent valuation scope [2/9]
Positions excluded:
o the EBA RTS, art. 4.2 and 8.1, allow Institutions to exclude partially or totally from the
prudent valuation scope those positions for which a change in their accounting fair
value has only a partial or zero impact on Common Equity Tier 1 capital. These
positions must be included in proportion to the impact of the relevant valuation
change on CET1 capital.
o In particular these positions are the following:
1. positions subject to prudential filters,
2. exactly matching, offsetting positions (back to back),
3. positions in hedge accounting.
o Notice that, since the size of the positions above may be relevant, the prudent
valuation scope is the primary driver of the AVA figures.
o How to compute inclusion/exclusion in practice ? See next slides.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 54
3: RegulationEBA RTS: prudent valuation scope [3/9]
1. Positions subject to prudential filers
o Positions subject to prudential filters refer to the "Financial assets available for sale"
(AFS). The inclusion/exclusion of these positions from the prudent valuation scope
of application follows the CRR requirements.
o The exact percentages of partial inclusions follows the transitional provisions that
each local Regulator issued in compliance with the above CRR requirements.
o Partial inclusion means, for instance, that if 40% of fair value gains and losses are
filtered in CET1, the residual 60% of fair value gains and losses are included in the
prudent valuation scope. In case of 100% filter, the position is completely excluded
by prudent valuation.
Position under prudential filters (AFS) Inclusion
Government bonds issued by EU countries 0%
Other debt securities (excluding the EU
government bonds above)
Partial inclusion depending on the sign of
the reserve and on local prescriptions
EquityPartial inclusion depending on the sign of
the reserve and on local prescriptions
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 55
Transitional provisions issued by national regulators.
3: RegulationEBA RTS: prudent valuation scope [4/9]
Circolare 285 Banca dβItalia
The applicable percentage following art. 467, par. 3 CRR is:
a) 20% since 1 Jan. 2014 to 31 Dec. 2014
b) 40% since 1 Jan. 2015 to 31 Dec. 2015
c) 60% since 1 Jan. 2016 to 31 Dec. 2016
d) 80% since 1 Jan. 2017 to 31 Dec. 2017
Local
regulation
in Italy
Article 467 CRR
[β¦] institutions shall include in the calculation of their Common
Equity Tier 1 items only the applicable percentage
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 56
3: RegulationEBA RTS: prudent valuation scope [5/9]
Institutions may not include in own funds unrealized gains and losses related to AFS
positions with central administrations.
Circolare 285 Banca dβItalia
The applicable percentage following art. 468, par. 3 CRR is:
a) 100% 1 Jan. 2014 to 31 Dec. 2014
b) 60% since 1 Jan. 2015 to 31 Dec. 2015
c) 40% since 1 Jan. 2016 to 31 Dec. 2016
d) 20% since 1 Jan. 2017 to 31 Dec. 2017
Article 468 CRR
[β¦] institutions shall remove in the calculation of their Common
Equity Tier 1 items only the applicable percentage
Local
regulation
in Italy
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 57
3: RegulationEBA RTS: prudent valuation scope [6/9]
According to Regulation (EU) 2016/445 of the European Central Bank of 14 Mar 2016
(published OJEU on 26 Mar. 2016), art. 14 and 15, the corresponding art. 467 and 468
of CRR (setting prudential filters for AFS positions) are modified such that AFS positions
in EU government Bonds shall no longer subject to 100% filter, but shall be subject to
standard prudential filters holding for other AFS position:
Inclusion of unrealized losses (art. 14 -> art. 467 CRR):
o 60% in [1/1/2016 β 31/12/2016]
o 80% in [1/1/2017 β 31/12/2017]
Exclusion of unrealized gains (art. 15 -> art. 468 CRR):
o 40% in [1/1/2016 β 31/12/2016]
o 20% in [1/1/2017 β 31/12/2017]
First application date: Q4-2016
This regulatory change will change substantially the AVA figures for institutions
with huge positions in EU govies (more or less all banks...).
NEW
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 58
3: RegulationEBA RTS: prudent valuation scope [7/9]
2. Exactly matching, offsetting positions (back to back)
o Back to back positions are groups of trades with total null valuation exposure to
market risk factors (interest rates, volatility, etc.), since any variation in the relevant
market valuation inputs generates opposite variations in the value of the trades in
the group, such that the total value is constant. In other words, the group has null
total sensitivity to market risk factors.
o We stress that back to back positions are neutral w.r.t. other risk factors, such as
counterparty defaults, since the trades into the group may be subscribed with
different counterparties.
o From a prudent valuation point of view:
β’ Simplified approach: 100% exclusion (EBA RTS art. 4.2)
β’ Core approach: AVAs must be calculated based on the proportion of the
accounting valuation change that impacts CET1 capital (EBA RTS art. 8.1). In
practice:
β’ AVA MPU, CoCo and MoRi are null,
β’ AVA UCS, IFC, CoPo, FAC, EaT, OpR must be computed on the total
valuation exposure of the back to back portfolio.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 59
3: RegulationEBA RTS: prudent valuation scope [8/9]
3. Hedge accounting positions
o Hedge accounting positions are characterized by a hedged instrument (e.g. one ore
more securities, loans or mortgages, etc.) and an hedging instrument (e.g. one ore
more interest rate swaps, credit default swaps, etc.).
o The total package of hedged + hedging instruments has, by construction, a reduced
sensitivity to the underlying risk factors.
o From a prudent valuation point of view, all AVAs must be computed on the total
valuation exposure of the hedge accounting portfolio.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 60
3: RegulationEBA RTS: prudent valuation scope [9/9]
Positions subject
to prudential
filters (AFS)
Positions in
hedge
accounting
Positions for which a
change in their
accounting fair value
has only a partial or
zero impact on CET 1
Art. 4.2 and 8.1
EBA RTS Prudent Valuation scope: exclusions
Positions in
back to back
EU Gov. bonds
Other bonds
Equity
General criteria
for exclusionPositions excluded
% of
exclusion
100% until Sept. 16
Partial, phase in
Partial, phase in
Simplified appr.
Partial, residual exposure
of hedged + hedging items
Core appr.
100%
Partial, residual exposure
to UCS, IFC, CoPo, FAC,
EaT, OpR AVAs
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 61
3: RegulationEBA RTS: simplified approach
Simplified Approach
(EBA RTS, sec. 2)
Institutions may apply the Simplified Approach if the sum of the absolute value of
fair-valued assets and liabilities is less than EUR15 bn.
The Simplified Approach AVA is given by the 0,1% of the sum of the absolute value
of fair-valued assets and liabilities.
Example of AVA calculation under the simplified approach. Data do not refer to real portfolios.
Below
threshold
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 62
3: RegulationEBA RTS: core approach [1/3]
Core Approach (EBA RTS, sec. 3)
Institutions that at individual or consolidated level exceed the EUR15bn threshold must
apply the core approach.
Each AVA is the excess of valuation adjustments required to achieve the identified
prudent value, over any adjustment applied in the institutionβs fair value that can be
identified as addressing the same source of valuation uncertainty as the AVA.
Whenever possible, the prudent value of a position is linked to the 90% percentile of its
price distribution. In practice for AVAs i) Market price uncertainty ii) Close-out costs iii)
Unearned credit spreads, the Institutions must compute the prudent value using the
available market data and the 90% target confidence.
Whenever insufficient data exists to construct a plausible range of values, institutions
shall use an expert-based approach using qualitative and quantitative information
available to achieve a 90% level of certainty in the prudent value.
Additional Valuation
Adjustments
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 63
3: RegulationEBA RTS: core approach [2/3]
Core approach
Additional Valuation Adjustments
Market
Price
Uncertainty
(MPU)
Art. 9
Close Out
Costs
(CoCo)
Art. 10
Model Risk
(MoRi)
Art. 11
Unearned
Credit
Spread
(UCS)
Art. 12
Investing &
Funding
Cost
(IFC)
Art. 13
Concen-
trated
Positions
(CoPo)
Art. 14
Future
Admin
Costs
(FAC)
Art. 15
Early
Termination
(EaT)
Art. 16
Main
AVAs
UCS/IFC
AVAs
Other
AVAs
Operational
Risk
(OpR)
Art. 17
The AVA hierarchy
Market risk factors
50% weights for diversification
Market risk factors
Split onto main AVAs
Non-market risk factors
100% weights, no diversification
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 64
3: RegulationEBA RTS: core approach [3/3]
Example of AVA calculation and aggregation under the core approach. IFC and UCS AVAs are split into their MPU, CoCo and MoRi components and pre-aggregated to the corresponding AVAs, then the total AVA is obtained from the aggregation of the other seven residual AVAs. In order to show toy but realistic figures, we assumed the principal AVAs equal to 1/7 of the 99% x 0.1% of the total FV under the core approach. AVA OpR has been calculated as for a non-AMA Institution. In the last line, we also add a possible AVA fall-back calculated on the remaining 1% x 0.1% of the total FV.
Above
threshold
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 65
3: RegulationEBA RTS: fall-back approach [1/2]
Fall back approach (EBA RTS, art. 7.2.b)
Institutions that exceed the EUR15bn threshold but cannot calculate the core approach
AVAs for certain positions, are allowed to apply a Β«fall-back approachΒ» (actualy very
capital intensive), and compute AVAs for those positions as the sum of:
100% of the net unrealised profit (NUP)
10% of the notional value in case of derivatives;
25% of the absolute difference between the fair value (FV) and the net unrealised
profit for non-derivatives.
In formulas:
"unrealised profit shall mean the change, where positive, in fair value since trade
inception, determined on a first-in-first-out basis.β
Aππ΄ππ = 100% πππ+ + 10% ππ·ππ + 25% πΉπ β πππ+ πππβπ·ππ
πππ+: = πππ₯
π=1
πππ
ππππ , 0 , ππ·ππ=
π=1
πππ
ππ , πΉπ =
π=1
πππ
πΉππ .
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 66
3: RegulationEBA RTS: fall-back approach [2/2]
Example of AVA calculation under the fall-back approach. We assume to apply the Fall-Back approach to the 1% portion of the previous core portfolio. The net unrealized P&Ls are the 0.1% of the fair values, positive for derivatives and negative for bonds. The notional for derivatives is assumed 10 times the fair value. The AVA Fall-Back is then summed to the remaining 99% of the previous AVA core to obtain the total AVA.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 67
The core approach is mandatory only for institutions above the threshold of β¬15 bln.
Institutions below the threshold may choose between simplified and core approaches.
Which one is more convenient (generate smaller capital absorption) ?
There is no precise mathematical relation between the simplified and core AVAs.The actual figures depend principally on the actual positions
included in the prudent valuation scope.
3: RegulationSimplified vs core approaches [1/2]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 68
3: RegulationGlobal view of key regulatory concepts
Fair
value
CRR art. 34, 105
EBA RTS
Prudent
value
Scope
90% confidence level
Simplified approach
Mark to market
Mark to model
IPV
Systems
and
controls
Core approach
Expert based
Fall back
Diversification
0.1% Formula
9 AVAs
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 69
3: RegulationAVAs vs XVAs
Simple question, difficult answerShould XVAs be included into the prudent valuations scope ?
Letβs look atthe state of the art...
...and try some forecast
XVA Accounting standards Accounting practice
CVA, DVA YES, both IFRS13 and GAAP mention
about counterparty and own credit
risk.
Some news on DVA expected
YES, CVA and DVA are normally included
into accounting fair value and reported in
public balance sheet disclosures
FVA NO, at least not explicitly YES, most banks have included FVA into
accounting fair value and report some
(scarce) information in public balance
sheet disclosures
MVA NO, see recent survey NO, see recent survey and public balance
sheet disclosures
KVA NO, see Kenyon&Kenyon, Risk Mag.
Mar. 2016
NO, see recent survey
xxxVA Who knows...
NEW
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 70
Recently, two regulators proposed a consultation on enhancements to the reporting of prudent valuation figures.
The industry (ISDA, IIF, AFME, etc.) is actively discussing the proposed template and comments to BCBS are expected. Main issues are the following:o Partial overlapping and consistency of AVA definitions under BCBS and EBA RTSo Different AVA scopes of applications, since EBA RTS allows for many exclusions.o AVAs break down by asset class is problematic for EU Institutions because EBA RTS
requires AVA calculation at valuation exposure level. For example, AVA MPU for some risk factor (e.g. IR/vols and FX rates/vols) naturally include multiple asset classes.
1. BCBS Consultative Document, βPillar 3 disclosure requirements βconsolidated and enhanced frameworkβ, March 2016, issued for comment by 10 June 2016.
Template PV1, in particular, aims to disclose prudent valuation figures under Pillar 3, consistently with previous BCBS requirements:o BCBS βInternational Convergence of Capital Measurement and
Capital Standardsβ (Basel 2, comprehensive version) June 2006, paragraphs 698-701.
o BCBS βSupervisory guidance for assessing banksβ financial instrument fair value practicesβ, April 2009 (in particular Principle 10).
3: RegulationPrudent valuation reporting [1/3]
NEW
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 71
Template PV1 proposed in BCBS Consultative Document, βPillar 3 disclosure requirements β consolidated and enhanced frameworkβ, March 2016, issued for comment by 10 June 2016.
3: RegulationPrudent valuation reporting [2/3]
NEW
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 72
2. EBA consultation paper (EBA/CP/2016/02), βDraft implementing Technical Standards amending Commission Implementing Regulation (EU) 680/2014 on supervisory reporting of institutionsβ, 4 March 2016, issued for comment by 31 March 2016.
The proposed amendement of prudent valuation supervisory reporting is articulated into four new templates.
Template C 32.01: fair valued asset and liabilitieso Rows: accounting categorisation (HFT, AFS, etc.)o Columns: fair value amounts of inclusions and
exclusions according to EBA RTS
Template C 32.02: core approacho Rows: break down by portfolio/trade class (vanilla/exotic), diversification benefit, fall back app.o Columns: AVAs and fair value adjustments according to EBA RTS.
Template C 32.03: focus on AVA MoRi
Template C 32.01: focus on AVA CoPo
Main issues are the following: breakdown by portfolio/trade class (vanilla/exotic) is not consistent with AVA calculation by
valuation exposures, amount of data required
3: RegulationPrudent valuation reporting [3/3]
NEW
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 73
FV under prudent valuation scope = FV asset & liabilities β FV under prudential filters
3: RegulationPrudent valuation data: QIS [1/3]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 74
The EBA conducted a QIS to estimate the total impact of the requirements of the RTSincluding 59 banks across 15 jurisdictions, with the following results.
Small banks: < 15 β¬/bln Medium banks: 15 - 100 β¬/bln Large banks: > 100 β¬/bln
Average
227 β¬/mln
per bank
3: Regulation Prudent valuation data: QIS [2/3]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 75
According to EBA: [*]
approximately 6,500 credit institutions across EEA Member States (as of 2013) reportsupervisory data to their respective competent authorities.
Total value of assets: approximately EUR 42,000 billion.
Approximately 750 institutions (11%) are above the EUR 15 billion threshold.
[*] European Banking Authority, Consultation Paper, βDraft Implementing Technical Standards amendingCommission Implementing Regulation (EU) 680/2014 on supervisory reporting of institutionsβ, 4 March 2016,https://www.eba.europa.eu/-/eba-seeks-comments-on-reporting-of-prudent-valuation-
information
3: Regulation Prudent valuation data: QIS [3/3]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 76
3: RegulationPrudent valuation data: 2014-2015 [1/3]
Source: elaboration of public data (in collaboration with Ernst Young).
NEW
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 77
3: RegulationPrudent valuation data: 2014-2015 [2/3]
Source: elaboration of public data (in collaboration with Ernst Young).
NEW
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 78
Comments
Fair value is given by FV assets + FV liablities includingo Held for trading (HFT)o Fair Value Option (FVO)o Hedging Derivatives (HD)o Available For Sale (AFS)
Fair value for prudent valuation has been estimated from fair value excluding HD and AFS (100%, no AFS filters applied, slightly underestimated).
AVA/CET1 figures are rather different, ranging from negligible to important %.
AVA core / AVA simplified > 1 in a few cases, thus AVA simplified is neither an AVA cap nor an AVA floor.
Prudent valuation not driven by L3 instruments: moving from AVA/L3 to AVA /(L2+L3) changes the figures by a factor of 100.
2014-2015 average AVAs double the 2013 QIS result (500 vs 227 mlnβ¬).
3: RegulationPrudent valuation data: 2014-2015 [3/3]
NEW
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 79
1. XVAs
3: RegulationPrudent valuation data: survey [1/4]
Restricted access to clients only Dec.2015 30 respondents (18 GSIBs, 15 UK) 60 questions EBA RTS not yet in place at the time
One third does not account FVA in fair value, more than half does account AVA IFC in prudent value.
MVA and KVA are not accounted both in fair and prudent values.
NEW
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 80
1. XVAs (contβd)
3: RegulationPrudent valuation data: survey [2/4]
Only 30% use a spread term structure
Β«Peer estimateΒ» is a possible answer to the question Β«what is an exit price for FVA ?Β»
Possible use of Markit XVA service
Both funding spreads sources and term structures vary considerably, both for FVA (Fair Value) and for AVA IFC (prudent value)
NEW
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 81
2. P&L variance test
3: RegulationPrudent valuation data: survey [3/4]
The P&L variance test is difficult to run and pass in case of many relevant risk factors, and may lead to huge AVA MPU.
60% ignore the P&Lvariance test
Only 7% run extensive application
Only 14% apply with quarterly frequency
NEW
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 82
3. Other
3: RegulationPrudent valuation data: survey [4/4]
One half does apply/does not apply offsetting between AVAs and other regulatory capital reserves.
Possible offsets should be clarified, to avoid possible capital double countings.
One third reduces the valuation exposure.
NEW
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 83
4. AVA calculationo Definitions and basic assumptionso Market price uncertainty AVAo Close-out costs AVAo Model risk AVAo Unearned credit spreads AVAo Investing and funding costs AVAo Concentrated positions AVAo Future administrative costs AVAo Early termination AVAo Operational risk AVAo Case studies & examples
Summary
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 84
4: AVA calculationDefinitions and basic assumptions [1]
In other words, a valuation position will display valuation exposures to its valuation inputs. Clearly the degree of valuation exposure to a valuation input depends on the particular valuation position.
Definitions (EBA RTS art. 2)
Item Definition Example
Valuation
position
A portfolio of financial instruments or
commodities measured at fair value, held in
both trading and non-trading books
E.g. a portfolio of
derivatives
Valuation
input
A set of parameters (observable or non-
observable) that influences the fair value of a
valuation position
E.g. yield curve,volatility
cube, market/historical
correlations, prepayment,
etc.
Valuation
exposure
The amount of a valuation position which is
sensitive to the change in a valuation input
E.g. the trades in portfolio
above sensible to the
valuation inputs above.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 85
4: AVA calculationDefinitions and basic assumptions [2]
Fair value
In general, we denote the fair value of a valuation position ππ at time t with πΉπ π‘, ππ or, shortly, with πΉππ π‘ , with π = 1,β¦ , ππ. Given a set of valuation positions subject to
prudent valuation, we denote the total fair value as
πΉπ π‘ =
π=1
ππ
πΉππ π‘
In the context of prudent valuation, we consider the following properties of fair value FV. FV is positive for assets (πΉππ π‘ > 0) and negative for liabilities (πΉππ π‘ < 0). Financial institutions have appropriate internal IPV process in place (EBA RTS, p. 7). FV is computed by the institution consistently with the applicable financial reporting
standards, e.g. IFRS13, and with its internal fair value policy. The institution possibly applies and reports a number of valuation adjustments to the
FV, according to its internal fair value policy.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 86
4: AVA calculationDefinitions and basic assumptions [3]
Fair value (contβd)
The FV of a valuation position may be subject to the sources of uncertainty mentioned in the CRR, art. 105.10-11, and thus associated to a specific AVA under the core approach described in the EBA RTS.
According to EBA RTS art. 8.3, the FV of a valuation position associated to a specific AVA under the core approach must include all the fair value adjustments possibly applied by the institution associated to the same source of valuation uncertainty as the specific AVA. In case a fair value adjustment cannot be associated to the same source of valuation uncertainty of a specific AVA, it must not be included in the FV for the specific AVA calculation. In case of impossible association with any AVA, the fair value adjustment cannot be included at all in the prudent valuations scope.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 87
4: AVA calculationDefinitions and basic assumptions [4]
Fair value (contβd)
Fair value for derivativesIn general, we may consider the fair value for derivatives split into various components,
πΉπ π‘ = π0 π‘ + ππ΄ππ π‘
ππ΄ππ π‘ = πππΆππ΄ π‘ + ππΉππ΄ π‘ + ππ΅πππ΄π π π‘ + πππππππ ππ π π‘ + β―
where o π0 π‘ is the βbaseβ fair value component at valuation time t, as if the contract were
covered by a perfect CSA;o the other components gathered in ππ΄ππ π‘ corresponds to the value of the various
risk components underlying the financial instrument, such as the bilateral counterparty risk πππΆππ΄ π‘ , funding risk ππΉππ΄ π‘ , bid-ask ππ΅πππ΄π π π‘ , model risk πππππππ ππ π π‘ , etc. Such components may be considered or not in the FV or in in ππ΄ππ π‘ according to the fair value policy of the institution.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 88
4: AVA calculationDefinitions and basic assumptions [5]
Fair value (contβd)
Fair value for securitiesWe consider the fair value for securities, instead, as a single value, without splitting into distinct components. In other words, the value of the various risk components is included in the credit spread associated to the security.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 89
4: AVA calculationDefinitions and basic assumptions [6]
Valuation input
The FV of a valuation position ππ depends on its valuation inputs, denoted with π’π , π = 1, β¦ , ππ’,
The FV may be also denoted as πΉπ(π‘, ππ , π’1, β¦ , π’ππ’). We stress that different
valuation positions depend, in general, on different valuation inputs.
The valuation input π’π is associated to a single elementary risk factor, or source of
valuation uncertainty.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 90
4: AVA calculationDefinitions and basic assumptions [7]
Valuation exposure
The valuation exposure of a valuation position ππ to the valuation input π’π is the
amount of that valuation position which is sensitive to the change in the valuation input π’π.
The valuation exposure can be also associated to the sensitivity of the valuation position ππ to the valuation input π’π.
In a wider sense, the valuation exposure is anything that measures the dependency of the FV of the valuation position ππ to the valuation input π’π.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 91
4: AVA calculationDefinitions and basic assumptions [8]
Prudent value
We denote the prudent value of category k for a valuation position ππ associated to the source of valuation uncertainty π’π at time t with ππ (π‘, ππ , π’π , π) or, shortly, with
πππππ π‘ , with π = 1,β¦ , ππ’ and π = 1,β¦ ,ππ΄ππ΄. The category is the AVA type (MPU,
CoCo, etcβ¦).
Degree of certaintyThe CRR (article 105.1) requires a prudent value that achieves an ββ¦ appropriate degree of certaintyβ. The EBA RTS specifies the appropriate degree of certainty as follows.
o AVA MPU, CoCo e MoRi (art. 9-11):β’ where possible, the prudent value of a position is linked to a range of
plausible values and a specified target level of certainty (90%);β’ in all other cases, an expert-based approach is allowed, using qualitative
and quantitative information available to achieve an equivalent level of certainty as above (90%).
o AVA UCS and IFC (art. 12-13): these AVAs must be split into their MPU, CoCoand MoRi components, and aggregated to the corresponding MPU, CoCo and MoRi AVAs, respectively. Thus, the same level of certainty in the prudent value (90%) must be statistically achieved.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 92
4: AVA calculationDefinitions and basic assumptions [9]
Prudent value (contβd)
o Other AVAs (CoPo, FAC, ET, OpR, art. 14-17): it must be statistically achieved the same level of certainty in the prudent value (90%) as for the previous AVAs (art. 8.3).
o For positions where there is valuation uncertainty but it is not possible to statistically achieve a specified level of certainty, the same target degree of certainty in the prudent value (90%) is required.
o βThe EBA accepts that for the majority of positions where there is valuation uncertainty, it is not possible to statistically achieve a specified level of certainty; however, specifying a target level is believed to be the most appropriate way to achieve greater consistency in the interpretation of a βprudentβ valueβ.β
In conclusion, the same degree of certainty in the prudent value (90%) must be achieved for all AVAs.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 93
4: AVA calculationDefinitions and basic assumptions [10]
Prudent value (contβd)
o Notice that, by definition, the prudent value is always equal to or lower than the fair value, both for assets and liabilities. Taking into account the FV definition above we have, for both assets and liabilities,
πππππ π‘ β€ πΉππ π‘ β π = 1, β¦ , ππ, π = 1, β¦ , ππ’, π = 1,β¦ , ππ΄ππ΄
o Hence, PV is generally positive for assets (πππππ π‘ > 0) and negative for
liabilities (πππππ π‘ < 0). This is not strictly true in all cases, since some asset
(e.g. an OTC swap) may have positive FV and negative PV (not viceversa).
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 94
4: AVA calculationDefinitions and basic assumptions [11]
Additional Valuation Adjustment (AVA)
Simplified approachGiven the total fair value of assets and liabilities, πΉππ΄π π ππ‘π π‘ > 0, πΉππΏπππππππ‘πππ π‘ < 0, the total AVA under the simplified approach is given by the following expression
π΄ππ΄ π‘ = 0.1% Γ πΉππ΄π π ππ‘π + πΉππΏπππππππ‘πππ
where
πΉππ΄π π ππ‘π β
π=1
ππ΄π π ππ‘π
πΉππ π‘ ,
πΉππΏπππππππ‘πππ β
π=1
ππΏπππππππ‘πππ
πΉππ π‘ .
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 95
4: AVA calculationDefinitions and basic assumptions [12]
Additional Valuation Adjustment (AVA) (contβd)
Core approachGiven the fair value of a valuation position ππ, πΉππ π‘ , and the corresponding prudent value of category k associated to the source of valuation uncertainty π’π, πππππ π‘ , the
AVA under the core approach is given by the following expressions
π΄πππ΄ π‘, ππ , π’π , π : = π€π πΉπ π‘, ππ β ππ π‘, ππ , π’π , π ,
π΄ππ΄ π‘, π : =
π=1
ππ
π=1
ππ’
π΄πππ΄ π‘, ππ , π’π , π ,
where:o π€π is the aggregation weight, such that π = 0.5,0.5,0.5,1,1,1,1 for the seven
AVAs MPU, CoCo, MoRi, CoPo, FAC, ET, OpR, respectively.
o π΄πππ΄πππ π‘ β π΄πππ΄ π‘, ππ , π’π , π is the k-th AVA for valuation position ππ and source
of valuation uncertainty π’π at time t, weighted for aggregation;
o π΄ππ΄ π‘, π is the total k-th category level AVA associated to all relevant sources of valuation uncertainty π’1, β¦ , π’ππ’ and valuation positions π1, β¦ , πππ. Also this AVA is
already weighted for aggregation by construction of π΄πππ΄πππ π‘ .
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 96
4: AVA calculationDefinitions and basic assumptions [13]
Additional Valuation Adjustment (AVA) (contβd)
Notice that:
π΄ππ΄π π‘ always include the aggregation weight π€π at any level (valuation exposure, total AVA, total PVA);
π΄ππ΄π π‘ β₯ 0 β π at any level (valuation exposure, total AVA, total PVA), both pre and post aggregation;
π΄ππ΄π π‘ = 0 when the fair value is already prudent w.r.t. the π΄ππ΄π source of valuation
uncertainty, πΉππ π‘ = πππππ π‘ ;
the previous expressions holds both for assets (πΉπi π‘ > 0) and liabilities (πΉπi π‘ <0).
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 97
4: AVA calculationDefinitions and basic assumptions [14]
Additional Valuation Adjustment (AVA) (contβd)
AVA for derivatives
Remind that for derivatives the total value may be split across different components
πΉπ π‘ = π0 π‘ + ππ΄ππ π‘
ππ΄ππ π‘ = πππΆππ΄ π‘ + ππΉππ΄ π‘ + ππ΅πππ΄π π π‘ + πππππππ ππ π π‘ + β―
We assume that such components are not strongly correlated. In particular, we assume that the market value is not strongly correlated with credit and funding risk.
In this case, also the AVAs results to be split across the same components
π΄πππ΄ π‘, ππ , π’π , π = π΄πππ΄0 π‘, ππ , π’π , π + π΄πππ΄ π‘, ππ , π’π , πΆππ΄ + π΄πππ΄ π‘, ππ , π’π , πΉππ΄ +β―
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 98
4: AVA calculationDefinitions and basic assumptions [15]
Prudent Valuation Adjustment (PVA)
The total Prudent Valuation Adjustment (PVA), to be deduced from the CET1, is computed as follows.
πππ΄ π‘ β
π΄ππ΄(π‘) Simplified approach,
π=1
ππ΄ππ΄
π΄ππ΄π π‘ Core approach.
The detailed AVA aggregation rules under the core approach are discussed within thedetailed AVA calculation rules in the following.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 99
4: AVA calculationDefinitions and basic assumptions [16]
AVA aggregation
The total AVA under the core approach is computed using the following algorithm.
CoPo, FAC, EaT, OpR AVAs are aggregated each as the sum of its corresponding individual components at valuation positions level, each weighted at 100%.
UCS and IFC AVAs are decomposed each into 3 components related to MPU, CoCoand MoRi uncertainties, which are taken into account in the total MPU, CoCo and MoRi AVA aggregation discussed below.
MPU, CoCo and MoRi AVAS are aggregated each as the sum of:o its individual components at valuation positions levelo the corresponding UCS and IFC AVA contributions above, o all weighted at 50%.
The total AVA is computed as the simple sum of the residual MPU, CoCo, MoRi, CoPo FAC, EaT, OpR AVAs determined above.
In conclusion, the final aggregation includes 50% of MPU, MoRi, CoCo, UCS and IFC AVAs (5 out of 9), and 100% of CoPo FAC, EaT, OpR AVAs (4 out of 9).
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 100
4: AVA calculationDefinitions and basic assumptions [17]
Definitions summary
Item Definition Comments
Fair value πΉπ π‘ =
π=1
ππ
πΉππ π‘ i = index for valuation positions
Prudent Valueπππππ π‘ β€ πΉππ π‘
β π = 1, β¦ , ππ, π = 1, β¦ , ππ’, β π = 1,β¦ , ππ΄ππ΄
o j = index for risk factors
o k = index for AVAs
Additional
Valuation
Adjustment
(simplified)
π΄ππ΄ π‘ = 0.1%
π=1
ππ΄π π ππ‘π
πΉππ π‘ +
π=1
ππΏπππππππ‘πππ
πΉππ π‘π΄ππ΄ π‘ is the total valuation
adjustment at time t
Additional
Valuation
Adjustment
(core)
π΄πππ΄πππ π‘ βΆ= π€π πΉππ π‘ β πππππ π‘ ,
π΄ππ΄π π‘ : =
π=1
ππ
π=1
ππ’
π΄πππ΄πππ π‘
o π΄πππ΄πππ π‘ is the k-th AVA
associated to source of
valuation uncertainty j and
valuation position i at time t,
o π΄ππ΄π π‘ is the total k-th AVA at t
Prudent
Valuation
Adjustment
πππ΄ π‘ β
π΄ππ΄(π‘) Simplified
π=1
ππ΄ππ΄
π΄ππ΄π π‘ Core
πππ΄ π‘ is the total valuation
adjustment at time t
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 101
Price distribution, fair value, fair value adjustment, prudent value, AVA
What about realprice distributions...?
Fair value
(mean)Fair value
adjusted
Prudent value
(quantile)
Fair value adjustment
AVA
4: AVA calculationDefinitions and basic assumptions [18]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 102
4: AVA calculationData sources
Market
based
Data sourcing
(EBA RTS Art. 3)
Expert
based
Consensus service data
Proxy data based on similar instruments
Application of prudent shifts to valuation inputs
Exchange prices in a liquid market
Trades in the exact same or very similar instrument,
either from internal records or from the market
Tradable quotes from brokers and other market
participants
Identification of natural bounds to the value of an
instrument
Indicative broker quotes
Counterparty collateral valuations
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 103
4: AVA calculationAVA discussion scheme
Since AVAs are rather involved and diversified, we need to discuss each AVA using a fixed scheme, including:
AVA definition and regulatory references AVA scope of application Fair Value related to the AVA AVA calculation scheme Examples Applications
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 104
4: AVA calculationAVA Market Price Uncertainty (MPU) [1]
AVA definitionAVA Market Price Uncertainty (MPU) refers to the valuation uncertainty of a valuation exposure arising from uncertainty of a valuation input.
This kind of uncertainty is rather common in price evaluation and may appear in different situations, for example:o when the financial instrument is marked to market (e.g. a bond listed), and there
are multiple reliable price contributors;o when the financial instrument is marked to model using some valuation input (e.g.
an OTC IRS valued using multiple yield curves based on IRS market quotes), and there are multiple price contributors for the valuation inputs (e.g. multiple IRS market makers).
AVA main referenceso EBA RTS, article 9.o EBA FAQs 6.1, 21, 23, 23.1, 28, 30, 31, 40.1, 40.3.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 105
4: AVA calculationAVA Market Price Uncertainty (MPU) [2]
AVA scope of applicationWithin the general prudent valuation scope (see before), AVA MPU regards in particular those valuation positions without either a firm tradable price, or a price that can be determined from reliable data based on a liquid two-way market, and such that at least one valuation input has material valuation uncertainty.
AVA MPU shall be computed for all valuation positions ππ , π = 1, β¦ , ππ showing a
valuation exposure to a valuation input π’π , π = 1, β¦ , ππ’ (valuation exposure level).
We stress that a single valuation position ππ may show a valuation exposure to either none, or one, or a few, or many, or all valuation inputs π’π. Thus we may have
Aπππ΄πππ π‘, ππ , π’π1 = 0 and π΄πππ΄πππ π‘, ππ , π’π2 β 0 for the same valuation position
ππ and two different valuation inputs π’π1 β π’π2.
AVA Fair Value The FV of the trades subject to AVA MPU may include or not the effect of possible MPU. In some particular cases, Institutions may account FV adjustments in their balance sheets to cover possible losses related to MPU. In this case the FV subject to prudent valuation for AVA MPU must include these FV adjustments, or, in other words, such FV adjustments must be subtracted from the AVA MPU (keeping the AVA non-negative).
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 106
4: AVA calculationAVA Market Price Uncertainty (MPU) [3]
Does the valuation position have a valuation
exposure ππ , π = 1,β¦ ,ππ, to uncertainty of
valuation inputs π’π , π = 1,β¦ ,ππ’?
o Is there firm evidence of a tradable price for the valuation
exposure ππ ?
o Or can the price for the valuation exposure ππ be determined
from reliable data based on a liquid two-way market (as
defined in art. 338 of CRR) ?
π΄πππ΄πππ π‘, ππ , π’π = 0
YES
Compute individual π΄πππ΄πππ π‘, ππ , π’πfor each valuation exposure ππ to
each valuation input π’π
Do sources of market
data indicate no
material valuation
uncertainty ?
YES
YES
NO
NO
AVA Market Price Uncertainty (MPU) (EBA RTS, article 9) refers to the valuation uncertainty of a
valuation exposure arising from uncertainty of a valuation input.
NO
Continue
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 107
4: AVA calculationAVA Market Price Uncertainty (MPU) [4]
o Use the data sources defined in Art. 3.
o Calculate AVAs on valuation exposures ππ related to each valuation input π’π used in the
relevant valuation model.
o For non-derivative valuation positions, or derivative positions which are marked to market,
refer to the instrument price, or decompose into each valuation input required to calculate
the exit price, treated separately.
o If a valuation input π’π consists of a (D-dimensional) matrix of parameters, π’ππΌπ½πΎβ¦
, calculate
π΄πππ΄πππ π‘, ππ , π’π based on the valuation exposures related to each matrix element π’ππΌπ½πΎβ¦
.
o If a valuation input π’π does not refer to tradable instruments, map the valuation input and
the related valuation exposure to a set of market tradable instruments.
Do you reduce the number
of parameters of the
valuation input π’π (D-dim.
matrix) for the purpose of
calculating AVAs ?
ContinueNO
P&L
variance
test
Positive
YES
Negative
Subject to independent
control function review
and internal validation on
at least an annual basis
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 108
4: AVA calculationAVA Market Price Uncertainty (MPU) [5]
Estimate a point
ΰ·π’π within the
range with 90%
confidence to exit
the valuation
exposure at that
price or better.
Use expert-based
approach using
qualitative and
quantitative
information
available to achieve
a prudent value ΰ·π’πwith confidence
level equivalent to
90%.
Do sufficient data exists to
construct a range of
plausible values for a
valuation input π’π?
YES
NO
Notify competent
authorities of the
valuation
exposures for
which this
approach is
applied, and the
methodology used
to determine the
AVA.
Estimate a point
ΰ·π’π within the
range with 90%
confidence that
the mid value that
could be achieved
in exiting the
valuation
exposure would
be at that price or
better.
Continue
Is the range of
plausible values
of π’π is based on
exit prices ?
Is the range of
plausible values
of π’π is based on
mid prices ?
NO
YES
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 109
4: AVA calculationAVA Market Price Uncertainty (MPU) [6]
Compute individual AVA MPU
π΄πππ΄πππ π‘, ππ , π’π = π€πππ πΉπ π‘, ππ , π’π β πππππ π‘, ππ , π’π
Apply the valuation input uncertainties ΰ·π’π to valuation
exposures ππ and compute prudent value MPUs
By revaluation:
πππππ π‘, ππ , π’π = πΉππππ π‘, ππ , ΰ·π’πor (when the uncertain input is the
instrument price):
πππππ π‘, ππ , π’π = ΰ·π’π
By exposure
πππππ π‘, ππ , π’π = πΉπ π‘, ππ , π’π βππΉπ
ππ’πΰ·π’π β π’π
Compute total category level AVA MPU
π΄ππ΄πππ π‘ =
π=1
ππ
π=1
ππ’
π΄πππ΄πππ π‘, ππ , π’π
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 110
4: AVA calculationAVA Market Price Uncertainty (MPU) [7]
AVA calculation
o Securities
β’ Impaired/defaulted securities
π΄ππ΄πππ π‘ = 0 if the FV is already conservative and does not depend on
uncertain market data, otherwise go to next cases.
β’ Liquid securities accounted at Fair Value Level 1
π΄ππ΄πππ π‘ = 0, if the FV is calculated on market tradable prices with negligible
bid-ask, otherwise go to next cases.
β’ Contributed securities accounted at Fair Value Level 1
a possible approach is
Aππ΄πππ π‘ = π€πππ ΰ΅+0.9 Γ πΉπ π‘ β ππππ
πππ π‘ long positions,
β0.9 Γ πΉπ π‘ β πππ ππππ₯ π‘ short positions.
where πππππππ π‘ /ππππ
πππ π‘ are the lowest/highest bid/ask prices quoted at time t,
and π€πππ = 0.5.
β’ Securities accounted at Fair Value Level 2 or 3
AVA MPU shall be computed via sensitivity or full revaluation based on relevant
risk factors, in particular credit spread and interest rate curves, using prudent
MPUs.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 111
4: AVA calculationAVA Market Price Uncertainty (MPU) [8]
AVA calculation (contβd)
o Derivatives
AVA MPU is computed via sensitivity or full revaluation based on relevant risk
factors.
MPU estimation
AVA MPU calculation is based on the estimation of MPUs of relevant (possibly all)
risk factors, including volatilities and correlations.
Possible sources of MPUs are the following.
o Front office traders active in their respective markets.
o Appropriate selection of multiple contributors (brokers, market makers) available
from data providers (i.e. Bloomberg or Reuters).
o Consensus price services (e.g. Markit).
o Collateral counterparty valuations for derivatives.
o Historical series of prices and market data
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 112
4: AVA calculationAVA Market Price Uncertainty (MPU) [9]
Examples
o Bond for which there exist multiple price contributors.
o IRS valued using multiple yield curves based on market quotations (Fras, Futures, OIS, IRS, Basis IRS, etc.) for which there exist multiple market makers.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 113
4: AVA calculationAVA Market Price Uncertainty (MPU) [10]
Case study of AVA MPU calculation for a security.
β’ Top left: market bid and ask prices. FV is computed as average mid price = 162.25.
β’ Bottom left: ranking and percentiles of mid prices, AVA MPU for long and short positions, equal to 0.14 and 0.12, respectively.
β’ Top right: distribution chart.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 114
4: AVA calculationAVA Market Price Uncertainty (MPU) [11]
Examples with sensitivities.
See EBA RTS sec. 4.1.1 and ref. [23].
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 115
4: AVA calculationAVA Market Price Uncertainty (MPU) [12]
P&L variance test
Notation
π ππ , π = 1, β¦ , ππ , π = 0, β¦ , ππ = i-th risk factor (scalar, vector or matrix element,
generically indexed by i with some ordering) for j-th date (backward time ordered, j =
0 = today, j = 1 = yesterday business day, etcβ¦.).
Ξπ ππ β π ππ β π ππβ1 = j-th daily variation of risk factor π ππ.
ππ = fair value of todayβs valuation exposure at j-th date (static portfolio).
πΏππ β Ξ€πππ ππ ππ = first-order sensitivity of todayβs valuation exposure to risk factor π ππ(delta, vega, rho, etc.).
Discussion
We know the valuation exposure and its fair value at todayβs date, π0. Instead, itβs much
more difficult to recompute the past fair values of the present valuation exposure,
π1, β¦ , πππ . Thus, we approximate such values using first order Taylor expansion and
todayβs risk factors sensitivities as follows
ππ β ππβ1 +
π=1
ππ
πΏππ Ξπ ππ +β― β ππβ1 +
π=1
ππ
πΏπ,0 Ξπ ππ .
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 116
4: AVA calculationAVA Market Price Uncertainty (MPU) [13]
P&L variance test (contβd)
Notice that weβre assuming that first order sensitivities are fairly constant w.r.t. the risk
factors levels, πΏπ,π β πΏπ,0 β π. This is consistent with first order expansion and the static
portfolio assumption. Second order sensitivities (gamma in particular) can be introduced
in the Taylor expansion if required.
Hence we may define the j-th daily profit & loss of the valuation exposure as
ππΏπ: = ππ β ππβ1 β
π=1
ππ
πΏπ,0 Ξπ ππ , π = 1, β¦ , ππ,
and we may compute the variance of the historical series as
πππ ππΏ = πππ ππΏ1, β¦ , ππΏππ ,
Where the EBA RTS requires ππ = 100.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 117
4: AVA calculationAVA Market Price Uncertainty (MPU) [14]
P&L variance test (contβd)
The calculations above may refer to both unreduced and reduced sets of risk factors as
well. Denoting reduced quantities with a hat, the reduced set is characterized by a lower
number of risk factors, ππ < ππ . We may calculate the profit & loss of the reduced
valuation exposure as
ππΏπ: = ππ β ππβ1 β
π=1
ππ
απΏπ,0 Ξπ ππ , π = 1, β¦ , ππ,
with the constrain on the total reduced and unreduced sensitivities,
π=1
ππ
απΏπ,0 =
π=1
ππ
πΏπ,0 ,
for each single risk factor class (e.g. delta, vega, etc.).
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 118
4: AVA calculationAVA Market Price Uncertainty (MPU) [15]
P&L variance test (contβd)
Finally, the P&L variance ratio test required by EBA RTS [1], art. 9 can be calculated as
ππΏ π£πππππππ πππ‘ππ =πππ ππΏ β ππΏ
πππ ππΏβ€ 0.1,
where
πππ ππΏ β ππΏ = πππ ππΏ1 β ππΏ1, β¦ , ππΏππ βππΏππ .
Comments
The approach above is based on common approximations and requires, beyond the
present value and sensitivities of the valuation exposures, just the historical series of
the relevant market risk factors. The most important factor driving the result of the test is
obviously the choice of the reduced valuation exposure and itβs robustness over time.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 119
4: AVA calculationAVA Market Price Uncertainty (MPU) [16]
P&L variance test (contβd)
Possible issues
How to define the unreduced set of risk factors ? -> choose the tradable nodes.
How to choose the reduced set of risk factors ? This is arbitrary: in principle,
institutions are allowed, for each prudent valuation reporting date, to look for the
most convenient level of aggregation that minimizes the AVA and passes the test.
How to ensure test stability from time to time ? The test success/failure strongly
depends on the distribution of the sensitivity w.r.t. the chosen level of aggregation.
Thus the same test applied to a dynamical portfolio may be positive one day and
negative another day.
Facts
Recent experience shows that:
at least for some important cases (i.e. EUR interest rate yield curves and volatilities),
extreme aggregations onto a few (1-3) risk factors (pillar, pillar/strike) is often
sufficient to pass the test.
Principal component analysis is helpful to understand the most important risk factors
and to select the possible aggregations to be tested.
As a consequence, it seems that AVA MPU can be drastically reduced.
NEW
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 120
4: AVA calculationAVA Close-Out Costs (CoCo) [1]
AVA definitionAVA Close-Out Costs (CoCo) refers to the valuation uncertainty of a valuation exposure arising from uncertainty in the exit price of the valuation positions, or, in other terms, the cost of liquidity that a particular valuation exposure can exhibit in particular market conditions. Both situations lead to relevant bid-ask spreads to exit the valuation position. Since illiquidity can also be seen as uncertainty around the mid price, AVA CoCooverlaps with AVA MPU. Thus, when AVA MPU is based on tradable prices, AVA CoCo may be set to zero.
AVA main referenceso EBA RTS, article 10. o EBA FAQs 23, 24, 24.1, 28, 30, 31, 37, 37.1, 40.1, 40.3, 42.5.
AVA scope of applicationWithin the general prudent valuation scope (see before), AVA CoCo refers in particular to those valuation positions for which there is not sufficient liquidity to exit the valuation exposure at mid price (at 90% confidence level), and there are relevant bid-ask spread.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 121
4: AVA calculationAVA Close-Out Costs (CoCo) [2]
AVA Fair Value The FV of the trades subject to AVA CoCo may include or not the effect of possible bid-ask spread. In some particular cases, Institutions may account FV adjustments in their balance sheets to cover the most relevant bid-ask uncertainties. In this case the FV subject to prudent valuation for AVA CoCo must include such FV adjustments, or, in other words, such FV adjustments must be subtracted from the AVA CoCo (keeping the AVA non-negative).
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 122
4: AVA calculationAVA Close-Out Costs (CoCo) [3]
Did you calculate π΄ππ΄πππ for the same valuation exposure
based on exit prices ?
o Did you compute the mark to market on the assumption to
close out at mid market (see CRR art. 105.5) ?
o Is there evidence that sufficient liquidity exists to exit the
valuation exposure at mid-price at 90% confidence level ?
NO
Compute individual π΄πππ΄πΆππΆπ for each valuation exposure ππto each bid-offer spread Ξπ for each valuation input π’π
YES
YES
AVA Close Out Cost (CoCo) (EBA RTS, article 10) refers to the valuation uncertainty of a
valuation exposure arising from uncertainty in the exit price of the valuation positions.
NO
Continue
π΄πππ΄πΆππΆπ π‘, ππ = 0
Does the valuation position have a valuation exposure
ππ , π = 1, β¦ ,ππ, to uncertainty of exit price ?
NO
YES
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 123
4: AVA calculationAVA Close-Out Costs (CoCo) [4]
o Use the data sources defined in Art. 3.
o For non-derivative valuation positions, or derivative positions which are marked to market,
either refer to the instrument price, or decompose into each valuation input required to
calculate the exit price, treated separately.
o If a valuation input π’π consists of a matrix of parameters, calculate AVA based on the
valuation exposures related to each matrix element.
o If a valuation input π’π does not refer to tradable instruments, map the valuation input and
the related valuation exposure to a set of market tradable instruments.
Reduce the number of
parameters of the valuation
input for the purpose of
calculating AVAs ?
Continue
NO
P&L
variance
test
Positive
YES
Negative
Subject to independent
control function review
and internal validation on
at least an annual basis
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 124
4: AVA calculationAVA Close-Out Costs (CoCo) [5]
Estimate a point Ξπwithin the range with
90% confidence that
the bid-ask spread
that could be achieved
in exiting the valuation
exposure would be at
that price or better.
Use expert-based
approach using
qualitative and
quantitative information
available to achieve a
level of certainty in the
prudent valueΞπ that is
equivalent to 90%.
Do sufficient data exists to
construct a range of plausible bid-
offer spreads Ξπ for a valuation
input π’π?
YES
NO
Notify competent
authorities of the
valuation exposures for
which this approach is
applied, and the
methodology used to
determine the AVA.
Continue
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 125
4: AVA calculationAVA Close-Out Costs (CoCo) [6]
Compute individual APVA CoCo
π΄πππ΄πΆππΆπ π‘, ππ , π’π = π€πΆππΆπ πΉπ π‘, ππ , π’π β πππΆππΆπ π‘, ππ , π’π
Apply half of the bid-offer spread Ξπto valuation exposure ππ and compute prudent value
Compute total category level AVA CoCo
π΄ππ΄πΆππΆπ π‘ =
π=1
ππ
π=1
ππ’
π΄πππ΄πΆππΆπ π‘, ππ , π’π
By exposure:
πππΆππΆπ π‘, ππ , π’π = πΉπ π‘, ππ , π’π β1
2
ππΉπ
ππ’πΞπ
By revaluation:
πππΆππΆπ π‘, ππ , π’π = πΉπ π‘, ππ , π’π Β±1
2Ξπ ,
or (when the uncertain input is the
instrument price):
πππΆππΆπ π‘, ππ , π’π = πΉπ π‘, ππ , π’π β 0.5 Γ Ξπ
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 126
AVA calculation
o Securities
β’ Securities held in market making portfolios
π΄ππ΄πΆππΆπ π‘ = 0, since, in these cases, the Institution makes both the bid and
the ask prices.
β’ Liquid securities accounted at Fair Value Level 1
a possible approach is
Aππ΄πΆππΆπ π‘ = π€πΆππΆππΉπ(π‘) ΰ΅βΰ΄€ππππ π‘ long positions,
+ΰ΄€πππ π π‘ short positions.
where ΰ΄€ππππ(π‘)/ ΰ΄€πππ π π‘ are the average bid/ask prices quoted at time t, and
π€πΆππΆπ = 0.5.
β’ Any other security
π΄ππ΄πΆππΆπ π‘ = 0 if, according to the Institution Fair Value Policy, they are
already priced at prudent bid or ask,
otherwise AVA CoCo shall be computed via sensitivity or full revaluation
based on relevant risk factors, in particular credit spread and interest rate
curves, using prudent bid-ask spread.
4: AVA calculationAVA Close-Out Costs (CoCo) [7]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 127
AVA calculation (contβd)
o Derivatives
AVA CoCo is computed via sensitivity or full revaluation based on relevant risk
factors and on market price uncertainty in the bid-offer spread.
Exchange Traded Derivatives (ETD)
Aππ΄πΆππΆπ π‘ = 0, since the FV is quoted and actively traded on the exchange
with negligible bid-ask, otherwise go to next case.
OTC Derivatives (OTCD)
AVA CoCo may be computed typically via full revaluation or sensitivity based
on relevant risk factors, similarly to AVA MPU.
Bid-ask MPU estimation
AVA CoCo calculation is based on the estimation of bid-ask MPUs of relevant risk
factors. Possible sources of such MPUs are restricted to those cases where the
market quotes multiple sources of bid-ask spread.
Examples
o Bond for which there exist multiple bid-ask contributors.
4: AVA calculationAVA Close-Out Costs (CoCo) [8]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 128
Case study of AVACoCo calculation for a security.
Top left: longpositions, ranking and percentiles of mid-bid differences, AVA CoCo = 0.71.
Top right: shortpositions, ranking and percentiles of ask-mid differences, AVA CoCo = 0.71.
4: AVA calculationAVA Close-Out Costs (CoCo) [9]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 129
AVA definitionAVA Model Risk (MoRi) refers to the valuation uncertainty of a valuation exposure arising from uncertainty in models and model calibrations used by market participants. In particular, AVA MoRi does not refers to the uncertainty in market risk capital arising from model risk (see FAQ 23.1).
AVA main referenceso EBA RTS, article 11. o EBA FAQs 10, 23.1, 28.
AVA scope of applicationWithin the general prudent valuation scope (see before), AVA MoRi refers in particular to those valuation positions for which the Institution estimates that there is a lack of firm exit price due to model and/or model calibration choices. Of course, instruments which can be replicated by exact static combination of mark-to-market instruments should not contribute to AVA MoRi.
4: AVA calculationAVA Model Risk (MoRi) [1]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 130
AVA Fair Value The FV of the trades subject to AVA MoRi may include or not the effect of possible model risk. In some particular cases, Institutions may account FV reserves in their balance sheets to cover the most relevant model risk uncertainties. In this case the FV subject to prudent valuation for AVA CoCo must include these reserves, or, in other words, the reserves must be subtracted from the AVA MoRi (keeping the AVA non-negative).
4: AVA calculationAVA Model Risk (MoRi) [2]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 131
Does the valuation position ππ , π = 1,β¦ , ππ, valued with
model ππ , π = 1,β¦ ,ππ, lacks of a firm exit price ?
YES
AVA Model Risk (MoRi) (EBA RTS, article 11) refers to the valuation uncertainty of a valuation
exposure arising from uncertainty in model usage and calibrations used by market participants.
Continue
4: AVA calculationAVA Model Risk (MoRi) [3]
NO
Is the valuation position ππ, valued with model ππ, sensitive
to the usage of different valuation models or model
calibrations π1, β¦ ,πππ used by market participants ?
π΄πππ΄πππ π π‘, ππ , ππ = 0
YES
Compute individual π΄πππ΄πππ π π‘, ππ , ππ for each
applicable valuation model π1, β¦ ,πππ
Does the valuation model risk arise from
calibrations from market derived parameters ?
NO
NO
YES
To be included
into π΄ππ΄πππ
Notation: the model scenarios π1, β¦ ,πππ includes all the
possible models and calibrations appropriate to revaluate all
the valuation positions
Notation: typically, for a
given valuation exposure
ππ, a single valuation
model ππ is used
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 132
4: AVA calculationAVA Model Risk (MoRi) [4]
Estimate a point πΉπ π‘, ππ , ππ within the
range with 90%
confidence to exit the
valuation exposure at
that price or better.
Use expert-based approach to estimate a
prudent value πΉπ π‘, ππ , ππ considering:
o complexity of products relevant to the
model;
o diversity of possible mathematical
approaches and model parameters,
not related to market variables;
o one way market for relevant products;
o existence of unhedgeable risks in
relevant products;
o model adequacy to capture the
behavior of the pay-off of the products
in the portfolio.
Is it possible to construct a range of plausible valuations
produced from model scenarios π1, β¦ ,πππ ?
YES
NO
Notify competent
authorities of the
models for which
this approach is
applied, and the
methodology used
to determine the
AVA.
Model risk test
Continue
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 133
4: AVA calculationAVA Model Risk (MoRi) [5]
Compute individual APVA MoRi
π΄πππ΄πππ π π‘, ππ , ππ = π€πππ π πΉπ π‘, ππ , ππ β πππππ π π‘, ππ , ππ
Compute total category level AVA MoRi
π΄ππ΄πππ π π‘ =
π=1
ππ
π=1
ππ
π΄πππ΄πππ π π‘, ππ , ππ
Compute individual prudent value MoRi
πππππ π π‘, ππ , ππ = πΉπ π‘, ππ , ππ
Notation: πΉπ π‘, ππ , ππ denotes
the prudent value of the valuation
exposure ππ evaluated with model
ππ determined as above
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 134
4: AVA calculationAVA Model Risk (MoRi) [6]
Find a material sample of valuation models ΰ·©π β π1, β¦ ,ππ for which
AVA MoRi is computable via range of plausible values (art. 11.3)
Model risk test
For each valuation position subject to AVA MoRi
computed via expert-based approach (EBA RTS art. 11.4)
Compute AVA MoRi using expert based
approach (art. 11.4) applied to the
sample of models ΰ·©π
Compute AVA MoRi using a range of
plausible values (art. 11.3)
applied to the sample of models ΰ·©π
Compare the results and check the prudence of the expert-based
approach with annual frequency
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 135
AVA calculation
o Securities
β’ Securitizations
AVA MoRi may be calculated by stressing cash flows w.r.t. constant default rate
(CDR) and constant prepayment rate (CPR).
β’ CDOs
AVA MoRi my be calculated by stressing correlations, recoveries and weighted
average life (WAL).
β’ Impaired/defaulted securities
AVA MoRi is calculated by stressing the recovery rate.
o Derivatives
AVA MoRi may be computed using alternative models and/or model calibrations
applied to the corresponding valuation exposures.
4: AVA calculationAVA Model Risk (MoRi) [7]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 136
Alternative models and calibrationsAVA MoRi is not based on any possible alternative model or model calibration, but on those specific alternative models or model calibrations that may reasonably used by market participants to price the same or similar valuation exposures.
Examples
o alternative but reasonable models, β’ calibrated to the same calibration basket
β’ Referred to the same group of financial instruments
o Same model, alternative calibration approaches, e.g. β’ different calibration baskets
β’ different calibration weights (e.g. flat, or vega weighted)
β’ different objective functions
β’ different optimization algorithm (e.g. global vs local)
β’ Etc.
o Same model, same calibration, alternative numerical approaches, e.g. β’ analitycal approximations
β’ semi-analitycal approximations
β’ numerical PDE solution
β’ Monte Carlo simulation
β’ etc.
4: AVA calculationAVA Model Risk (MoRi) [8]
Inspiration: Β«Thereβs
plenty of room at the
bottomΒ»Richard Feynman, 1959
www.its.caltech.edu/~feynm
an/plenty.html
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 137
Market Risk Scenarios vs Model Risk Scenarioso Risk measures are typically linked to scenarioso Scenarios are related to the risk factors relevant for a particular risk typology
4: AVA calculationAVA Model Risk (MoRi) [9]
Risk class Scenarios Risk measures
Market risk Present market data VaR, Expected shortfall, etc.
Counterparty risk Future market data EPE, Effective EPE, etc.
Operational risk Operational loss event frequency
and severity
VaR 99.9%
Model risk Model scenarios
o Alternative models
o Alternative numerical approaches
o Alternative calibrations
K-th percentile of distribution
of model prices (10Β°
percentile for Prudent
Valuation)
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 138
Processes and controls relevant to model risk (EBA RTS art. 19.2, 19.3)o Annual review of model performanceo Independence in the validation process between risk taking and control units,o Institution-wide product inventory ensuring that every valuation position is
uniquely mapped to a product definitiono Defined valuation methodologies for each product of the inventory, including
calibration and measurement of the valuation uncertainty.o Validation process ensuring that for each product, the product level
methodologies are approvedo Defined thresholds based on observed market data for determining when
valuation models are no longer sufficiently robusto A new product approval process referencing the product inventory
4: AVA calculationAVA Model Risk (MoRi) [10]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 139
4: AVA calculationAVA Model Risk (MoRi) [11]
Relationships between AVA MoRi and AVA MPU, AVA CoCo, fair value, fair value adj.
AVA = 0.5xMPU + 0.5xCoCo + 0.5xMoRi
Fair value
(mean)
Fair value
adjusted
MPU
adj.
Fair value adj.MoRi
AVA MoRi
CoCo
adj.
AVA CoCo
AVA MPU
MoRi
adj.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 140
4: AVA calculationAVA Model Risk (MoRi) [12]
Historical sources of model riskPeriod Main driver Main risk factor Effects1987 Black Monday Volatility Volatility smile
2004 CMS market VolatilitySwaption volatility smile and CMS convexity adjustment
2004 IAS39 Credit Credit Risk Adjustment (CRA)2007 Credit crunch Credit, liquidity Subprime writedown2007 Credit crunch Interest rate basis Multiple yield curves
2009-2010 Credit crunch Interest rate basis CSA discounting2009-2010 Credit crunch Bilateral credit CVA & DVA (IFRS13, 2013)2013-2015 Credit crunch Funding Funding Valuation Adjustment (FVA)
2013-2014 Credit crunch Interest rateNegative interest rates and inflation, negative Floor strikes, Bond floater coupons floored, end of Blackβs model.
2014- Credit crunch Capital charges Capital Valuation Adjustment (KVA)2017 Credit crunch Funding Bilateral initial margins
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 141
Market Risk Scenarios vs Model Risk Scenarioso Risk measures are typically linked to scenarioso Scenarios are related to the risk factors relevant for a particular risk typology
3: AVA calculationAVA MoRi: model risk scenarios vs traditional scenarios
Risk class Scenarios Risk measures
Market risk Present market data VaR, Expected shortfall, etc.
Counterparty risk Future market data EPE, Effective EPE, etc.
Operational risk Operational loss event frequency
and severity
VaR 99.9%
Model risk Model scenarios
o Alternative models
o Alternative numerical approaches
o Alternative calibrations
K-th percentile of distribution
of model prices (10Β°
percentile for Prudent
Valuation)
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 142
3: AVA calculationAVA MoRi: model risk scenarios for interest rate derivatives
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 143
3: AVA calculationAVA MoRi: model risk scenarios nested simulation
Pricing
model
OnePricing
model
Two
Pricing
model
Three
Idea of model risk in nested Monte Carlo Simulations for XVAso Scenarios are related to the risk factors relevant for a particular risk typologyo Primary scenarios are tranched into different groups, associated to different
simulation dynamicso At each future time simulation date, we use different pricing models, each
consistent with its underlying risk factors dinamics.
NEW
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 144
4: AVA calculationAVA Model Risk (MoRi): case study 1 [1]
Case study 1: model risk in interest rate yield curve construction
Interest rate yield curves are used everywhere for discounting and for interest rate derivatives and securities with floating rate coupons. So, this is an important case study.
Yield curve construction is based on recursive application of pricing formulas applied to interest rate market instruments. So, there is a lot of modelling inside.
In particular, the interpolation algorithm is very important, both pre and post bootstrapping:
o Simple but non-smooth linear interpolation algorithms are very simple and robust, but produces irregular forward curves
o Standard spline interpolation is less simple but produces oscillating yield curves
o Monotonic cubic spline interpolation is regular.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 145
4: AVA calculationAVA Model Risk (MoRi): case study 1 [2]
Linear interpolation on zero interest rates
Monotonic cubic spline interpolation on zero interest rates
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 146
4: AVA calculationAVA Model Risk (MoRi): case study 1 [3]
Differences in bps between three different interpolation algorithms (linear, natural cubic spline and monotonic cubic spline) for a portfolio of 3 standard IRS on Euribor 1M, 6M, 12M + 3 standard Basis Swaps.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 147
4: AVA calculationAVA Model Risk (MoRi): case study 2 [1]
Case study 2: model risk experiment with Numerix
Sensitivity of prices to modelso Various dimensions of modelling decisionso Example of Bermudan swaption pricing with HW1F, HW2F, CIR, and BK modelso Impact of calibration choiceso AVA MoRi for a Bermudan swaptiono Model implied European swaption smile
Impact of changing market environment on model performanceo Handling of negative rateso Example of floor pricing with very low strikes by using various models
Joint work with Ilja Faerman and Laure Darleguy, Numerix webinar, 12 Nov. 2014, available at www.numerix.com
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 148
4: AVA calculationAVA Model Risk (MoRi): case study 2 [2]
Case study 2: model risk experiment with Numerix (contβd) Global modelling approach
Trade
FX spotBasis
spreadYield Curve Correlation
Model
underlying
Forward
curveSwap rate
Risk factor
Short-rate
Distribution
typeNormalLog-normal Mixture
Chi-
squared
Model type HW1F HW2F
Calibration
instruments Caplets Swaptions
Instruments
configuration
10Y
diagonal
20Y
diagonal10Y column
10Y diag +
10Y column
CIR BK
CMS
β¦
β¦
β¦
β¦
β¦
β¦
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 149
4: AVA calculationAVA Model Risk (MoRi): case study 2 [3]
Case study 2: model risk experiment with Numerix (contβd)
Experiment
#Instruments Models Calibrations
Bermudan
swaption
β’ Coterminal bermudan payer
swaption
β’ Euribor 6M
β’ 10Y maturity
β’ Annual callability
β’ Sstrike ATM 10Y swap
β’ OIS discounting
β’ Hull-White 1 Factor
(HW1F)
β’ Black-Karasinski (BK)
β’ Cox-Ingersoll-Ross 1
Factor (CIR1F)
β’ Hull-White 2 Factors
(HW2F)
β’ Cox-Ingersoll-Ross 2
Factors (CIR2F)
β’ Set 1: 10 Y diagonal
swaption ATM
β’ Set 2: 10Y diagonal
and 1Y column
swaption ATM
β’ Set 3: 20Y diagonal
and 1Y column
swaption ATM
Caps/Floors
with negative
rates
β’ 5Y Floor
β’ Euribor 6M
β’ Negative and positive strikes
β’ Yield curves with negative
rates
β’ Linear interpolation and flat
extrapolation
β’ SABR interpolation and flat
extrapolation
β’ Black (analytic)
β’ Hull-White 1 Factor
(HW1F)
β’ Shifted Black-Karasinski
(SBK)
β’ Set 1: Cap volatility
columns for strikes
ATM and 1%
β’ Set 2: full Cap volatility
surface, with strikes
from 1% to 10%
Joint work with Ilja Faerman and Laure Darleguy, Numerix webinar, 12 Nov. 2014, www.numerix.com
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 150
4: AVA calculationAVA Model Risk (MoRi): case study 2 [4]
Overview of results
Prices range from 1.45% to 3.91% Normal models produce consistently higher PVs for all calibration sets compared to
non-normal models
HW1FBK
CIR1FHW2F
CIR2F
0.00%
1.00%
2.00%
3.00%
4.00%
Set1
Set2
Set3
Bermudan swaption prices per model and calibration set
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 151
4: AVA calculationAVA Model Risk (MoRi): case study 2 [5]
Results by calibration set
Calibration set 1 (10Y diagonal) produces highest distribution of prices Average price is fairly stable across different calibration sets Same model stays consistently below or above the average price for all calibration
sets
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
4.50%
Set1 Set2 Set3
Bermudan swaption prices per calibration set
HW1F BK CIR1F HW2F CIR2F Average
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 152
4: AVA calculationAVA Model Risk (MoRi): case study 2 [6]
Results by model
HW1F and BK models exhibit lowest variations in prices with changing calibration set Prices of 1F and 2F models of the same model type can differ significantly
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
4.50%
HW1F BK CIR1F HW2F CIR2F
Bermudan swaption prices per model
Set1 Set2 Set3
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 153
4: AVA calculationAVA Model Risk (MoRi): case study 2 [7]
Results
Notional is 10m EUR Assuming Fair Value is the average of all price
Long swaption:o Fair Value: FV = 258k EURo Prudent value is the 10% percentile of all prices: PV = 177k EURo AVA MoRi = 0.5x(FV-PV) = 40.5k EUR
Short swaption:o Fair Value: FV = -258k EURo Prudent value is the 90% percentile of all prices: PV = -317k EURo AVA MoRi = 0.5x(FV-PV) = 29.5k EUR
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 154
4: AVA calculationAVA Model Risk (MoRi): case study 2 [8]
Excluding models
All models All except HW2F All models All except HW2F
Fair Value (1) 258 258 -258 -258
Prudent Value 177 158 -317 -315
Model Risk AVA 40.5 50 29.5 28.5
Long swaption Short swaption
Fair Value (1) is computed as the average of all model prices
Fair Value (2) for βAll except HW2Fβ is computed excluding the price of the HW2F model
All models All except HW2F All models All except HW2F
Fair Value (2) 258 240 -258 -240
Prudent Value 177 158 -317 -315
Model Risk AVA 40.5 41 29.5 37.5
Short swaptionLong swaption
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 155
4: AVA calculationAVA Model Risk (MoRi): case study 2 [9]
Exercise probabilities
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
Oct-15 Oct-16 Oct-17 Oct-18 Oct-19 Oct-20 Oct-21 Oct-22 Oct-23
Call probabilities per couponCalibration set 1
HW1F
BK
CIR
HW2F
CIR2F
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
Oct-15 Oct-16 Oct-17 Oct-18 Oct-19 Oct-20 Oct-21 Oct-22 Oct-23
Call probabilities per couponCalibration set 2
HW1F
BK
CIR
HW2F
CIR2F
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
Oct-15 Oct-16 Oct-17 Oct-18 Oct-19 Oct-20 Oct-21 Oct-22 Oct-23
Call probabilities per couponCalibration set 3
HW1F
BK
CIR
HW2F
CIR2F
Exercise probability per coupon CIR-type models imply a higher
probability of early exercise than HW models
The term structure of exercise probabilities is regular for all models for calibration set 1, humped for calibration sets 2 and 3.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 156
AVA definitionAVA Unearned Credit Spread (UCS) refers to the valuation uncertainty in the credit valuation adjustment (CVA) to include, according to the applicable accounting framework, the current value of expected losses due to counterparty default on derivative positions. Such valuation uncertainty refers, in particular, to MPU, CoCoand MoRi uncertainties in the calculation of CVA. Hence, the RTS specifies that the AVA UCS shall be split into such components, to be aggregated to their corresponding AVA.Since the definition of AVA UCS specifies βlosses due to counterparty defaultβ (not βprofits due to own defaultβ), and the CRR, art. 33 states that the debt valuation adjustment (DVA, the gain on liabilities due to own credit quality) should not be included in the calculation of own funds, then AVA UCS shall not include the DVA component.
AVA main referenceso EBA RTS, article 12. o EBA FAQs 10, 25, 28.
4: AVA calculationAVA Unearned Credit Spread (UCS) [1]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 157
AVA scope of applicationWithin the general prudent valuation scope (see before), AVA UCS refers in particular to those valuation positions subject to a credit valuation adjustment, and specifically, to OTC derivatives, with a particular focus on uncollateralized derivatives. Securities are excluded, since credit risk is already included in the security credit spread.
AVA Fair Value The FV of the trades subject to AVA UCS may include full, partial or null CVA. In any case the FV subject to prudent valuation for AVA UCS must include these CVAs.
4: AVA calculationAVA Unearned Credit Spread (UCS) [2]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 158
4: AVA calculationAVA Unearned Credit Spread (UCS) [3]
AVA Unearned Credit Spread (UCS) (EBA RTS, article 12) refers to the valuation uncertainty in
the credit valuation adjustment to include, according to the applicable accounting framework, the
current value of expected losses due to counterparty default on derivative positions.
o Is the valuation position ππ , π = 1,β¦ , ππ, a derivative position, and
o according to the applicable accounting framework, is an
adjustment necessary to include the current value of expected
losses due to counterparty default (CVA) ?
YES
NO
π΄πππ΄ππΆπ π‘, ππ = 0
Aggregate
π΄πππ΄ππΆπ π‘, ππ , πππto APVA MPU.
Go to AVA MPU and apply
those rules to compute
individual AVA UCS w.r.t.
MPU, π΄πππ΄ππΆπ π‘, ππ , πππ
Aggregate
π΄πππ΄ππΆπ π‘, ππ , πΆππΆπto APVA CoCo.
Go to AVA CoCo and apply
those rules to compute
individual AVA UCS w.r.t.
CoCo, π΄πππ΄ππΆπ π‘, ππ , πΆππΆπ
Aggregate
π΄πππ΄ππΆπ π‘, ππ , πππ πto APVA MoRi.
Go to AVA MoRi and apply
those rules to compute
individual AVA UCS w.r.t.
MoRi, π΄πππ΄ππΆπ π‘, ππ , πππ π
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 159
AVA calculation
o Securities: excluded
o Derivatives
β’ DVA component
π΄ππ΄ππΆπ π‘ = 0, since DVA is excluded from the prudent valuation scope.
β’ CVA component
π΄ππ΄ππΆπ π‘ shall be calculated considering the following components.
Unilateral CVA: since DVA is excluded, Institutions shall consider the
unilateral CVA, without first to default conditioning.
π΄ππ΄ππΆπ π‘,πππ : uncertainty in CDS spreads, PDs and recovery rates,
uncertainty in risk factors used to compute the exposure (e.g. curves,
volatilities)
π΄ππ΄ππΆπ π‘, πΆππΆπ : bid/ask in CDS spreads.
π΄ππ΄ππΆπ π‘,πππ π : unilateral vs bilateral CVA, time simulation grid, risk free vs
risky close-out, wrong way risk, different dynamics to simulate underlying risk
factors and compute the exposure.
β’ No CVA case
if the CVA is not included in the accounting fair value for some valuation
positions, π΄ππ΄πΆππ΄ π‘ shall be equal to the full CVA of those position, calculated
using prudent parameters as above.
4: AVA calculationAVA Unearned Credit Spread (UCS) [4]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 160
AVA definitionAVA Investing and Funding Costs (IFC) refers to the valuation uncertainty in the funding costs used when assessing the exit price of a valuation position, according to the applicable accounting framework. Such valuation uncertainty refers, in particular, to MPU, CoCo and MoRiuncertainties in the calculation of the funding cost. Hence, AVA IFC shall be split into such components, to be aggregated to their corresponding AVAs.
AVA main referenceso EBA RTS, article 13. o EBA FAQs 26, 35, 36.
AVA scope of applicationWithin the general prudent valuation scope (see before), AVA IFC refers in particular to those valuation positions subject to a funding valuation adjustment and specifically, to OTC derivatives. Securities are excluded, since funding risk is already included in the security credit spread
AVA Fair Value The FV of the trades subject to AVA IFC may include full, partial or null FVA. In any case the FV subject to prudent valuation for AVA IFC must include these FVAs.
4: AVA calculationAVA Investing and Funding Costs (IFC) [1]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 161
4: AVA calculationAVA Investing and Funding Costs (IFC) [2]
AVA Investing and Funding Cost (IFC) (EBA RTS, article 13)
refers to the valuation uncertainty in the funding costs used when assessing the exit price
according to the applicable accounting framework
o Is the valuation position ππ , π = 1,β¦ ,ππ, a derivative position, and
o according to the applicable accounting framework, is an
adjustment necessary to include the funding costs in the exit
price (FVA) ?
YES
NO π΄πππ΄πΌπΉπΆ π‘, ππ = 0
Aggregate
π΄πππ΄πΌπΉπΆ π‘, ππ , πππto APVA MPU.
Go to AVA MPU and apply
those rules to compute
individual AVA IFC w.r.t.
MPU, π΄πππ΄πΌπΉπΆ π‘, ππ , πππ
Aggregate
π΄πππ΄πΌπΉπΆ π‘, ππ , πΆππΆπto APVA CoCo.
Go to AVA CoCo and apply
those rules to compute
individual AVA IFC w.r.t.
CoCo, π΄πππ΄πΌπΉπΆ π‘, ππ , πΆππΆπ
Aggregate
π΄πππ΄πΌπΉπΆ π‘, ππ , πππ πto APVA MoRi.
Go to AVA MoRi and apply
those rules to compute
individual AVA IFC w.r.t.
MoRi, π΄πππ΄πΌπΉπΆ π‘, ππ , πππ π
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 162
AVA calculation
o Securities: excluded
o Derivatives
β’ Strongly collateralized derivatives
π΄ππ΄πΉππ΄ π‘ = 0 if the funding cost is already included in the FV using OIS
discounting methodology.
β’ Non-Strongly collateralized derivatives
If the FVA is included in the accounting FV for some valuation positions, AVA
IFC shall be calculated as the FVA uncertainty, resulting from the uncertainty
in the funding curve.
If the FVA is not included in the accounting FV for some valuation positions,
π΄ππ΄πΉππ΄ π‘ shall be equal to the full FVA of those position, calculated using
prudent parameters.
β’ CSA with initial margins
AVA IFC shall computed on the initial margins, using a discounting approach
applied to an exposure profile assigned to the future initial margin.
4: AVA calculationAVA Investing and Funding Costs (IFC) [3]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 163
4: AVA calculationAVA Investing and Funding Costs (IFC) [4]
β’ π΄ππ΄πΌπΉπΆ π‘ shall be calculated considering the following components.
π΄ππ΄πΌπΉπΆ π‘, πππ : uncertainty in funding spreads, PDs and recovery rates,
uncertainty in risk factors used to compute the exposure (e.g. curves,
volatilities)
π΄ππ΄πΌπΉπΆ π‘, πΆππΆπ : bid/ask in funding spreads.
π΄ππ΄πΌπΉπΆ π‘, πππ π : time simulation grid, different dynamics to simulate
underlying risk factors and compute the exposure.
Funding spread estimationAVA IFC calculation is based on the estimation of a prudent funding curve. Possible sources of such yield curve is the bond yield curve based on own Institution bond emissions.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 164
4: AVA calculationAVA Investing and Funding Costs (IFC) [5]
Switch to FVA accounting
β[JPM] implemented a FVA framework this quarter for its OTC derivatives and structured notes, reflecting an industry migration towards incorporating the cost or benefit of unsecured funding into valuations. For the first time this quarter, we were able to clearly observe the existence of funding costs in market clearing levels. As a result, the firm recorded a $1.5 billion loss this quarter.β (source: M. Cameron, Risk Magazine, 14 Jan. 2014)
Bank 2012 2013
Barclays -Β£101 MM ?
Deutsche Bank -- -β¬364 MM
Goldman Sachs ? ?
JP Morgan -- -$1.500 MM
Lloyds Banking Group - Β£143 MM -Β£135 MM
Nomura -- -Β₯10.000 MM (-$98 MM)
Royal Bank of Scotland - Β£475 MM -Β£424 MM
Societè Generale ? ?
UBS -- --
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 165
AVA definitionAVA Concentrated Positions (CoPo) refers to the valuation uncertainty in the exit price of concentrated positions.Such valuation uncertainty refers, in particular, to those valuation positions showing concentrated exposures related to:o the size relative to the liquidity of the related market;o the average daily market volume and typical daily trading volume of the institution;o the institutionβs ability to trade in that market, and to exit the valuation position
within the time horizon implied by the market risk capitalization (10 days) without impacting the market.
AVA main referenceso EBA RTS, article 14. o EBA FAQs 32, 33, 34.
AVA scope of applicationWithin the general prudent valuation scope (see before), AVA CoPo refers in particular to those valuation positions subject to concentration risk as defined above.
AVA Fair Value The FV of the trades subject to AVA CoPo typically does not include a CoPocomponent.
3: AVA calculationAVA Concentrated Positions (CoPo) [1]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 166
3: AVA calculationAVA Concentrated Positions (CoPo) [2]
AVA Concentrated Positions (CoPo) (EBA RTS, article 14)
refers to the valuation uncertainty in the exit price of concentrated positions
Identify concentrated valuation positions ππ , π = 1,β¦ ,ππ, considering:
o the size of all valuation positions relative to the liquidity of their related market,
o the institutionβs ability to trade in that market,
o the average daily market volume and typical daily trading volume of the institution.
YES
NO
π΄πππ΄πΆπππ π‘, ππ = 0
For each concentrated valuation position ππ, there exists
a market price applicable for the size of the position ?
Estimate a prudent exit period
Does the prudent exit period exceed 10 days ?
Continue
YES
NO
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 167
3: AVA calculationAVA Concentrated Positions (CoPo) [3]
Compute individual AVA CoPo taking into
account:
o the volatility of the valuation input,
o the volatility of the bid offer spread,
o the impact of the hypothetical exit
strategy on market prices.
Document the methodology
applied to determine
concentrated valuation positions
for which a concentrated
positions AVA is calculated
Compute total category level AVA CoPo
π΄ππ΄πΆπππ π‘ =
π=1
ππ
π΄πππ΄πΆπππ π‘, ππ
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 168
AVA calculation
o Securities
AVA CoPo may be calculated as follows:
β’ Look for possible concentrated positions by comparing the size held w.r.t. the
outstanding amount of the security circulating on the market,
β’ estimate coefficients of uncertainty related to the sizes above,
β’ compute AVA CoPo via sensitivity on the credit risk factors and uncertainties
above.
o Derivatives
OTC derivatives typically do not show concentrated positions in the sense defined
above. Possible exceptions shall be documented and AVA CoPo shall be
calculated as described in the previous scheme.
Exampleso Concentrated positions into single stock w.r.t. typical stock trading volumeso Concentrated positions into single bond emissions w.r.t. typical bond trading
volumes and outstanding amount.
3: AVA calculationAVA Concentrated Positions (CoPo) [4]
w.r.t. typical stock trading volumes
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 169
AVA definitionAVA FAC takes into account the valuation uncertainty emerging from possible administrative costs and future hedging costs on valuation positions for which a direct exit price is not applied for the close-out costs AVA. Thus, future administrative costs are complementary to close-out costs. If the close-out costs are assessed on a full exit price basis then, after executing the corresponding close out strategy, the positions disappear, and there are no future administrative costs. However, where close-out costs are assessed on a "cost-to hedge" basis, as with derivative portfolios, the positions are maintained, and therefore there are possible future administrative costs in running the portfolio until maturity.
AVA main referenceso EBA RTS, article 15. o EBA FAQs 37, 37.1.
AVA scope of applicationWithin the general prudent valuation scope (see before), AVA CoPo refers in particular to those valuation positions subject to FAC as defined above.
4: AVA calculationAVA Future Administrative Costs (FAC) [1]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 170
AVA Fair Value The FV of the valuation positions typically does not include the effect of possible future administrative costs, since such costs are specific of each institution and do not regard an exit price according to IFRS. Hence, the AVA FAC must be applied directly to the full FV of valuation positions.
4: AVA calculationAVA Future Administrative Costs (FAC) [2]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 171
4: AVA calculationAVA Future Administrative Costs (FAC) [3]
AVA Future Administrative Costs (FAC) (EBA RTS, article 15)
refers to the valuation uncertainty due to future administrative and hedging costs
YES π΄πππ΄πΉπ΄πΆ π‘, ππ = 0Do you calculate π΄πππ΄πππ and π΄πππ΄πΆππΆπ for a valuation
exposure ππ , π = 1,β¦ ,ππ,, which imply fully exiting the exposure ?
Compute individual APVA FAC taking into account:
o administrative costs, including all incremental staffing and fixed costs that will be incurred in
managing the portfolio, over the expected life of the valuation exposures,
o the future hedging costs over the expected life of the valuation exposures,
o the cost reduction as long as the size of the valuation exposure reduces,
o the term structure of discounts at risk free rate.
NO
Compute total category level AVA FAC
π΄ππ΄πΉπ΄πΆ π‘ =
π=1
ππ
π΄πππ΄πΉπ΄πΆ π‘, ππ
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 172
4: AVA calculationAVA Future Administrative Costs (FAC) [4]
AVA calculationConsidering the regulatory requirements, we may write a general formula for AVA FAC
π΄πππ΄πΉπ΄πΆ π‘, ππ = ΰΆ±π‘
π
π π‘, π’ π΄ππΆ π‘, π’, ππ ππΉπ΄πΆ π‘, π’, ππ ππ’
whereo π π‘, π’ = discount factor over the time interval π‘, π’ ,o π΄ππΆ π‘, π’, ππ = administrative costs expected at time t for future time interval
π’, π’ + ππ’ , per unit of currency,o ππΉπ΄πΆ π‘, π’, , ππ = nominal of the valuation exposure at future time u,o T = exipry date of the valuation exposure
Considering constant administrative costs and a decreasing step-wise constant notional struck on dates π1, β¦ , ππ , π‘ < π1, ππ = π, we may write a discrete formula
π΄πππ΄πΉπ΄πΆ π‘, ππ β π΄ππΆ π‘, ππ
π=π1
ππ
π π‘, ππ ππΉπ΄πΆ π‘, ππ , ππ ππ β ππβ1 .
Considering furthermore a single (weighted) average lifetime πππ£π (WAL) we may
further simplify to
π΄πππ΄πΉπ΄πΆ π‘, ππ β π΄ππΆ π‘ π π‘, πππ£π ππΉπ΄πΆ π‘, πππ£π πππ£π β π‘ .
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 173
4: AVA calculationAVA Future Administrative Costs (FAC) [5]
AVA calculation (contβd)Clearly, the administrative cost π΄ππΆ π‘, ππ is the most difficult data to obtain. We stress that in the formula above π΄ππΆ π‘, ππ refers to the cost per unit of time and currency, not to the total cost of the desk or the institution, which manage other portfolios not subject to AVA.
AVA dataAVA FAC calculations require the following input data.o Valuation positions not at full exit price, with nominal amounts and maturities.o Administrative and hedging costs per unit of time, per currency, per desk, per
activity.o Risk free (OIS) discount term structure until portfolio maturity.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 174
AVA definitionAVA Early Termination (EaT) refers to the valuation uncertainty emerging from potential losses arising from non-contractual early terminations of client trades.
AVA main referenceso EBA RTS, article 16. o EBA FAQs 38.
AVA scope of applicationWithin the general prudent valuation scope (see before), AVA EaT regards in particular client trades, that is, trades with client counterparties that may be subject to non-contractual early termination because of litigations or commercial reasons.
AVA Fair Value The FV of the client trades subject to AVA EaT typically does not include the effect of possible non-contractual early terminations by clients. In some particular cases, Institutions may account reserves in their balance sheets to cover possible losses related to early terminations of some trades or portfolios with specific counterparties. If these reserves are accounted as a FV component, the FV subject to prudent valuation for AVA EaT must include the reserves. In other words, the reserves must be subtracted from the AVA EaT.
4: AVA calculationAVA Early Termination (EaT) [1]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 175
4: AVA calculationAVA Early Termination (EaT) [2]
AVA Early Termination (ET) (EBA RTS, article 16)
reflects the valuation uncertainty arising from potential losses
due to possible non-contractual early terminations of client trades.
YES
Is the valuation position ππ , π = 1,β¦ ,ππ,
subject to possible non-contractual early termination ?
Identify a suitable past time window π; π‘ and historical trades π’π =
1,β¦ , ππΈππ subject to non-contractual early terminations at past dates
πππΈππ , β¦ , π1 such that π β€ πππΈππ β€ β― β€ π1 β€ π‘.
NO
Retrieve the corresponding historical fair values πΉπ ππ , π’πand actual termination prices π ππ , π’π .
Continue
π΄πππ΄πΈππ π‘, ππ = 0
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 176
4: AVA calculationAVA Early Termination (EaT) [3]
The 10th percentile
may be negative (loss)
or positive (profit), and
represents the highest
loss or the smallest
profit realized with
90% historical
probability.
Compute individual APVA EaT according to the formula
π΄πππ΄πΈππ π‘, ππ = α0, ππ ππΏ10% β₯ 0,
ππΏ10% Γ πΉπ π‘, ππ ππ ππΏ10% < 0.
Calculate
o the historical profit and loss values, ππΏ ππ , π’π βΆ= ΰ΅π ππ , π’π β πΉπ ππ , π’π πΉπ ππ , π’π ,
o the historical P&L distribution, Ξ€Ξπ ΞππΏ ,o the 10th percentile of the P&L distribution, ππΏ10% β β Ξ€Ξπ ΞππΏ , 10% ,
Compute total category level AVA EaT
π΄ππ΄πΈππ π‘ =
π=1
ππ
π΄πππ΄πΈππ π‘, ππ
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 177
4: AVA calculationAVA Early Termination (EaT) [4]
AVA calculationSee flow chart above.
AVA dataAVA EaT calculations require a database of historical early terminations, including, for each trade:o termination date,o nominal,o fair value at EaT time instant,o actual EaT price at EaT time instant.
Exampleso Trades early terminated because of litigationso Trades early terminated because of commercial relationships
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 178
4: AVA calculationAVA Early Termination (EaT) [5]
Case studySee figure below.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 179
4: AVA calculationAVA Early Termination (EaT) [6]
Case study (contβd)o The nominal of the present portfolio of client trades subject to possible non-contractual EaT
(cols. 2-4 top, 12 β¬mln) is taken from βDerivatives HFTβ in the sample portfolio. o The absolute FV is set to 5% of the nominal for 1,000 trades. o The past portfolio is set to half the present portfolio and may be seen as an average over the
EaT historical window (so, trading volume increased from past to present). o The portfolio of client trades that were historically early terminated (cols. 5-7 top) is set to 1%
of the past portfolio, hence the historical probability of non-contractual EaT is 1%. o In the bottom table we show a possible drill-down of the 10 trades historically affected by
non-contractual EaT. We generated the absolute EaT price (col. 4) as P=FV(1+10%Ξ΅), where Ξ΅ is a random number with uniform distribution in [-1,1].
o Hence, the P&L (cols. 5-6) may be positive or negative (we chose a negative case). o Given the relative P&L% distribution (col. 6), we calculated the 10th percentile (which, in this
simple case with 10 trades, is just the 2nd higher P&L%), representing the highest loss happened with 90% historical probability after non-contractual EaT.
o Finally, we applied such historical estimate to the absolute FV of the present portfolio in the top table (col. 9-10).
o The AVA (col. 11) is just the absolute value of the corresponding expected loss (col. 9). o We notice that the historical P&L%(10) (-9.64%) corresponds to a small historical loss (-
28,917β¬) originated by a single deal with limited fair value (300.000β¬) but generates a much larger expected loss (-578,346β¬) once applied to the fair value of the present portfolio (6,000,000β¬). This is consistent with the idea of prudent value at 90% confidence level required by the regulation.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 180
AVA definitionAVA Early Termination (EaT) takes into account the valuation uncertainty emerging from potential losses that an institution may incur because of the operational risk related to valuation processes. This risk is mainly related, but not limited, to the balance sheet substantiation process and to possible legal disputes (RTS art. 17.1). The main driver for AVA OpR is the operational risk framework adopted by the Institution. Institutions adopting the Advanced Measurement Approach (AMA) Operational Risk defined in the CRR, title III, ch. 4, art. 321-324 (AMA Institutions) are allowed a lighter AVA OpR, as described below. This facilitation is intended to avoid double counting of capital reserves related to the same source of risk. In all other cases (non-AMA Institutions), the AVA OpR is given by 10% of the sum of AVA MPU and AVA CoCo, which can result in high figures. In particular, FAQ 39, remarks that Institutions using the Standardized Method for Operational Risk defined in the CRR, title III, ch. 3, art. 317-320, cannot show that they already take into account the operational risk related to valuation processes. Thus they are not allowed to calculate AVA OpR as AMA institutions. .
AVA main referenceso EBA RTS, article 17. o EBA FAQs 39, 40, 42.
4: AVA calculationAVA Operational Risk (OpR) [1]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 181
AVA scope of applicationWithin the general prudent valuation scope (see before), AVA OpR regards in particular those positions that:o can be considered subject to operational risk during the valuation process;o for which in the balance sheet there are provisions for operational risk.Evidences of operational risk related to valuation process are the inclusion of those valuation processes as part of the AMA accounting for the mispricing, misselling and the process execution errors. Furthermore, an AMA usually accounts provision for legal disputes with clients where the underlying of the contract is a fair value position.
AVA Fair Value The fair values of positions under AVA OpR typically does not include any component or adjustment related to operational risk, since these factors do not concur to an exit price. From a risk management point of view, expected operational risk losses may be evaluated using scenario analysis and historical data related to realized operational risk losses.
4: AVA calculationAVA Operational Risk (OpR) [2]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 182
4: AVA calculationAVA Operational Risk (OpR) [3]
AVA Early Termination (ET) (EBA RTS, article 17) reflects the
reflects the valuation uncertainty arising from potential losses
that may be incurred as a result of operational risk related to valuation processes.
Identify valuation positions ππ , π = 1, β¦ ,ππ, judged to be at-risk during the balance sheet
substantiation process, including those due to legal disputes.
Compute individual APVA OpR according to the formula
π΄πππ΄πππ π‘, ππ = 10% Γ π΄πππ΄πππ π‘, ππ + π΄πππ΄πΆππΆπ π‘, ππ
Is the AMA (Advanced Measurement Approach) applied to Operational Risk (as defined
in Title III Chapter 4 of Regulation (EU) No 575/2013) for valuation positions ππ ?
Is there evidence that the operational risk relating to valuation processes of valuation positions ππ is fully accounted for by the AMA calculation ?
YES
NO
π΄πππ΄πππ π‘, ππ = 0
NO
YES
Compute total category level AVA OpR
π΄ππ΄πππ π‘ =π=1
πππ΄πππ΄πππ π‘, ππ
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 183
Summary
5. Prudent valuation frameworko Implementationo Methodological frameworko Operational frameworko IT frameworko Documentation & reportingo Example of prudent valuation framework
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 184
5: Prudent valuation framework Areas: overview
Governance Methodology
TechnologyDocumentation
and reporting
Institution
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 185
5: Prudent valuation framework Areas: governance
Define Prudent Valuation processes and controls
throughout the operative chain
Apply Indipendent Price Verification (IPV) processes
Guarantee effective controls to govern all fair valued
positions
Implement controls to ensure robust evaluation
processes even in stressed situations
Design reports for Senior Management (information,
frequency and recipients)
Deliver an exhaustive information set to guarantee
an appropriate understanding of the valuation
uncertainty of the assets and liabilities portfolio.
Implement the governance area in terms of roles, responsabilities and processes for
measurement, management and control.
Governance
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 186
5: Prudent valuation framework Areas: methodology
Design AVA calculation methodologies and
aggregation rules
Define scope at single legal entity level and
consolidated level
Design, realisation and maintenance of a prudent
valuation policy, subject to senior management
approval and revision.
Define robust methodologies to estimate and aggregate prudent values at banking group
level and consolidated level.
Methodology
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 187
5: Prudent valuation framework Areas: documentation and reporting
Production chain of prudent values (AVAs)
Match calculation schedule with regulatory deadlines
Deliver AVAs for internal and external reporting
Integrate prudent valuations (AVAs) calculation into the management and regulatory
reporting processes.
Documentation
and reporting
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 188
5: Prudent valuation framework Areas: technology
Integration with accounting repositories to determine
the prudent valuation scope
Implementation of feeds and calculation engine
Integration with regulatory reporting platform
Monitoring and control input/output data
Development management reporting tools
Design and implement an automatic IT chain for feeding and calculation processes of
prudent values
Technology
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 189
5: Prudent valuation framework Example of Prudent Valuation framework [1/4]
Scope Calculation Reporting
Identify fair value positions
Apply exlusionsprovided by the regulator:
o Positions subject to prudential filters such that fiar
value variations has no or partial impact on CET1
(es. AFS)
o Hedge Accounting positions
o Back to back positions
Monitor of output data quality
Data mining
Legal entities
scope
Prudent Valuation
scope
Prudent
valuation
scope
Accounting
systems
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 190
Scope Calculation Reporting
Identifiy uncertainty levels
Retrieval information from market operators
Retrieval Markit information
Data mining
Front
office
systems
External
sources
Uncertainty
levels
5: Prudent valuation framework Example of Prudent Valuation framework [2/4]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 191
Scope Calculation Reporting
Check the threshold for core approach (EUR15 bn)
If > = EUR15 bn :
o Apply association rules between each single trade and
the corresponding AVAs
o Apply netting rules
o Aggregation and association of uncertainty levels with
single trades and AVAs
o Apply core AVA calculation rules
if < EUR15bn:
o 0,1% Prudent Valuation scope fair value
Data mining
Prudent Value
calculation
Prudent
valuation
scope
Uncertainty
levels
Methodology
5: Prudent valuation framework Example of Prudent Valuation framework [3/4]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 192
Custom
reporting
Scope Calculation Reporting
Prepare management reporting
Prepare regulatory reporting (quarterly)
Transmit information to each stakeholder inside the bank
Data mining
Methodology
Management
reporting
Regulatory
reporting
5: Prudent valuation framework Example of Prudent Valuation framework [4/4]
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 193
6: ConclusionsHot topics (1/2)
The CRR is in place since 1st Jan. 2014, and EBA RTS are in the final phase ofapproval, so prudent valuation is mandatory.
AVA calculation for all fair value positions under the core approach is resourceintensive.
The practical application of the EBA RTS requires a lot of expert judgment, inparticular to achieve the required 90% level of certainty in the prudent value.
P&L variance test for AVA market price uncertainty and close out costs is ratherdifficult and controversial.
AVA Investing & Funding cost is a βprudent versionβ of the FVA, so banks still notaccounting FVA in their balance sheets should account the full FVA in the prudentvaluation, with the benefit of the diversification factor 0.5. Banks already accountingFVA must calculate a prudent FVA. .
Other XVAs, i.e. MVA (Margin Valuation Adjustment), and KVA (Capital ValuationAdjustment) are controversial. Rule of thumb could be βno fair value accounting, noprudent value capitalβ.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 194
6: ConclusionsHot topics (2/2)
Unclear how to manage exclusions for back to back and hedge accounting positions.Is it referred to both Cash Flow Hedge (for which prudential filter is applied) and FairValue Hedge ?
AVAs have to be deducted from CET1. Hence, possible double counting w.r.t. othercapital deductions should be considered, e.g. expected loss amounts (CRR, art. 158-159), day one profits, etc.
Possible uneven playing field between institutions subject or not to the EU prudentvaluation rules.
New regulation and lack of standard market practices allows for widely differentapplications of the same rules across different institutions. It is reasonable to expectfollow ups from Regulators.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 195
6: Conclusions
Questions & Answers
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 196
7: Selected ReferencesRegulations [1]
1) BCBS, βInternational Convergence of Capital Measurement and Capital Standards β A revised frameworkβ, June 2004, http://www.bis.org/publ/bcbs107.htm
2) BCBS, βRevision of the Basel II market risk frameworkβ, July 2009, http://www.bis.org/publ/bcbs158.htm
3) Financial Services Authority, βDear CEO Letter: Valuation and Product Controlβ, August 2008, http://www.fsa.gov.uk/pubs/ceo/valuation.pdf
4) Financial Services Authority, βProduct Control Findings and Prudent Valuation Presentationβ, November 2010, http://www.fsa.gov.uk/pubs/other/pcfindings.pdf
5) Financial Services Authority, βRegulatory Prudent Valuation Returnβ, Policy Statement 12/7, April 2012, http://www.fsa.gov.uk/library/policy/policy/2012/12-07.shtml
6) International Accounting Standards Board, Β«International Financial Reporting Standards 13 βFair Value MeasurmentΒ», 1Β° Jan. 2013, www.ifrs.org
7) Regulation EU N.575/2013 of the European Parliament and of the Council on prudential
requirements for credit institutions and investment firms and amending Regulation EU
N.648/2012, 26 June 2013
8) European Banking Authority, βDiscussion Paper relating to Draft Regulatory Technical
Standards on prudent valuation under Article 100 of the draft Capital Requirement Regulation (CRR)β EBA/DP/2012/03, 13 November 2012, http://www.eba.europa.eu/-/eba-
discussion-paper-on-draft-regulatory-standards-on-prudent-valuation.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 197
7: Selected ReferencesRegulations [2]
9) European Banking Authority, βConsultation Paper Draft Regulatory Technical Standards on
prudent valuation under Article 105(34) of Regulation (EU) 575/2013 (Capital Requirements
Regulation β CRR)β, EBA/CP/2013/28, 10 July 2013, http://www.eba.europa.eu/regulation-and-policy/market-risk/draft-
regulatory-technical-standards-on-prudent-valuation.
10) European Banking Authority, βQuestions and Answers on prudent valuationβ, October 2013, http://www.eba.europa.eu/-/revised-faqs-on-prudent-valuation-q-1.
11) European Banking Authority, βQuantitative Impact Study on prudent valuationβ, November 2013, http://www.eba.europa.eu/-/eba-launches-qis-exercise-on-prudent-
valuation.
12) Bank of Italy, Circolare 285, βDisposizioni di vigilanza per le bancheβ, 17 December 2013, https://www.bancaditalia.it/compiti/vigilanza/normativa/archivio-
norme/circolari/c285/index.html
13) European Banking Authority, βEBA final draft Regulatory Technical Standards Regulatory
Technical Standards on prudent valuation under Article 105(14) of Regulation (EU) 575/2013
(Capital Requirements Regulation β CRR)β, 31 March 2014, https://www.eba.europa.eu/regulation-and-policy/market-risk/draft-
regulatory-technical-standards-on-prudent-valuation
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 198
7: Selected ReferencesRegulations [3]
14) European Banking Authority, βEBA final draft Regulatory Technical Standards Regulatory
Technical Standards on prudent valuation under Article 105(14) of Regulation (EU) 575/2013
(Capital Requirements Regulation β CRR)β, rev1, 23 January 2015, https://www.eba.europa.eu/regulation-and-policy/market-risk/draft-
regulatory-technical-standards-on-prudent-valuation
15) European Commission, Commission delegated regulation (EU) 2016/101, supplementing
Regulation (EU) No 575/2013 of the European Parliament and of the Council with regard to
regulatory technical standards for prudent valuation under Article 105 (14), 26 Oct. 2015, http://ec.europa.eu/transparency/regdoc/rep/3/2015/EN/3-2015-7245-
EN-F1-1.PDF
16) European Banking Authority, Consultation Paper, βDraft Implementing Technical Standards
amending Commission Implementing Regulation (EU) 680/2014 on supervisory reporting of institutionsβ, 4 March 2016, https://www.eba.europa.eu/-/eba-seeks-comments-
on-reporting-of-prudent-valuation-information
17) BCBS Consultative Document, βPillar 3 disclosure requirements β consolidated and enhanced
frameworkβ, March 2016, issued for comment by 10 June 2016, http://www.bis.org/bcbs/publ/d356.htm
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 199
7: Selected ReferencesPapers
1) Richard Roll, βA simple implicit measure of the effective bid-ask spread in an efficient
marketβ, The Journal of Finance, Vol. XXXIX, n. 4, Sept. 1984.
2) E. Derman, "Model Risk", Goldman Sachs Quantitative Strategies Research Notes, Apr.
1996.
3) R. Rebonato, "Theory and Practice of Model Risk Managementβ, Quantitative Research
Centre (QUARC) of the Royal Bank of Scotland, 2002.
4) R. Cont, "Model uncertainty and its impact on the pricing of derivative instruments",
Mathematical Finance, Vol. 16, No. 3, July 2006, 519β547.
5) R. Brar, βA Regulatory Perspective on Prudent Valuation and Best Practice in Product
Controlβ, in βManaging Illiquid Assetsβ, E. Takagawa editor, Risk Books, 2012.
6) Tanguy Dehapiot, βPrudent Valueβ, Risk Minds presentation, Dec. 2014.
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 200
7: Selected ReferencesOthers
1) Ernst & Young, βPrudent Valuationβ, 24 May 2013.
2) Ernst & Young, βBIS III β Prudent Valuation β AVAs Overview and relations to IFRS13β,
July 2013.
3) Deloitte, βPrudent Valuationβ, August 2013, http://www.deloitte.com/assets/Dcom-
Belgium/Local%20Assets/Documents/EN/Insights/FSI/be-fsi-
prudentvaluation_ebaconsultationpaper_aug2013.pdf.
4) Financial Machineries, http://www.financial-machineries.com.
5) AIFIRM, Associazione Italiana Financial Industry Risk Managers, βPrudent Valuation -Guidelines and sound practicesβ, Mar. 2016, http://www.aifirm.it/position-paper-prudent-valuation
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 201
10 Dec. 2014: Risk Minds Conference, joint talk on prudent valuation with T. Dehapiot.
28 May 2014: London Stock Exchange, Milano, prudent valuation course, M.
Bianchetti, U. Cherubini, E&Y.
16 May 2014: ABI conference, Roma, talk βFunding Valuation and Prudent Valuation
Adjustments (PVA & FVA)β, M. Bianchetti, U. Cherubini
24 Sept. 2014: corso ABI, Milano, talk βPrudent valuationβ, M. Bianchetti, P. Virgili.
12 Nov. 2014: webinar Numerix, βPrudent Valuation: Bridging the Gap Between
Pricing & Risk Managementβ, M. Bianchetti (link).
24 Nov. 2014: London Stock Exchange, Milano, prudent valuation course, M.
Bianchetti, U. Cherubini, E&Y.
10 Dec. 2014: Risk Minds, Amsterdam, talk βPrudent Valuation - Bridging Pricing And
Risk Managementβ, M. Bianchetti (link).
25 Mar. 2015: WBS 4th CVA conference, London, corso βPrudent valuationβ, M.
Bianchetti, U. Cherubini (link)
May 2015: Global Derivatives, Amsterdam, talk βPrudent Valuation - Bridging Pricing
And Risk Managementβ, M. Bianchetti (link).
7: Selected ReferencesEvents
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 202
APVA = Additional Prudent Valuation Adjustment AVA = Additional Valuation Adjustmento MPU = Market Price Uncertaintyo CoCo = Close out Costso MoRi = Model Risko UCS = Unearned Credit Spreado IFC = Investing and Funding Costso CoPo = Concentrated Positionso FAC = Future Administrative Costso EaT = Early Terminationo OpR = Operational Risks
CRR = Capital Regulatory Requirements EBA = European Banking Authority EU = European Union FV = Fair Value FVP = Fair Value Policy PV = Prudent Value PVA = Prudent Valuation Adjustment PVP = Prudent Value Policy QA = EBA Questions & Answers to DP and QIS RTS = EBA final draft Regulatory Technical Standards
8: Glossary
M. Bianchetti - Prudent Valuation β Global Derivatives β Budapest, 10 May 2016 p. 203
Disclaimer and acknowledgments
Disclaimer
The views and the opinions expressed here are those of the author and do not
represent the opinions of his employer. They are not responsible for any use that may
be made of these contents. No part of this presentation is intended to influence
investment decisions or promote any product or service.
Acknowledgments
The authors gratefully acknowledges
o E. Maffi, S. Vasconi, F. Bertolini, M. Benvenuti, A. Pignataro, S. Vella from E&Y for
their contribution to develop the prudent valuation framework and some data
analysis.
o I. Faerman from Numerix for his contribution for model risk examples.
o T. Dehapiot for sharing information and experties on the subject.
o Members of the AIFIRM committee on market risk for the stimulating discussions on
prudent valuation methodology and applications.
o Many other colleagues in Front Office and Risk Management of Intesa Sanpaolo for
creating a fertile environment to grow the seeds of prudent valuation.