gianluca farina - unibggianluca farina gf2107@columbia.edu universita’ di bergamo 12 june 2014....

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Systemic risk

Gianluca Farinagf2107@columbia.edu

Universita’ di Bergamo

12 June 2014

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Systemic riskOutline

IntroductionThe problem of the definition

MeasuresFeaturesPortfolio lossesNetwork modelsEconometric indicatorsDefault counting

CIMDOIntroductionMethodologyStability study

Infectious defaults with immunizationPrevious works in the areaThe new modelApplication to CDO pricing

Contagion Losses RatioA thought experimentIntroducing the CLRApplication to a banking system

Bibliography

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Systemic riskIntroduction

Sometimes things go wrong

1997 Asian financial crisis The crisis started when the Thai currency collapsed. As thecrisis spread, most of Southeast Asia and Japan saw slumpingcurrencies, devalued stock markets and other asset prices.

1998 LTCM default Considerable hedge funds losses that spilled over to the tradingfloors of both commercial and investment banks.

2008 Sub-prime mortgage crisisand liquidity crunch

Started from special investments vehicles, it affected financialmarkets worldwide and lead to the demise of Bear Stearns andLehman Brothers and to the bail out of AIG.

2008 Icelandic banking crisis Short-term liquidity and depositors runs were the major causesof the collapse of most of the country’s banking system.

2010 Flash crash On the 6th of May, the Down Jones index experienced a sud-den downward jump of around 9% in less than 30 minutes. Thesimultaneous interaction of many high frequency trading algo-rithms and the high uncertainty of the markets caused by theongoing Euro debt crisis were later blamed.

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Why is systemic risk important? 1/2

I Recent banking crises show we have little or no choice (large

bailouts and real economy welfare losses have been estimated on the

order of 10%-20% GDP)

I Monitoring systemic risk is today on the agenda of virtuallyevery financial supervisory authority. Huang et al. (2012):

[This new] perspective has become an overwhelming theme inthe policy deliberations among legislative committees, bankregulators, and academic researchers.

I Far from being only an academic concern. Financial StabilityBoard (report 2009):

financial institutions should be subject to requirementscommensurate with the risks they pose to the financial system

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Why is systemic risk important? 2/2

...because people talk about it!

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The problem of the definition

A universally accepted definition does not exist

I i.e., by the time we leave today you will not know whatsystemic risk is!

I Few attempts (G-10 Working Group [2001], Billio, Getmansky, Lo, and

Pelizzon [2012], Adrian and Brunnermeier [2011])

the risk that an event will trigger a loss of economic value orconfidence in [...] a substantial portion of the financial system thatis serious enough to [...] have significant adverse effects on the realeconomy

any set of circumstances that threatens the stability of or publicconfidence in the financial system

the risk that the intermediation capacity of the entire financialsystem is impaired, with potentially adverse consequences for thesupply of credit to the real economy

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Even more attemptsDe Bandt and Hartmann [2000]

A systemic crisis can be defined as a systemic event that affects aconsiderable number of financial institutions or markets in a strongsense, thereby severely impairing the general well-functioning of thefinancial system. While the special character of banks plays a majorrole, we stress that systemic risk goes beyond the traditional view ofsingle banks’ vulnerability to depositor runs. At the heart of theconcept is the notion of contagion, a particularly strong propagationof failures from one institution, market or system to another.

Schwarcz [2008]

the risk that an economic shock such as market or institutionalfailure triggers (through a panic or otherwise) either the failure of achain of markets or institutions or a chain of significant losses tofinancial institutions, resulting in increases in the cost of capital ordecreases in its availability, often evidenced by substantialfinancial-market price volatility

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Definitions: common themes

Structureinitial shock (often unspecified) affects thewell-functioning or the stability of the financialsystem

Real economyincrease of the cost of money and/or evaporatingcredit supplies

Loss of confidenceimpact on the market perception more importantthat the actual losses caused by the initial shock

Contagionboth cross-sectors and cross-countries infectionchannels should be considered

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Possible causes

I Direct: contractual obligations that link together thecomponents of the system.

I Interbank deposit market (short-term funding)I Syndicated loansI Counter party exposures

I Indirect: contains all sorts of inter-dependencies betweenmarket participants

I Depositors runsI Common factors/markets exposures (systematic risk)I Asset bubbles (volatility paradox)I Fire salesI Information contagion (herding behaviors)I OTC derivatives (AIG example)

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Regulators actions

I US: Supervisory Capital Assessment Program - SCAPI 2 different scenarios that differ on macroeconomics forecastsI results published in May 2009: 10 companies were required to raise

a total of $74.6 billion in capital

I UK: FSA guidelines for stress testingI Firms own stress testing (firm’s capital and liquidity requirements)I Supervisory stress testing of specific high impact firmsI Simultaneous system-wide stress testing undertaken by firms using a

common scenario for financial stability purposes

I EU: Committee of European Banking SupervisorsI An (imperfectly) integrated banking system but with national based

regulationsI The sovereign debt crises increased markets instability

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Systemic riskMeasures

Systemic risk measures

I Features

I Literature review

I Measures comparison

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Measuring systemic risk

I Not an easy task: we can’t even agree on a definition!

I Two (entangled) aspects:

What to measureWhat indicators we need to monitor? Howoften?

How to measure itConcerns the modelling framework necessary toestimate the indicators

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Features

Granularity

How much info can the measure provide on the system and itscomponents?

I System wide: most measures assess the systemic risk of theentire system

I Individual: provide info on single components of the system.Two complementary point of view

I How much a firm is exposed to global crisesI How much a firm is responsible for a global crises

I Pairwise: interaction between single componentsI Symmetric: effects of firm i default on firm j survival is equal

to the effects of j on iI Asymmetric: more flexible

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Features

Starting data

I Statistical/econometric tools applied to economicfundamentals

I Balance sheet and accounting infoI Common in studies performed by supervisory agenciesI ...but difficult to retrieve

I Market observables: CDS prices, bonds yields, options data.Benefits from market efficiency hypothesis:

I summarize opinion of market participants based on theinformation at their disposal

I are forward looking, i.e. they encompass market participantsexpectations about future events

I are easily available on a timely basisI ..but are exposed to model uncertainty

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Features

Additivity

The ability to allocate systemic risk to individual firms. Importantfor

I Firms: they can measure their exposure to global shocks

I Supervisors: necessary for setting up taxation/incentivesschemes to make firms responsible for the overall systemic risk

Herding behaviour

...a group of 100 institutions that act like clones can beas precarious and dangerous to the system as the largemerged identity...

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Features

A possible mechanism to allocate measures

I Tarashev, Borio, and Tsatsaronis [2009, 2010]I Based on game theory Shapley value for cooperative games

I Requires the knowledge of characteristic function θ of thegame that assigns an output value to any coalition

I super-additive: θ(S ∪ T ) ≥ θ(S) + θ(T ) for S ∩ T = ∅I monotonic: θ(S) ≥ θ(T ) for S ⊇ TI θ(∅) = 0

I The Shapley value for player x is calculated as the average ofthe marginal increase in the output that x can bring to everypossible coalition

I Many theoretical benefits among which: linearity in θ,additivity, fairness

I This attribution methodology can be applied to any linearcombination of systemic risk measures

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Literature review

I The field of research is relatively youngI There are no orthodox or canonical ways of doing thingsI Plenty of space for new approachesI Corpus of literature is rapidly growing

I Systemic risk measures arranged according to the modellingassumptions used

I Detailed reviews on the subjectI Markeloff, Warner, and Wollin [2011, 2012]I De Bandt and Hartmann [2000]I Malz [2013]

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Models review by category

Portfolio lossesThe system is seen as a portfolio of assets andsystemic risk is measured as extreme/conditionalscenarios

Network modelsFinancial entities are modelled as connected nodes ofdirected graphs and systemic risk is measured vianetwork fragility

Econometric indicatorsEconometric and statistical indicators as warningsignals for systemic risk crises

Default countingBased on multivariate distribution of defaults andsystemic risk is monitored via tail dependence

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Portfolio losses

Portfolio losses 1/2

CoVaR, Adrian and Brunnermeier [2011], Cao [2012]I For a generic variable Y , VaRq(Y ) = x if P {Y ≤ x} = q

I Conditional version of VaR, CoVaRq(Y |C) = x defined viaP {Y ≤ x |C} = q

I ∆CoVaRq(Y ,X ) is the difference between the CoVaRq(Y |X in distress)

and CoVaRq(Y |X at normal state)

1. ∆CoVaRq(X S ,X i ): analyze entire system return conditionedon i th entity state (attribution)

2. ∆CoVaRq(X i ,X S ): study entity i th conditioned on entiresystem state (exposure)

I Multi-CoVaR: similar but conditioned on multiple entities in distress atthe same time

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Portfolio losses

Portfolio losses 2/2

I MES, Acharya et al. [2010], assume system return can besplit via X S =

∑wi · Xi

I ES =∑

wi · E (X i∣∣X S ≤ VaRS

)I MESi = ∂ES

∂wi= E (X i

∣∣X S ≤ VaRS)

I Distress Insurance Premium, Huang et al. [2012]I Based on losses rather than returnsI DIP = EQ [L|L ≥ Lm] where Lm is a threshold for systemic

distressI ∂DIP

∂Li= EQ [Li |L ≥ Lm]

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Network models

I Systemic risk measuresI Number of links in and/or out of a given nodeI Average path lengthI Clustering coefficientsI Nodes degree distribution

I Selected literatureI Haldane (2009) uses cross-border networks to support the

assert that financial systems are becoming robust yet fragileI Espinoza-Vega and Sole (2011) perform scenario analysis on

banking system, domino effects via direct lending, fire salesand counter party exposures

I Billio et al. (2012) build a network connecting shadow and realbanking systems using Granger causality on indices and equities

I Thurner (2011) uses on an agent model that exhibits defaultclustering

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Econometric indicators

Econometric indicators 1/2

Co-Risk, Chan-Lau, Espinosa, Giesecke, and Sole [2009]

I pairwise quantile regression on CDS data:

CDSi = βjCDSj +∑

I The Y s cover:I Economy wide default risk: difference between daily returns

on the S&P 500 index and 3-month US treasury rateI Business cycle: slope of the US yield curveI Interbank default: one-year LIBOR spread over 1-year

constant maturity US treasury yieldI Liquidity: yield spread between 3-month collateral repo rate

and 3-month US treasury rateI Risk appetite: implied volatility index VIX

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Econometric indicators

Econometric indicators 2/2

PCA, principal component analysis, Billio, Getmansky, Lo, andPelizzon [2012] and Kritzman, Li, Page, and Rigobon [2010]

I statistical tool based on eigenvalue decomposition of thecovariance matrix M of time series

I a system where few eigenvectors are responsible for most ofthe variance is seen as carrying an high degree of systemic risk

I absorption ratio (AR)

∑5i=1 σ

2i∑M

j=1 σ2j

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Default counting

Default counting 1/2

Segoviano and Goodhart [2009] and Radev [2012b]I JPoD = joint probability of system default

JPoD = P{Xi ≥ Ki , i = 1, · · · , n}

I ∆ CoJPoD = conditional JPoD

CoJPoDh =JPoD

P{Xh ≥ Kh}, ∆CoJPoDh = CoJPoDh−JPoDh

I SFM = probability at least 2 defaults

SFM = P{Xi ≥ Ki ,Xj ≥ Kj , i 6= j}I BSI = expected number of defaults given at least one occurred

∑ni=1 P{Xi ≥ Ki}

1− P{X1 < K1, · · · ,Xn < Kn}

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Default counting

Default counting 2/2

Segoviano and Goodhart [2009] and Radev [2012b]

I PAOj = probability at least another entity defaults given jdefault

I System PAO = probability at least another entity defaultsgiven one default occurred

system PAO =P{Nd ≥ 2}P{Nd ≥ 1}

I PNEDn(i) = P{at least n entities default | entity i defaulted}I DiDe{i ,j} = probability i defaults given j defaulted

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Default counting

A pictorial comparison when n = 2...I Comparison between four measures: JPoD, PAO, BSI and SFMI They sample the distributional space <n across different regions

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Default counting

...and when n = 3

I Now we can appreciate the difference between JPoD and SFMI The JPoD measure relies on a tiny corner of the distribution

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What about a break?

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Systemic riskCIMDO

CIMDO stability study

I Study of the behaviour of the methodology with respect tochanges in its inputs

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Systemic riskCIMDO

Introduction

I CIMDO stands for Consistent Information MultivariateDensity Optimizing, Segoviano [2006]

I Motivation:I Finding a multivariate distribution from marginal information is

an under-identified mathematical problemI Relying on parametric distribution can impose arbitrary

restrictions on the solutionI CIMDO limits the impact of the choice of the parametric

family by using it only as a Bayesian prior

I Selected applicationsI Used in many official banking stability reports as well as in

several papers from both the academia and the industryI Jin and De Simone [2013] used it as a building block toward a

dynamic t-copula model

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Systemic riskCIMDO

Methodology

Inputs and cross entropy

1. Individual default probabilities PoDm

2. Historical default thresholds Km (Merton style)

3. Prior multivariate density q

The output is a multivariate density p (posterior) that is as close aspossible to q as measured via the Kullback cross-entropy function

C (p, q) =

p(x) · ln[p(x)

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Systemic riskCIMDO

Methodology

Mathematical formulation

Minimize: L(p, µ, λ) = C(p, q) + µ

[∫<n

p(x)dx− 1

n∑m=1

[∫<n

p(x) · χmd (x)dx− PoDm

]where χm

d (x) = 1⇔ xm ∈ [Km,∞), 0 otherwise.

∇L(p, µ, λ) = 0

p(x) = q(x) · exp

[−1− µ−

n∑m=1

λmχmd (x)

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Systemic riskCIMDO

Methodology

Pros and cons

I The goodI Elegance and simplicityI Model agnostic

I The badI Computational burden: O(2n)I Limit on the choices of priors p

I The uglyI Radev [2012b] showed default

independence is transferred to posteriorif prior is Normal and Σ = I

←− He is not Radev. We have no reason to assume

he is ugly

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Systemic riskCIMDO

Methodology

Independence extended

Radev’s result can be extended by relaxing the normal assumption:

Default/survival events are independent under the prior

Default/survival events are independent under the posterior

Sketch of the ⇒ proof

1. The prior density q can be factorized into product of marginals across thedefault/survival area thanks to the independence assumption

2. Any integral on a default/survival area can be split into sub-integralswhere the posterior density becomes the product of a constant times theprior density

3. Make use of the CIMDO constraints

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Systemic riskCIMDO

Stability study

Strategy

Sensitivity analysis

I Distributions: elliptical (t-Student, Normal), Archimedeancopulas (Clayton, Frank, Gumbel)

I Measures: JPoD, BSI, SFM, PAO(Segoviano and Goodhart [2009], Huang [1992], Radev [2012a])

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Systemic riskCIMDO

Stability study

Prior’s impact

Family issues Parametrization

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Systemic riskCIMDO

Stability study

CIMDO probability inputs study

I Default probabilities PoD

I Default thresholds KI Fair comparison:

multiplicative bump ω

Bumped PoDi = ω · PoDi

Bumped Ki = 1−Φ−1i (ω · HistPoDi )

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Systemic riskCIMDO

Stability study

Conclusions

I The choices around theprior are crucial

I prior ’s systemic riskmeasures are excellentproxies for posterior ’sones

I Inputs importance order

1. Parametric dependenceand marginal PoD

2. Copula choice anddefault thresholds K

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Systemic riskInfectious defaults with immunization

Infectious defaults with immunization

I A new contagion model inspired by Davis and Lo [2001]

I High tractability even for heterogeneous case

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Previous works in the area

Davis and Lo and extensions

I Model by Davis and Lo [2001]

I Based on n2 independent Bernoulli’s variables

Zi = Xi + (1− Xi )[1−

∏j 6=i (1− XjYi,j )

]I Xi drives idiosyncratic default, Yi,j infection attempt (j → i)I Results for the distribution of Gn =

∑i Zi available only in the

homogeneous case

I Few extensions

I Sakata et al. [2007]: positive recovery spillageI Cousin et al. [2013]: multiple time step, generalized trigger for

contagion, high level of abstractionI Both require strict assumptions in order to get usable results

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Previous works in the area

ProblemTwo (equally unusable) extremes:

1. Generic but slow versions of the models (simulation-based 2n2)

2. Analytical results only for homogenous portfolios

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The new model

Description

I Main differences from past contagion models:

1. infection from defaulting names to the entire system2. immunization from infections

I Based on 3n independent Bernoulli’s variables

Zi = Xi + (1− Xi ) · (1− Ui ) ·

1−∏i 6=j

(1− Xj · Vj )

I Five parameters per name:

I P[Xi = 1] = pi , P[Ui = 1] = ui , P[Vi = 1] = vi

I LGDi : di for idiosyncratic default, ci for infection

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The new model

Marginals

Given any subset of names A, then the probability of an infectionstarting in A is given by

1−∏j∈A

(1− pj · vj )

Marginal Let pi := P{Zi = 1}

pi = pi + (1− pi ) · (1− ui ) · I{1,··· ,i−1,i+1,··· ,n}

Expected loss LGDi = pi · di + (pi − pi ) · ci

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The new model

Joint and conditional distribution

I Given any two subset of names A and B such that A ∩ B = ∅, letP(A,B) represent the probability that all names in A default and allnames in B survive

I We have

ΠA(bd) · (1− IC ) · ΠB (1− p) +

P(A,B) =[∑mA

∑mA−hk=0 Θh,k

A (id , ps, bd)]· (1− IC ) · ΠB (us) +[∑mA

h=0 ΛhA(p, ps)

]· IC · ΠB (us)

where ps = (1− p) · (1− u), us = (1− p) · u, bd = p · (1− v) andid = p · v and where

ΛhA(x , y) = xt · Λh−1

A\{t}(x , y) + yt · ΛhA\{t}(x , y)

Θh,kA (x , y , z) = xt ·Θh−1,k

A\{t}(x , y , z)+ yt ·Θh,k−1A\{t}(x , y , z)+ zt ·Θh,k

A\{t}(x , y , z)

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The new model

Portfolio loss distribution

I Let Ln represent portfolio losses (LIn idiosyncratic, LC

contagion-driven) and let LRn be the amount of potential

losses in an uncontaminated world

αn(h, k) := P{LIn = h, LC

n = 0, LRn = k}

βn(h, k) := P{LIn = h, LC

n = k , LRn = 0}

P{Ln = h} =∑

k βn(k , h − k) +∑

k αn(h, k)

I Calculate α and β by adding one name at the time.Similar toAndersen et al. [2003] for obtaining convolution of conditionalmarginal probability of defaults in CID modelsP{Ln+1 = h

∣∣V } = P{Ln = h∣∣V } · (1− pV

j ) + P{Ln = h − dj

∣∣V } · pVj

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The new model

Efficient algorithm for portfolio lossesRecursive relationships (adding name j)

(1− pj ) · uj · αn(h, k) +αn+1(h, k) = (1− pj ) · (1− uj ) · αn(h, k − cj ) +

pj · (1− vj ) · αn(h − dj , k)

(1− pj ) · uj · βn(h, k) + pj · βn(h − dj , k) +βn+1(h, k) = (1− pj ) · (1− uj ) · βn(h, k − cj ) +

pj · vj · αn(h − dj , k)

Boundary conditions: α0(0, 0) = 1, α0(i , j) = 0, β0(i , j) = 0

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Application to CDO pricing

CDO structure and base approach

I OFG ρ is for CDOs what Black-Scholes σ isfor options

I Base ρ approach

I V (att, det) = V (0, det)− V (0, att)I One ρ per seniority: correlation skewI ρ for 3% detach calibrated from 0-3%

tranche priceI ρ for 6%, from 3-6% price...and so onI Interpolation and extrapolation

needed for non-standard tranches

I Need to reduce degree of freedom for the

contagion model

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OFG: conditional probability of default

Conditional (y -axis) vs. marginal (x-axis) probability of default.

The blues lines correspond to V = −1.5 while the red ones to

V = 1.5. Lines are obtained with increasing values of correlation

ρ (low for lines closer to the diagonal, high for external ones).

Conditional probability of default vs. the value of the common

factor V on the x-axis. The gradient of the curves increases as

the value of the correlation ρ is increased. The marginal

probability of default used is 30%

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OFG: loss distribution as a function of ρ

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Simplified model

I Let pi := P{Zi = 1}I Refined assumptions:

I Bigger infection rate for unexpected defaults: vi = 1% · (1− pi )I A single parameter ω controls the importance of contagion

(ω = 0 independence case, ω → 1 high contagion)

pi = (1− ω) · pi

I Calibration strategy:I ui calibrated to solve marginal default probabilityI di , ci calibrated to match LGDi

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Portfolio and quotes description

I Underlying portfolio:I N=100, CDS quotes for 3Y, 5Y, 7Y and 10YI Based upon ITraxx

I CDO quotes complicated and expensive:

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Smile, please

Monotonic, wider price range⇒ easier to calibrate

Skew in the ω space less pronounced⇒ arbitrages less likely

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Single name deltas

Magnitude Generally, risk smaller for mezzanine tranches

Convexity Less convexity, delta hedging strategies more effective

Shape Independent on ω level

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Systemic riskContagion Losses Ratio

A new systemic risk measure: CLR

I Defined in the context of contagion models

I Different from other (loss based) systemic risk measures

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A thought experiment

SettingThree systems with 4 names each:

System A System B System C

IPD LGD IPD LGD IPD LGD

First 3 names 50% 1$ 1% 1$ 0% 1$

Last name 50% 1$ 49.25% 4$ 50% 1$

Dep structure Independent Independent Survival hierarchy

Survival hierarchy

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What can we say about systemic risk 1/2

I EL not a good indicator (all systems have same EL = 2$)

I Loss distribution...

...better but...

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What can we say about systemic risk 2/2

The EL for systems B and C is achieved via a single catastrophicevent (default of the 4th name) with few key differences:

System B

I LGD of name 4 is huge (biggerthan the rest of the system)

I Other firms unaltered, no dominoeffect

I Easy to spot: look at relativesizes!

System C

I Nothing spectacular about defaultof the 4th name on its own

I It is the chain of defaults ittriggers that causes the damage!

I Detailed knowledge of dependencystructure is needed

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Introducing the CLR

CLR and CoCLR

I Major difference between systems B and C: the role played bycontagion-driven losses

I Contagion losses ratio (CLR): ratio of infection-drivenlosses versus the total portfolio expected loss

CLR =E [LC

E [Ln]CoCLR =

E [LCn |Ln ≥ T ]

E [Ln|Ln ≥ T ]I Advantages:

I Percentage number (no need for normalization)I Intuitive: easy to understand/communicateI Simple to calculate

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Introducing the CLR

Measuring CLR - theory

I Define γn(h, k) as the probability of having h idiosyncraticlosses and k contagion-driven onesγn(h, k) = P{LI

n = h, LCn = k}

I We can use γn to describe useful quantities...I P{Ln = z} =

∑h γn(h, z − h)

I CLR =∑

k [k·∑

h γn(h,k)]∑z z·[

∑h γn(h,z−h)]

I CoCLR =∑

k [k·∑

h≥T−k γn(h,k)]∑z≥T z·[

∑h γn(h,z−h)]

I ...or to create special effects!

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Introducing the CLR

Measuring CLR - practice

I In Davis and Lo [2001]

γn(h, k) = Cnh+k ·Ch+k

h ·ph(1−p)n−h[1−(1−q)h]k (1−q)h[n−(h+k)]

I In Sakata et al. [2007]

γn(h, k) =∑

h+kCh+kh C

n−(h+k)m pn−k−m·

(1− p)k+m(1− q)m(n−k−m)·(1− q′)h(k+m)

[1− (1− q)n−k−m

]k ·[1− (1− q′)k+m

]n−(h+k+m)

I In the contagion model introduced earlier

γn(h, k) = βn(h, k) + δk,0

αn(h, i)

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Introducing the CLR

Is CLR really adding something new?

I Davis and Lo [2001] modelI 15 namesI p idiosyncratic defaultI q pairwise contagion

I Both BSI and DIP follow ELclosely - little info added

I CLR offers a freshperspective

I Unlike others, decreasingin p

I Quantitatively andqualitatively different

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Application to a banking system

An application to fictional banking systemA fictional banking system of 10 banks divided in 4 types

Safe old style banks, big size, small idiosyncratic pd, very infective

Risky investments banks, medium size, very high idiosyncratic pd,small infection rate

Local regional banks, small size, small idiosyncratic pd, noimmunization

Central bank, zero LGD, 1% idiosyncratic pd, catastrophic infection

Type (num) p u v d c

Safe (3) 10 80 90 5 6

Risky (3) 70 40 10 3 4

Local (3) 20 0 1 1 2

Central (1) 1 100 100 0 0

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Comparison

CLR is based on a different information set than other measures

I Default counting : BSI (Segoviano and Goodhart [2009])

I Loss based : DIP (Huang et al. [2012])

They react differently to the presence of contagion events

Measure No contagion With contagion % increase

BSI 3.34 4.40 6.85%

DIP 12.26 18.25 18.76%

CLR 0% 31% 50.00%

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Regulator’s jobI What are the most effective initiatives in order to reduce systemic risk?

I Obvious approach: move system towards independence (increasedefenses, weaken infectivity)

I A less obvious strategy...

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Systemic riskBibliography

Selected resources I

V. Acharya, L. Pedersen, T. Philippon, and M. Richardson. Measuring systemic risk.NYU Working Paper, 2010.

T. Adrian and M. Brunnermeier. Covar. Technical report, National Bureau ofEconomic Research, Inc, 2011.

L. Andersen, J. Sidenius, and S. Basu. All your hedges in one basket. Risk Magazine,16(11):67–72, 2003.

M. Billio, M. Getmansky, A. Lo, and L. Pelizzon. Econometric measures ofconnectedness and systemic risk in the finance and insurance sectors. Journal ofFinancial Economics, 104(3):535–559, 2012.

Z. Cao. Multi-covar and shapley value: A systemic risk measure. Technical report,2012.

J. Chan-Lau, M. Espinosa, K. Giesecke, and J. Sole. Assessing the systemicimplications of financial linkages. IMF Global Financial Stability Report, 2, 2009.

A. Cousin, D. Dorobantu, and D. Rulliere. An extension of davis and lo’s contagionmodel. Quantitative Finance, 13(3):407–420, 2013.

M. Davis and V. Lo. Infectious defaults. Quantitative Finance, 1(4):382–387, 2001.

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M. Segoviano and C. Goodhart. Banking stability measures. IMF Working Papers,pages 1–54, 2009.

N. Tarashev, C. Borio, and K. Tsatsaronis. The systemic importance of financialinstitutions. BIS Quarterly Review, 75:87, 2009.

N. Tarashev, C. Borio, and K. Tsatsaronis. Attributing systemic risk to individualinstitutions. Technical report, Bank for International Settlements, 2010.

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