afgap prmia– april, 5th 2012 -1- the impact of funding liquidity on market products valuation a...

AFGAP PRMIA– April, 5th 2012AFGAP PRMIA– April, 5th 2012

-1--1-

The impact of funding liquidity on market products valuation

A new paradigm?

Alexandre RamehAlexandre Rameh

The impact of funding liquidity on market products valuation

A new paradigm?

Alexandre RamehAlexandre Rameh

AFGAP PRMIA


-2-

A paradigm shift

Towards a new paradigm: How risk free are the sovereign bonds? How liquid is the interbank money market? How homogeneous are the major banks short-term funding costs? How liquid are off-shore currencies? How important is the collateralization impact on derivatives pricing? How accurate are models assumptions?


-3-

Agenda

A paradigm shift Credit Risk Funding Liquidity Risk Collateralization of market products

Funding a collateralized deal From a market point of view The real life The risk-oriented approach From an ALM point of view

Assessment of the liquidity adjustment One IRS: the stand alone liquidity adjustment Two IRS: the marginal liquidity adjustment A book of OTC… The approach challenges conventional wisdom


-4-

Towards a defaultable sovereign debt

The old paradigm: The sovereign bonds rates of return were considered as Risk-Free

The government can perpetually increase its taxation rate The government can increase its debt nominal

High discrepancy

between sovereign

funding costs


-5-

Towards costly interbank liquidity

The old paradigm : The interbank short-term funding liquidity is infinite (~“cost-free”)

The BOR-OIS spreads term structure was flat and close to zero Swap rates from different tenors were quite similar

High funding liquidity

premiums between

different Libor € tenors

Libor - OIS


-6-

Towards an heterogeneous interbank market

The old paradigm : The interbank short-term funding costs were considered as stable within the panel

banks The contributions were in a few bps range BOR term-structure was a good proxy for any bank Short-Term funding cost

High discrepancy between panel

banks short-term funding costs

Libor € 3Mth Panel Banks contributions spreads (%)

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Jan-

06

Mar

-06

May

-06

Jul-0

6

Sep

-06

Nov

-06

Jan-

07

Mar

-07

May

-07

Jul-0

7

Sep

-07

Nov

-07

Jan-

08

Mar

-08

May

-08

Jul-0

8

Sep

-08

Nov

-08

Jan-

09

Mar

-09

May

-09

Jul-0

9

Sep

-09

Nov

-09

Jan-

10

Mar

-10

May

-10

Jul-1

0

Sep

-10

Nov

-10

Jan-

11

Mar

-11

May

-11

Jul-1

1

Sep

-11


-7-

Towards liquidity pricing

The old paradigm: The interest rate Zero-Coupon curve was used as the funding curve of any bank and

was calibrated on: Libor quotes for the ST part of the curve Swap (VS 3Mth) quotes for the MLT part of the curve

Funding liquidity premium

Different swap curves depending on the tenor rate

+

The unsecured funding curve is different from one bank to

the other

+

Many curves depending on the collateral for secured

trades


The new paradigm

-8-

Consequences: Sovereign bonds are not risk-free anymore => Reliance on interest rate

derivatives markets to benchmark long-term interest rates Funding (even short-term) is costly, this cost is different from one bank to the

other and resilience over time is questionable => Increasing cost to secure funding on long term horizons

Assuming no reliance on the Central Bank and illiquid credit lines markets, the funding liquidity risk can only be hedged through term funding

Above points should be taken into account when pricing market products: The BOR-OIS spread has been addressed in different academic papers The Bank funding liquidity costs term structure VS the 3Mth curve should be

taken into account

“How to include funding liquidity in collateralized market products valuation?”

Knowing that sometimes you cannot borrow, no matter the price…


-9-

Agenda





10Y Fix payer collateral path

-20%

-15%

-10%

-5%

0%

5%

10%

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121

Time (in months)

PV

(%

No

min

al)

10Y Fix payer collateral path

From a market point of view

The market assumptions concerning collateralized deals: The cost of funding the deal equals the Euribor 3Mth The collateral is remunerated on an EONIA basis

The cost of carry is equal to E3Mth-EONIA The collateralized deals cashflows should be discounted with an OIS curve

Paying the BOR-OIS spread The graph gives a

simulation path of the collateral

posted(i.e. Minus the

Present Value of the Fixed leg payer swap under the

perfect collateralization

assumption) for a 10Y ABB,

EURIBOR3M payer swap.

Receiving the BOR-OIS spread

-10-


Different Collateral Simulation Path

-70%

-60%

-50%

-40%

-30%

-20%

-10%

0%

10%

20%

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121

The real life

Different Posted Collateral Simulation Path:

-11-

(x N

omin

al)

The graph gives different simulation

paths of the collateral posted

(i.e. Minus the Present Value of the

Fixed leg payer swap under the

perfect collateralization

assumption) for a 10Y ABB,

EURIBOR3M payer swap.


Posted Collateral Simulation under different confidence intervals

-20%

-15%

-10%

-5%

0%

5%

10%

15%

Sep

-11

Dec

-11

Mar

-12

Jun-

12

Sep

-12

Dec

-12

Mar

-13

Jun-

13

Sep

-13

Dec

-13

Mar

-14

Jun-

14

Sep

-14

Dec

-14

Mar

-15

Jun-

15

Sep

-15

Dec

-15

Mar

-16

Jun-

16

Sep

-16

Dec

-16

Mar

-17

Jun-

17

Sep

-17

Dec

-17

Mar

-18

Jun-

18

Sep

-18

Dec

-18

Mar

-19

Jun-

19

Sep

-19

Dec

-19

Mar

-20

Jun-

20

Sep

-20

Dec

-20

Mar

-21

Jun-

21

Sep

-21

Quantile 10% Quantile 20% Quantile 30% Quantile 40% Quantile 50% Quantile 60% Quantile 70%

Quantile 80% Quantile 90%

The real life - 2

The risk for the bank is to be unable to fund the future margin calls at Euribor 3Mth (rollover risk) The only way to hedge funding liquidity risk is to term fund the position The collateral demand of a deal can potentially be infinite The collateral needs can only be term funded with a given confidence interval

The graph gives the forecast of the

Collateral at Risk with a given

confidence interval.

A €1bn 10y swap requires a €100mm liquidity reserve (at the 90% confidence

interval)

Liquidity buffer with a 90% confidence

interval

-12-

(x N

omin

al)


)(; sCaRMaxBufferLiquidity Ttst Liquidity Buffer under a 90% confidence interval

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121

Liquidity Buffer CaR(90%)

The risk-oriented approach

We will assume that the part of the buffer not

used as collateral is lent at 3 month Euribor

-13-

(x N

omin

al)

Principal to be Term Funded for €1bn Fixed Payer 10Y swap

Maturity 1Y 2Y 3Y 4Y 5Y 6Y 7Y 8Y 9Y 10YPrincipal(in €mm) 0 7 7.8 6.4 13.4 5.5 14.7 9.4 13.7 14

EONIA??

~ + 2bps


-20%

-15%

-10%

-5%

0%

5%

10%

15%

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121

10Y Fix payer PV path Liquidity Buffer

The ALM point of view

There is a need to term fund the liquidity buffer in order to be able to fund the deal at Euribor 3Mth

Consequently, the funding liquidity costs against the 3Mth curve should be taken into account

As two banks have different funding liquidity premiums, their prices will not be the same!!

The cost of carrying the deal is much greater once the funding liquidity

position is hedged

Paying the BOR-OIS spread

Receiving the BOR-OIS spread

Bank funding liquidity premium

-14-

(x N

omin

al)


-15-

Agenda





CaR (90%)

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

Sep-1

1

Jan-

12

May

-12

Sep-1

2

Jan-

13

May

-13

Sep-1

3

Jan-

14

May

-14

Sep-1

4

Jan-

15

May

-15

Sep-1

5

Jan-

16

May

-16

Sep-1

6

Jan-

17

May

-17

Sep-1

7

Jan-

18

May

-18

Sep-1

8

Jan-

19

May

-19

Sep-1

9

Jan-

20

May

-20

Sep-2

0

Jan-

21

May

-21

Sep-2

1

10Y fixed receiver 10Y fixed payer

The stand alone liquidity adjustment

We take the example of a 10Y Fixed leg payer/receiver interest rate swap: We assess the Collateral at Risk (CaR) with a certain confidence interval (90%)

-16-

Asymmetry between fixed payer and

receiver

Swap rate

= 2.4%


The stand alone liquidity adjustment - 2

From the CaR forecast: We assess the liquidity buffer We assess this buffer Present Value Dividing by the Swap Level, we have a liquidity spread equivalent

-17-

On the pricing date, we approximate the funding liquidity premium term structures of bank A, B, C and D with a logarithm function:

)ln()(bsasl

We give the four banks funding liquidity premium parameters:

From which we derive the four banks corresponding spreads (i.e. the buffer PV/Swap level):

Bank A B C D

Fixed leg payer adjustment spread (bps)

3.1 6.3 9.4 12.5

Fixed leg receiver adjustment spread (bps)

7.22 14.4 21.5 28.7

Bank A B C D

a (bps) 35 70 105 140

b 10 20 30 40

Average premium (bps)

50 100 150 200


The marginal liquidity adjustment

We now deal with two swaps: IRS VS BOR 3 months (5Y and 10Y)

We show the stand alone CaR:

-18-

CaR (90%)

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

Sep-1

1

Jan-

12

May

-12

Sep-1

2

Jan-

13

May

-13

Sep-1

3

Jan-

14

May

-14

Sep-1

4

Jan-

15

May

-15

Sep-1

5

Jan-

16

May

-16

Sep-1

6

Jan-

17

May

-17

Sep-1

7

Jan-

18

May

-18

Sep-1

8

Jan-

19

May

-19

Sep-1

9

Jan-

20

May

-20

Sep-2

0

Jan-

21

May

-21

Sep-2

1

10Y fixed receiver 10Y fixed payer 5Y fixed payer 5Y fixed receiver


Marginal CaR(90%)

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

Sep-1

1

Jan-

12

May

-12

Sep-1

2

Jan-

13

May

-13

Sep-1

3

Jan-

14

May

-14

Sep-1

4

Jan-

15

May

-15

Sep-1

5

Jan-

16

May

-16

Sep-1

6

Jan-

17

May

-17

Sep-1

7

Jan-

18

May

-18

Sep-1

8

Jan-

19

May

-19

Sep-1

9

Jan-

20

May

-20

Sep-2

0

Jan-

21

May

-21

Sep-2

1

10Y fix payer 10Y fix payer + isolated 5Y fix payer

10Y fix payer + isolated 5Y floating payer 10Y fix payer + marginal 5Y fix payer

10Y fix payer + marginal 5Y floating payer

The marginal liquidity adjustment - 2

Let us assume there is only one fixed payer 10Y swap in the book and that we want to add a second deal:

We want to show the marginal effect when entering a fixed payer/receiver 5Y swap

-19-

5Y floating payer has a negative marginal impact because it

mitigates the directional position of

the collateralized book

5Y fixed payer marginal and isolated contributions are the

same


-20-

A book of OTC…

We will compute collateral needs from the net MtM Book value (equivalent to LCH practice)

It is interesting to stress that this collateral could be something else than € cash

For a Cross Currency Swap, the volatility of the exchange rate leads to a more important funding liquidity effect:

-80,00%

-60,00%

-40,00%

-20,00%

0,00%

20,00%

40,00%

60,00%

80,00%

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101

105

109

113

117

121

The methodology can be generalized to a book of OTC with different underlying market products The collateral needs will be assessed on the whole book One deal will have a marginal liquidity adjustment depending on the book

structure

Funding liquidity effect when synthesizing currency A borrowing currency B and entering a Cross Currency Swap

Collateralization in currency A or B? 20% buffer size for a 5y EURUSD CCS

~25bps annually buffer cost

CSA OTC with negative PVs

Collateral received

LIABILITIESASSETS

CSA OTC with positive PVs

Collateral

posted


The approach challenges conventional wisdom

“Received collateral can be used to fund the posted collateral” That’s why we assess the net collateral demand of a book

(posted – received) taking into account the correlation between different market products

“One can sell the position if the liquidity demand is too high” This is equivalent to selling the position at the worst time, when

the PV is very negative

-21-


“Collateralization mitigates the deal cash flows so that the funding requirement is lower for

collateralized trades than for uncollateralized ones”

This is true if the spot price follows the forwards (on average) The problem is precisely the impact of a market shift on the deal

cashflows Collateralization forces to immediately fund the Value coming

from a market move

The approach challenges conventional wisdom - 2

-22-

Expected Swap CF without collateralization

Expected Swap CF without collateralization

Uncollateralized IRS CF to be added after a market shift

Collateralized IRS CF to be added after a market shift

Collat Market Shift


Collateral Funding is also anAsset & Liability Management issue

The management consequences concern both: The management of the funding position of Fixed Income activities, The management of the funding adjustment for Interest Rate Swaps used to hedge Interest

Rate Risk. The collateral needs should be computed at the book level, consequently:

Management consequences

The deal price depends on:

1°/ The bank’s funding curve

2°/ The bank’s funding liquidity policy

3°/ The bank’s book structure

This approach can be generalized to other products: Synthetic funding of off-shore currencies with collateralized CCS, Delta-hedging of an equity option…

Despite the price of the hedging strategy, the funding liquidity hedging strategy should be initiated at inception of the deal…


-24-

Take Away From This Presentation

Funding Risk needs to be considered in managing and pricing derivatives, be they collateralized or not

This requires modifying the usual method that consists in spreading discount rates, and calls for building up a specific liquidity buffer…

… whose cost should be considered at deal level, or as a reserve-like mechanism

Definitely, there is no longer single “market value” since it depends on each bank funding cost, funding policy and book composition


-25-

Thank you…

Q & A

afgap prmia– april, 5th 2012 -1- the impact of funding liquidity on market products valuation a...

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