model risk & illiquidity

8/7/2019 Model Risk & Illiquidity

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Liquidity and ModelRisk

Pascal Gibart

Head of Model Validation

March 2010


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Liquidity & Model Risk March 2010

2Contents

03 Liquidity of the underlying

07 Distortion of Market Prices & Calibration

13 Liquidity trap25 Conclusion


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3Model and Model Risk

Model: framework to value complex derivative products

Model Risk: the risk that the model price is or will be in the future significantlydifferent from the market price (when such price is revealed) (Rebonato 2003: Theoryand Practice of Model Risk Management)

Models rely on a number of assumptionsmost models assume continuous prices

capacity to buy and sell unlimited amounts of underlying assettransaction costs (fees and bid ask) are negligible

Models use replication principlestatic replicationdynamic replication

hedge costs are associated with these replications


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4Liquidity can change


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5Liquidity of the underlying

What happens when bid-ask widen?Its quite easy to adjust quoted prices to clients in order to include initial hedge costs

10 bp for the delta, 0.5 volatility for the initial vega ..Add a shift to the correlation and other non-tradable model parameter

Make a price

How to integrate the impact of the change in liquidity over the life of a complex transaction?One could expect the subsequent hedges to be marginal compared to the size of the bookUnfortunately in some exotic books the trades tend to be more or less all the same!

Think of PRDC, Cancelable Range Accrual, Digital on CMS spreads, collar on stocksAs a result, the size of the book doesnt help anymore and the books will lose money on a daily

basis because of hedge costsAs the maturity of trades tends to lengthen in periods of low volatility, this creates positions that

will become hard to manage during the next crisis!


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6Liquidity of the underlying

What can be done?

Simulate future hedge costs and reserve them upfront

To be on the safe side one can also evaluate these costs in a stressed environment

Change the volatilities, the volatility of volatility in your calibrated models in order toestimate future hedge costs ( la Leland 1985)

whatever the approach it is not easy!


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7Distortion of Market Prices

Valuation Model are based on relative valuea model gives the price of a complex payoff as a function of the price of vanilla

We rely on the efficient market hypothesis to conduct relative value analysis

When liquidity disappears this nice market feature is not necessarily trueanymore

LTCM used to buy Off-the-Run long dated Treasuries and sell the On-the-Runequivalent Treasuries for a few basis points pick up

Looks like a very low risk strategy. Can yield of equivalent bonds (30-year against 29 year)really be apart by more than a few basis points?

Part of the back to normal or convergence type of tradesProblem: it takes time to lock in the profit and there is a hidden risk of squeeze in case of a

flight to liquidity and that is precisely what happened after the Russian default

arbitrage are very sensitive to liquidity issuesIn a Mark-to-Market environment such gap can even get wider when trader hit limits or funds

meet redemptions and need as a result to unwind the arbitrage


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8Distortion of Market Prices

2002 82.792003 70.852004 83.252005 99.042006 121.882007 146.522008 158.552009 115.5*

SX5E Dividend


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9Distortion of Market Prices and calibration

There is another tricky aspect behind such distortion of market prices when they arise incalibration instruments

Models will be calibrated based on these distorted prices and then prices of more complexproducts are affected in a non trivial manner!

10/09/2009 22/12/2008 20/06/2008 14/12/2007 05/12/20060,34% 0,28% 0,17% 0,14% 0,14%0,65% 0,67% 0,32% 0,26% 0,24%

CMS Spreads 10y-2Y compared to forward spread


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10Distortion of Market Prices and Calibration

Swap and CMS Spreads 10y-2y in 2009

-0,8%

-0,6%

-0,4%

-0,2%

0,0%

0,2%

0,4%

0,6%

0,8%

1,0%

1,2%

1,4%

1y 2y 3y 4y 5y 6y 7y 8y 9y 10y 11y 12y 13y 14y 15y 16y 17y 18y 19y 20y

CMS Spread Diff Swap


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Swap and CMS Spreads 10y-2y in 2006

-0,2%

-0,2%

-0,1%

-0,1%

0,0%

0,1%

0,1%

0,2%

0,2%

0,3%

0,3%

1y 2y 3y 4y 5y 6y 7y 8y 9y 10y 11y 12y 13y 14y 15y 16y 17y 18y 19y 20y

CMS Spread Diff Swap


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In some circumstances the models will not be able to calibrate market prices anymoreCDO Super Senior in Gaussian Copula

multi factor Interest Rate Model with smilecomplex copula for joint distribution of two currency pairs

Alternatively there might not be any market anymore for calibration instruments used by themodels

prices of deep out-of-the-money options

CMS spread options

More simple/robust models (Plan B) will be neededcalibrate more easily even if less precisely

use of historical estimates rather than implicit onesalways a good sanity check


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13Liquidity Trap

In some circumstances (a mix of market dynamic and position of the exoticcommunity) underlying markets can become too thin to sustain the hedgingrequirements of all exotic traders

This is a very difficult situation to identify particularly because historicalanalysis does not help

On top of that, there is no real natural interest in the market to take the oppositeposition: as a result the discrepancies tend to widen as exotic traders havenegative gamma positions


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14Liquidity Trap

A theoretical example

Short option position (Call) on a single stock for a large size

Large negative gamma position : when market moves up you need to buy the stock

This in return adds to the upside pressure on the stock

It may also turn out that you are not alone with this position !


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15Self Inflicted Liquidity Trap

Not so theoretical after all !


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16Liquidity Trap

It is (becoming) a regular situation in many markets

Volatility skew in Long Term FX options

Super senior CDO

CMS spreads in 2008

Whos next?


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17USD JPY Evolution of Risk Reversal

USD / JPY 10 Y Risk Reversal

-25

-20

-15

-10

-5

0

5

d - 9 9

d - 0 0

d - 0 1

d - 0 2

d - 0 3

d - 0 4

d - 0 5

d - 0 6

d - 0 7

d - 0 8

10d RR

25d RR


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18USD JPY Evolution of Risk Reversal

USD / JPY 5 Y Risk Reversal

-25

-20

-15

-10

-5

0

5

d - 9 9

d - 0 0

d - 0 1

d - 0 2

d - 0 3

d - 0 4

d - 0 5

d - 0 6

d - 0 7

d - 0 8

10d RR

25d RR


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19No offer on Super Senior Tranches .

CDX Main On the run (5Y) 30-100 Spread Mid

0

20

40

60

80

100

120

1 2 - s e p t - 0

5

0 9 - D e c - 2 0 0 5

1 0 - m a r s - 0 6

0 6 - j u i n - 0

6

3 1 - A u g - 2 0 0 6

2 9 - n o v - 0 6

2 8 - F e

b - 2 0 0 7

2 4 - M a y - 2 0 0 7

2 1 - A u g - 2 0 0 7

1 9 - n o v - 0 7

1 9 - F e

b - 2 0 0 8

1 5 - M a y - 2 0 0 8

1 2 - A u g - 2 0 0 8

0 7 - n o v - 0 8

0 9 - F e

b - 2 0 0 9

0 7 - M a y - 2 0 0 9

0 4 - A u g - 2 0 0 9


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20Risk Magazine Dec 2006: The Gamma Trap

Spread CMS10y- CMS2y EUR

-1

-0.5

0

0.5

1

1.5

2

2.5

j a n v . - 9

9

j a n v . - 0

0

j a n v . - 0

1

j a n v . - 0

2

j a n v . - 0

3

j a n v . - 0

j a n v . - 0

5

j a n v . - 0

6

j a n v . - 0

7

j a n v . - 0

8

j a n v . - 0

9


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21Liquidity Trap

Model are particularly poor to anticipate a change of regime

Generally they will not perform very well in such circumstances: prices of thereplication products will change abruptly in a way not predicted by the model andlosses will mount quickly

Some bet on a return to normal situation but it is a dangerous game since whatstarted the whole situation is very unlikely to disappear anytime soon and can indeedeasily get worse as more and more counterparties include the new market conditionsand adapt their hedge portfolio accordingly creating even more demand and pricedistortion on these hedges that every one needs


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22Liquidity Trap

What can be done?

Unfortunately the solution is not in better models but surely in better market riskmanagement

Stress analysis: reverse engineeringWhat would affect the price of my book?

What would make my hedge more costly?

At what point will my hedge strategy be constrained by the liquidity of the market? Am Ithe only one with this hedge strategy or are all my colleagues in the same situation?

Will their be a natural flow of new interest to take on this hedge if the price move issignificant?


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23Liquidity Trap

What can be done?

Try to find hedging transactions and market them to other customers, proprietary traders,hedge funds that do not run exotic books

Be the first one to shoot! You will lose some money but that may help you save a lot!

Reduce the size of your portfolio: this will maybe allow you to sustain big market moves

as with a bigger size you would have hit your hedging and risk constraints and dispose ofthe risk at the worse time


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24Liquidity Trap

From the risk department point of view

Use all the intelligence gathered by the FOHit ratios and other elements that can help imagine the overall size of deals in the marketAsk for market quotesEncourage trading in small size out of a complex product: it will be very instructive

Try as much as possible to use outside intelligenceUse market consensusUse prices observed trough the collateral agreementsSome old friend in another bank or client will tell you how much your bank is out of market on

some specific trades!


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25Conclusion

Dont take liquidity for granted !

Be preparedAlways think of a Plan B model that can be used in dire circumstances

Use this alternative model regularly as a sanity check

Look at what may go wrong if the hedges you rely upon suddenly become illiquid / unavailable

Anticipate market saturation before you have to compete for the hedgetransactions

The solution is probably not in better models but rather in better risk management

model risk & illiquidity

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