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Liquidity and ModelRisk
Pascal Gibart
Head of Model Validation
March 2010
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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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Liquidity & Model Risk March 2010
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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Liquidity & Model Risk March 2010
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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Liquidity & Model Risk March 2010
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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11Distortion of Market Prices and calibration
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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12Distortion of Market Prices and calibration
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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Liquidity & Model Risk March 2010
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