wanted: mathematical models for financial weapons … · financial weapons of mass destruction. ......

Wim Schoutens, 23-10-2008 Eindhoven, The Netherlands - p. 1/23

WANTED: Mathematical Models forFinancial Weapons of Mass

Destruction.

Wim Schoutens - K.U.Leuven - [email protected]

http://www.schoutens.be

Outline

● Contents

Credit Risk

Models


Contents■ This talks overview some of the credit risk instruments currently in the

news.

■ Understanding these derivatives and the info they bring to us is essentialto understand the crisis.

■ Mathematical models to deal with these instruments are currently a majorline of research at EURANDOM.

■ The better your model, the better your insight, ...

■ You can’t solve the credit crunch crisis with it. The origin is essentiallygreediness, misuse of products and non transparency.BUT◆ at least you can better understand it◆ you can be better prepared to deal with it◆ it helps to set new regulations


Outline

Credit Risk

● Credit Risk Market

● Credit Market Players

● Credit Market Products

● Credit Default Swaps

● Credit Default Swaps: Philips

● Credit Default Swaps:

Lehman● Examples: Iceland BANKS

● Examples: Countries and

Benelux Banks● Credit Indices

● CDOs

● Collaterised Debt Obligation

(CDO)

● CDO Mechanisme

● Pricing Problems

Models


Credit Risk Market■ The credit market has seen an explosive growth the last decennium.

■ It is now around 60 trillion USD and is in size a multiple of the classicalequity market.


Outline

Credit Risk










● CDOs


(CDO)

● CDO Mechanisme


Models


Credit Market Players■ Over the last few years, participants’ profiles have evolved and diversified

along with the credit derivatives market itself.


Outline

Credit Risk










● CDOs


(CDO)

● CDO Mechanisme


Models


Credit Market Products■ Credit Default Swaps (CDS) are the most important credit derivatives.

■ Over the last few years, index products have gained significantly in volume.


Outline

Credit Risk










● CDOs


(CDO)

● CDO Mechanisme


Models


Credit Default Swaps■ Credit Default Swaps (CDSs) are instruments that provide the buyer an

insurance against the defaulting of a company (the reference entity) on itsdebt.


Outline

Credit Risk










● CDOs


(CDO)

● CDO Mechanisme


Models


Credit Default Swaps: Philips

20/09/0719/09/0820

30

40

50

60

70

80

90

100

110

date

cds

(bp)

Philips CDS evolution (last year)


Outline

Credit Risk










● CDOs


(CDO)

● CDO Mechanisme


Models


Credit Default Swaps: Lehman

25/sept/0715/sept/080

100

200

300

400

500

600

700

800

time

cds (

bp)

Lehman CDS evolution (last year)


Outline

Credit Risk










● CDOs


(CDO)

● CDO Mechanisme


Models


Examples: Iceland BANKS■ Recently Icelandic banks defaulted. They were already clearly in trouble

since beginning of the year.


Outline

Credit Risk










● CDOs


(CDO)

● CDO Mechanisme


Models


Examples: Countries and Benelux Banks

CDS 19-sep-08 26-sep-08. 3-oct-08. 10-oct-08 22-oct-08

ABN-Amro 133 159 161 114 76

BNP Paribas 81 89 67 63 60

Dexia 389 468 409 292 217

Fortis 185 641 259 108 72

ING 129 157 155 149 130

Glitnir 1276 1445 4555 - -

Kaupthing 1158 1344 3894 3385 -

Belgium 22 44 51 43 54

NL 10 26 30 29 35

Hungary 155 195 450 435 530


Outline

Credit Risk










● CDOs


(CDO)

● CDO Mechanisme


Models


Credit Indices■ Positions not just in one CDS are possible but can also be taken into full

indexes (cfr. AEX-index, BEL20, Dow Jones Industrial Average, ...)

■ The most known and liquid ones are: iTraxx and CDX.


Outline

Credit Risk










● CDOs


(CDO)

● CDO Mechanisme


Models


CDOs■ (Synthetic) Collateralized Credit Obligations (CDOs) are complex

multivariate credit risk derivatives.

■ A CDO transfers the credit risk on a reference portfolio (typically125 CDSs) of assets in a tranched way.


Outline

Credit Risk










● CDOs


(CDO)

● CDO Mechanisme


Models


Collaterised Debt Obligation (CDO)■ For example the situation on the 16th October 2008 for the iTraxx Europe

Main tranches (Series 10) for the 5 year structure is:

Tranche upfront running spread

[0% − 3%] 59.57 % 500 bp

[3% − 6%] 0 % 1086.58 bp

[6% − 9%] 0 % 576.66 bp

[9% − 12%] 0 % 288.12 bp

[12% − 22%] 0 % 115.99 bp

[22% − 100%] 0 % 41.89 bp


Outline

Credit Risk










● CDOs


(CDO)

● CDO Mechanisme


Models


CDO Mechanisme■ Each default among the 125 companies fills the "100 liter bath" with

60/125 = 0.48 liters of water.

■ You receive fee on the amount of your tranche that is not under water.

■ What does this mean : [3%-6%] is quoted 1086.58 bp on 5Y ?◆ You decide to bet 100 M EUR on this tranche: you sell protection.◆ You actually have not to come up with the money, it is just a bet ...◆ You receive per year 10.8658 M EUR until 5Y or until the 7th default in

the list of 125 companies.◆ If the 7th default occurs : the bath is filled with 7 × 0.48 = 3.36 liter and

you have to pay out 100M × 0.36/3 = 12 M EUR and will receive only0.88 × 10.8658 = 9.5620 M EUR per year.

◆ For each other default you have to pay out an additional100M × 0.48/3 = 16 M EURand your yearly fee payment is reduce by 1.7385 M EUR

◆ You do this until 5Y or until the 13th Default; you pay then 8M and then allyour 100 M is spent).

■ Your maximum profit over 5 Y (ignoring discount factors) : 54.329 M EUR.

■ Your maximum loss over 5 Y : 100 M EUR.


Outline

Credit Risk










● CDOs


(CDO)

● CDO Mechanisme


Models


Pricing Problems■ CDOs do not only exists out of CDSs from the iTraxx and CDX, but can

contain other "swap" instruments: other CDSs, tranches of CDOs,ABCDS, ...

■ Valuation is a very hard problem:◆ lots of dependency - correlation◆ extreme events◆ high volatile markets◆ not that super liquid markets◆ what about counterparty risk ?◆ domino effects - destabilization of financial markets

■ Risk management is even harder.

■ Positions need to be MtM.


Outline

Credit Risk

Models

● Crisis

● Normal Distribution


● Practice Models

● Crash Probability

● How Nervous is the Market ?

● Academic Models

● Conclusion


Crisis■ Over the past we have witnessed several other crisis: 1929, 1987, LTCM,

9/11, ...

■ In all these situations markets moved tremendously.

■ Quite often gains made over the preceding years were completely wipedout in a very short period of time.

■ Risk management limits were broken.

■ People were fired, companies went bankrupt, ...


Outline

Credit Risk

Models

● Crisis



● Practice Models



● Academic Models

● Conclusion


Normal Distribution■ Normal Distribution Normal(µ, σ2) on (−∞, +∞) :

f(x; µ, σ2) =1

√2πσ

exp

(

−(x − µ)2

2σ2

)

−10 −5 0 5 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

x

f(x)

Normal Distribution − effect of σ

Normal(0,1)Normal(0,2)Normal(0,3)


Outline

Credit Risk

Models

● Crisis



● Practice Models



● Academic Models

● Conclusion


Normal Distribution

σ probability freq. 16% vol. 25% vol.

1σ 0.68269 exceed once in 3 days ±1% ±1.5%

2σ 0.95450 exceed once per month ±2% ±3%

3σ 0.99730 exceed once per year ±3% ±4.5%

4σ 0.99994 exceed once per century ±4% ±6%


Outline

Credit Risk

Models

● Crisis



● Practice Models



● Academic Models

● Conclusion


Practice Models■ Shocks are hence very important, however most models do not

incorporate them:◆ Black-Scholes : based on Normal distribution and Brownian motion;◆ CDO models are based on Gaussian copula;◆ Black’s model for spread dynamics is again using Normal distribution

and Brownian motion;

■ How one can expect that models perform well in crisis times if crisisevents are not built in.

■ Jumps and heavy tails are important features in the modeling.

2.5 3 3.5 4 4.5 50

0.05

0.1

0.15

0.2

0.25Gamma tail (a=3, b=2) versus Gaussian tail with same mean and variance

x

f(x)

Gamma tailGaussian tail


Outline

Credit Risk

Models

● Crisis



● Practice Models



● Academic Models

● Conclusion


Crash Probability■ The ten largest relative down moves of the Dow Jones Industrial Average

over a fifty years period (1945-2008).

Date Closing logreturn Aver. freq. under Normal law (25% vol)

19-Oct-87 1738.74 -0.2563 once in 1053 years

UK : 100000 octillion

26-Oct-87 1793.93 -0.0838 once in 72503 years

15-Oct-08 8577.91 -0.0820 once in 41318 years

09-Oct-08 8579.19 -0.0762 once in 6068 years

27-Oct-97 7161.15 -0.0745 once in 3402 years

17-Sep-01 8920.7 -0.0740 once in 2914 years

29-Sep-08 10365.45 -0.0723 once in 1798 years

13-Oct-89 2569.26 -0.0716 once in 1405 years

08-Jan-88 1911.31 -0.0710 once in 1173 years

26-Sep-55 455.56 -0.0677 once in 448 years


Outline

Credit Risk

Models

● Crisis



● Practice Models



● Academic Models

● Conclusion


How Nervous is the Market ?■ The VIX (also called the ’fear’ index) gives an estimate of the volatility.


Outline

Credit Risk

Models

● Crisis



● Practice Models



● Academic Models

● Conclusion


Academic Models■ It is easy to criticize, but much more difficult to offer an valuable

alternative.

■ It is easy to write down a mathematical modeling incorporating: crashes,defaults, stochastic vol, long term dependency, tail dependency, dynamicspreads, non gaussian correlation, jumps, ...

■ Development and enhancement of models incorporating jumps andextreme events is a major research line at EURANDOM.

■ Last years we have for example developed models for CDS, CDO,ABS, vol, ...◆ based on more flexible distribution (incorporating crash scenarios,...);◆ using more sophisticated dependency structures;◆ with acceptable cpu times.


Outline

Credit Risk

Models

● Crisis



● Practice Models



● Academic Models

● Conclusion


Conclusion■ Consequences of more advanced models:

◆ typically they are slower;◆ trader’s have less intuition with parameters;◆ lead to higher capital reserves;◆ often no implied thinking (no perfect match with market);◆ no model is perfect;◆ there is always plenty of room for improvement.

■ QUESTION: What do we really want ?A popular, easy to use, wrong model for a short term partyoran unpopular, not that easy, a little bit less wrong model, to survive (a bitlonger) ?

CONTACT:Wim Schoutens (EURANDOM - K.U.Leuven)Celestijnenlaan 200 B, B-3001 Leuven, BelgiumEmail: [email protected] reports and more info on: www.schoutens.be


wanted: mathematical models for financial weapons … · financial weapons of mass destruction. ......

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