WANTED: Mathematical Models for Financial Weapons of Mass Destruction

Transcription

1 WANTED: Mathematical for Financial Weapons of Mass Destruction. Wim Schoutens - K.U.Leuven - wim@schoutens.be Wim Schoutens, Eindhoven, The Netherlands - p. 1/23

2 Contents 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 essential to understand the crisis. Mathematical models to deal with these instruments are currently a major line 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 essentially greediness, 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 Wim Schoutens, Eindhoven, The Netherlands - p. 2/23

3 Market Market Philips 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 classical equity market. Wim Schoutens, Eindhoven, The Netherlands - p. 3/23

4 Credit Market Players Over the last few years, participants profiles have evolved and diversified along with the credit derivatives market itself. Market Philips Wim Schoutens, Eindhoven, The Netherlands - p. 4/23

5 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 Market Philips Wim Schoutens, Eindhoven, The Netherlands - p. 5/23

6 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 its debt. Market Philips Wim Schoutens, Eindhoven, The Netherlands - p. 6/23

7 Credit Default Swaps: Philips 110 Philips CDS evolution (last year) Market Philips cds (bp) /09/08 date 20/09/07 Wim Schoutens, Eindhoven, The Netherlands - p. 7/23

8 Credit Default Swaps: 800 CDS evolution (last year) Market Philips cds (bp) /sept/08 time 25/sept/07 Wim Schoutens, Eindhoven, The Netherlands - p. 8/23

9 Examples: Iceland BANKS Recently Icelandic banks defaulted. They were already clearly in trouble since beginning of the year. Market Philips Wim Schoutens, Eindhoven, The Netherlands - p. 9/23

10 Examples: Countries and Benelux Ban CDS 19-sep sep oct oct oct-08 Market Philips ABN-Amro BNP Paribas Dexia Fortis ING Glitnir Kaupthing Belgium NL Hungary Wim Schoutens, Eindhoven, The Netherlands - p. 10/23

11 Credit Indices Market Philips 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. Wim Schoutens, Eindhoven, The Netherlands - p. 11/23

12 CDOs Market Philips (Synthetic) Collateralized Credit Obligations (CDOs) are complex multivariate credit risk derivatives. A CDO transfers the credit risk on a reference portfolio (typically 125 CDSs) of assets in a tranched way. Wim Schoutens, Eindhoven, The Netherlands - p. 12/23

13 Collaterised Debt Obligation Market Philips 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%] % 500 bp [3% 6%] 0 % bp [6% 9%] 0 % bp [9% 12%] 0 % bp [12% 22%] 0 % bp [22% 100%] 0 % bp Wim Schoutens, Eindhoven, The Netherlands - p. 13/23

14 CDO Mechanisme Market Philips 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 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 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 = 3.36 liter and you have to pay out 100M 0.36/3 = 12 M EUR and will receive only = M EUR per year. For each other default you have to pay out an additional 100M 0.48/3 = 16 M EUR and your yearly fee payment is reduce by M EUR You do this until 5Y or until the 13th Default; you pay then 8M and then a your 100 M is spent). Your maximum profit over 5 Y (ignoring discount factors) : M EUR. Your maximum loss over 5 Y : 100 M EUR. Wim Schoutens, Eindhoven, The Netherlands - p. 14/23

15 Pricing Problems Market Philips 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. Wim Schoutens, Eindhoven, The Netherlands - p. 15/23

16 Crisis Crisis Practice Crash Probability How Nervous is the Market? Academic Conclusion 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 wiped out in a very short period of time. Risk management limits were broken. People were fired, companies went bankrupt,... Wim Schoutens, Eindhoven, The Netherlands - p. 16/23

17 Normal Distribution Normal Distribution Normal(µ, σ 2 ) on (, + ) : Crisis Practice Crash Probability How Nervous is the Market? Academic Conclusion f(x; µ, σ 2 ) = 1 ) (x µ)2 exp ( 2πσ 2σ 2 Normal Distribution effect of σ Normal(0,1) Normal(0,2) Normal(0,3) f(x) x Wim Schoutens, Eindhoven, The Netherlands - p. 17/23

18 Normal Distribution Crisis Practice Crash Probability How Nervous is the Market? Academic Conclusion σ probability freq. 16% vol. 25% vol. 1σ exceed once in 3 days ±1% ±1.5% 2σ exceed once per month ±2% ±3% 3σ exceed once per year ±3% ±4.5% 4σ exceed once per century ±4% ±6% Wim Schoutens, Eindhoven, The Netherlands - p. 18/23

19 Practice Crisis Practice Crash Probability How Nervous is the Market? Academic Conclusion 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 crisis events are not built in. Jumps and heavy tails are important features in the modeling Gamma tail (a=3, b=2) versus Gaussian tail with same mean and variance Gamma tail Gaussian tail f(x) x Wim Schoutens, Eindhoven, The Netherlands - p. 19/23

20 Crash Probability Crisis Practice Crash Probability How Nervous is the Market? Academic Conclusion The ten largest relative down moves of the Dow Jones Industrial Average over a fifty years period ( ). Date Closing logreturn Aver. freq. under Normal law (25% vol) 19-Oct once in years UK : octillion 26-Oct once in years 15-Oct once in years 09-Oct once in 6068 years 27-Oct once in 3402 years 17-Sep once in 2914 years 29-Sep once in 1798 years 13-Oct once in 1405 years 08-Jan once in 1173 years 26-Sep once in 448 years Wim Schoutens, Eindhoven, The Netherlands - p. 20/23

21 How Nervous is the Market? The VIX (also called the fear index) gives an estimate of the volatility. Crisis Practice Crash Probability How Nervous is the Market? Academic Conclusion Wim Schoutens, Eindhoven, The Netherlands - p. 21/23

22 Academic Crisis Practice Crash Probability How Nervous is the Market? Academic Conclusion 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, dynamic spreads, non gaussian correlation, jumps,... Development and enhancement of models incorporating jumps and extreme 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. Wim Schoutens, Eindhoven, The Netherlands - p. 22/23

23 Conclusion Crisis Practice Crash Probability How Nervous is the Market? Academic 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 party or an unpopular, not that easy, a little bit less wrong model, to survive (a bit longer)? CONTACT: Wim Schoutens (EURANDOM - K.U.Leuven) Celestijnenlaan 200 B, B-3001 Leuven, Belgium wim@schoutens.be Technical reports and more info on: Wim Schoutens, Eindhoven, The Netherlands - p. 23/23