Synthetic CDOs: Industry Trends in Analytical and Modeling Techniques

1. Synthetic CDOs: Industry Trends in Analytical and Modeling Techniques By: Lawrence Dunnlawrence.dunn@riskmetrics.com 1-212-981-1060

2. Synthetic CDOs: Reasons for Popularity • Quick Valuations & Sensitivities • Transparency: no complicated waterfalls • Liquidity: will be further fueled by single tranche synthetics and tranched Trac-x and IBoxx indices • No need to place full structures

3. Modeling Synthetic CDOs • Conditional independence technique • No complicated waterfall • A few simplifying assumptions • Uses market observations • Results in explicit, quick-to-compute expressions for the mark-to-market value of synthetics

4. Modeling Synthetic CDOs • Model Inputs and Outputs

5. Modeling Synthetic CDOs • Model Inputs and Outputs

6. Modeling Synthetic CDOs • Model Inputs and Outputs

7. Modeling Synthetic CDOs • Model Inputs and Outputs

8. Modeling Synthetic CDOs • Model Inputs and Outputs

9. Modeling Synthetic CDOs • Model Inputs and Outputs

10. Model Features and Practical Uses • Fast – seconds, not minutes/hours • Accurate – no simulation error • Practical Uses for Valuations • Marking books • Deciding fair bid/offer • Practical Uses for Sensitivities • Investors – tailor credit views • Dealers – manage book, offer single tranches

11. Modeling Synthetic CDOs • Implications of Synthetic Model • Industry Standard Model – Universal Language Between Dealers and Investors • The Black-Scholes of the structured credit market • Implied Correlation • Sensitivities (the Greeks) • Influence on Cash Flow CDO Valuation • Pull to True Monte Carlo • Consistency Across Names and Correlations • Boost Primary and Secondary Markets

12. Methodology Overview • For each tranche: MTM = Exp(premium) – Exp(loss) Use collateral info to model the losses Exp(loss) ~ directly from loss distribution Exp(premium) ~ spread x remaining notional on each pay date ~ remaining notional is function of loss distribution

13. Methodology Overview – loss distribution • Structural 1-factor correlated default model • For each obligor j: • Asset value modeled as a random variable that’s a function of a market factor variable, an idiosyncratic variable, and correlation:where default signaled by Zj dipping under threshold aj • To get aj, start with term structure of CDS spreads • Derive one hazard rate per CDS spread • Calculate the obligor’s probability of default for a given payment date • Notice that if we fix the value of Z, then we can rewrite Zj falling below aj in terms of ej dipping below a function of aj, w, and the fixed z

14. Methodology Overview – loss distribution • For each obligor j (cont’d): • That relationship allows us to get the conditional default probability of the obligor • Using probability generating functions, generating functions for loss, convolution, and FFT, you can derive p(k|z), the conditional loss probability; specifically the probability of losing k units of base loss • Integrate over all values of z to turn your conditional loss probability into an unconditional loss probability p(k) • Finally these p(k) get you Exp(Loss)

15. Trac-X NA IG -- March 12, 2004Index=70; Rec=40%; EL=3.4%

16. Trac-X NA IG -- March 12, 2004Index=70; Rec=40%; EL=3.4%

17. Trac-X NA IG -- March 12, 2004Index=70; Rec=40%; EL=3.4%

18. Trac-X NA IG, 0-3% trancheMarch 12, 2004

19. Trac-X NA IG, 3-7% trancheMarch 12, 2004

20. Trac-X NA IG, 7-10% trancheMarch 12, 2004

21. Trac-X NA IG, 10-15% trancheMarch 12, 2004

22. Trac-X NA IG, 15-30% trancheMarch 12, 2004

23. Compound correlation skew

24. Base correlations are more smooth.

25. Summary • Quick valuation of synthetics and other reasons for their popularity • Conditional independence technique • Model inputs and outputs • Features and practical uses • Implications to marketplace • Methodology overview • Interesting Case: NA IG Trac-x