Synthetic CDOs: Industry Trends in Analytical and Modeling Techniques By: Lawrence Dunn

slide 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

slide 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

slide 4 Modeling Synthetic CDOs »Model Inputs and Outputs

slide 5 Modeling Synthetic CDOs »Model Inputs and Outputs

slide 6 Modeling Synthetic CDOs »Model Inputs and Outputs

slide 7 Modeling Synthetic CDOs »Model Inputs and Outputs

slide 8 Modeling Synthetic CDOs »Model Inputs and Outputs

slide 9 Modeling Synthetic CDOs »Model Inputs and Outputs

slide 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

slide 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

slide 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

slide 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 Z j dipping under threshold  j »To get  j, 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 Z j falling below  j in terms of  j dipping below a function of  j, , and the fixed z

slide 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)

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

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

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

slide 18 Trac-X NA IG, 0-3% tranche March 12, 2004

slide 19 Trac-X NA IG, 3-7% tranche March 12, 2004

slide 20 Trac-X NA IG, 7-10% tranche March 12, 2004

slide 21 Trac-X NA IG, 10-15% tranche March 12, 2004

slide 22 Trac-X NA IG, 15-30% tranche March 12, 2004

slide 23 Compound correlation skew

slide 24 Base correlations are more smooth.

slide 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