5. Gaussian Copula Model in Action Many sudden credit events occurring early Several credit events Few credit events Hedging simulation of [3-6%] long protection position, delta hedged only
19. The Toothpaste Tube Analogy Super Senior 22-100% Equity 0-3% 3-6% 6-9% Index [0-100%] 12-22% 9-12% Index = Sum of tranches [22-100%] = [0-100%] – [0-3%] – [3-6%] – [6-9%] – [9-12%] – [12-22%]
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22. Bespoke Tranches – Normalisation Methods If the portfolio is more risky then an equivalent tranche is more risky How to we adjust the correlation curve we use to account for this? Index portfolio Bespoke portfolio Expected loss Tranche
26. Index Correlation – off the run tranches Index rolls give us more maturity information detach maturity correlation CDX.5 CDX.6 CDX.7 CDX.8 CDX.5 CDX.6 CDX.7 CDX.8 CDX.5 CDX.6 CDX.7 CDX.8 5Y 7Y 10Y “ Base Correlation” Surface CDX.4 CDX.4 CDX.4
27. Index Correlation – HY/IG Different indices may provide complimentary information [15-30%] [25-35%] [10-15%] [15-25%] [7-10%] [10-15%] [3-7%] [0-10%] [0-3%] CDX HY CDX IG
28. Index Correlation – HY/IG (II) Test out your pricing method 3% 7% 10% 15% 30% IG HY 3% 35% 25% 15% 10% IG HY
29. Index Correlation – HY/IG (III) Obvious implications for Barbell portfolios [15-30%] [25-35%] [10-15%] [15-25%] [7-10%] [10-15%] [3-7%] [0-10%] [0-3%] CDX HY CDX IG
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32. The Challenges and Solutions Tranchelet pricing Bespoke Pricing Forward Starting Loss Surface Construction Tranche Options Enhanced Base Correlation Methods Implied Copula Approach Stochastic Intensity Models Dynamic Loss Models There is no one to one mapping in the above Tranche options pricing may be very sensitive to tranchelet pricing “ Exotic” CDOs
![A Decade of CDO Pricing World Congress on Computational Finance Jon Gregory [email_address] March 26 th 2007 trant: Cover Option 2](https://image.slidesharecdn.com/a-decade-of-cdo-pricing-4564/85/A-decade-of-CDO-pricing-1-320.jpg)
![Growth of Structured Credit Products Note: Notional excludes asset swaps Source: British Bankers Association Credit Derivatives Report 2006; Barclays Capital Credit Research 0 5 10 15 20 25 30 35 1996 1998 1999 2000 2001 2002 2003 2004 2006 2008E $ Trillion ,[object Object],Cash Flow Structured Finance CDOs Synthetic Balance Sheet CDOs; N th -to-Default Baskets Single Tranche CDOs; Managed CDOs; CDS Indices Bespoke Managed CDOs; Equity Default Swaps; Constant Maturity Default Swaps; Interest Rate Hybrids Options; Capital Structure Arbitrage; CDO 2 Synthetic Arbitrage CDOs Recovery Swaps; Dow Jones CDX/iTraxx Tranche Trades Leveraged super senior, CPPI and CPDO](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)