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