Optimal Static Hedging of Defaults in CDOs
by Andrea Petrelli of Credit Suisse,
Abstract: The optimal static hedging of a CDO tranche position with a portfolio of bonds that constitute the CDO reference pool is addressed here. The hedge ratio and tranche pricing that result in a fair bet on the average and minimum hedge error measures are found for synthetic CDO tranches, employing two default models (1) Reduced form Normal Copula; (2) Structural Variance-Gamma. The sensitivities of the break-even spread, optimal hedge ratios, and un-hedged risks to the underlying credits and the CDO structure are illustrated. The relationship between the no-default carry and residual default risks of hedged CDO tranches are illustrated. In the same framework hedging a bond with a CDS is also examined. The residual hedge error dependence on recovery uncertainty and deviation of bond price from par are shown.
Keywords: CDO, Hedging, Default, Carry, Expected Shortfall.