Optimal Static Hedging of Defaults in CDOs

by Andrea Petrelli of Credit Suisse,
Olivia Siu of Morgan Stanley,
Jun Zhang of Credit Suisse, and
Vivek Kapoor of UBS

April 2006

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.

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