Some short elements on hedging credit derivatives

Philippe Durand, Jean-Frédéric Jouanin
2007 E S A I M: Probability & Statistics  
In practice, it is well known that hedging a derivative instrument can never be perfect. In the case of credit derivatives (e.g. synthetic CDO tranche products), a trader will have to face some specific difficulties. The first one is the inconsistence between most of the existing pricing models, where the risk is the occurrence of defaults, and the real hedging strategy, where the trader will protect his portfolio against small CDS spread movements. The second one, which is the main subject of
more » ... he main subject of this paper, is the consequence of a wrong estimation of some parameters specific to credit derivatives such as recovery rates or correlation coefficients. We find here an approximation of the distribution under the historical probability of the final Profit & Loss of a portfolio hedged with wrong estimations of these parameters. In particular, it will depend on a ratio between the square root of the historical default probability and the risk-neutral default probability. This result is quite general and not specific to a given pricing model. Mathematics Subject Classification. 91B28. In the case of equity derivatives, this basic intuition was justified in El Karoui, Jeanblanc-Picqué and Shreve [4] . The authors show that the Black-Scholes pricing formula is robust with respect to a misspecification of the volatility. To be more specific, when a trader sells an option which he prices and replicates within a local volatility model 'à la Dupire' [3] (which includes the Black-Scholes case), if the option payoff is convex
doi:10.1051/ps:2007003 fatcat:e5g3exi56feobdhxh3ctpj3uea