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Some short elements on hedging credit derivatives

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PDF/Soon/ps0657.pdf.url ESAIM: PS ESAIM: Probability and Statistics February 2007, Vol. 11, p. 23–34 www.edpsciences.org/ps DOI: 10.1051/ps:2007003 SOME SHORT ELEMENTS ON HEDGING CREDIT DERIVATIVES ∗ Philippe Durand1 and Jean-Fre´de´ric Jouanin1 Abstract. 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 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. Invited paper accepted September 2005. Introduction The widespread use of models for pricing exotic options introduces some new parameters that cannot always be calibrated on available market data, and therefore may induce some model risk. When selling a derivative instrument, the price of which depends on such a coefficient, a technique commonly used by traders is to give that unknown parameter a value that ensures a conservative price and keep this value along time to hedge themselves. This is for example the case for an equity derivative trader who does not precisely know the level of the volatility of one asset, but assumes that it will remain in some prescri

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