Some short elements on hedging credit derivatives

Author： Durand Philippe Jouanin Jean-Frédéric

E-ISSN： 1262-3318|11|issue|23-34

ISSN： 1292-8100

Source： ESAIM: Probability and Statistics, Vol.11, Iss.issue, 2007-03, pp. : 23-34

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Abstract

In practice, it is well known that hedging a derivative instrumentcan never be perfect. In the case of credit derivatives (e.g.synthetic CDO tranche products), a trader will have to face somespecific difficulties. The first one is the inconsistence betweenmost of the existing pricing models, where the risk is theoccurrence of defaults, and the real hedging strategy, where thetrader will protect his portfolio against small CDS spreadmovements. The second one, which is the main subject of thispaper, is the consequence of a wrong estimation of some parametersspecific to credit derivatives such as recovery rates orcorrelation coefficients. We find here an approximation of thedistribution under the historical probability of the final Profit Loss of a portfolio hedged with wrong estimations of theseparameters. In particular, it will depend on a ratio between thesquare root of the historical default probability and therisk-neutral default probability. This result is quite general andnot specific to a given pricing model.