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Some short elements on hedging credit derivatives

Published online by Cambridge University Press:  01 March 2007

Philippe Durand  and
Jean-Frédéric Jouanin
Philippe Durand
Affiliation:
Natixis, 115 rue Montmartre, F-75002 Paris, France; philippe.durand@polytechnique.org; jean-frederic.jouanin@ponts.org
Jean-Frédéric Jouanin
Affiliation:
Natixis, 115 rue Montmartre, F-75002 Paris, France; philippe.durand@polytechnique.org; jean-frederic.jouanin@ponts.org
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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.

Keywords

Credit derivativeshedgingrobustness.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 11: Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthdaySpecial Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday , June 2007 , pp. 23 - 34
Copyright
© EDP Sciences, SMAI, 2007

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References

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