# Some short elements on hedging credit derivatives

Philippe Durand; Jean-Frédéric Jouanin

ESAIM: Probability and Statistics (2007)

- Volume: 11, page 23-34
- ISSN: 1292-8100

## Access Full Article

top## Abstract

top## How to cite

topDurand, Philippe, and Jouanin, Jean-Frédéric. "Some short elements on hedging credit derivatives." ESAIM: Probability and Statistics 11 (2007): 23-34. <http://eudml.org/doc/250117>.

@article{Durand2007,

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.
},

author = {Durand, Philippe, Jouanin, Jean-Frédéric},

journal = {ESAIM: Probability and Statistics},

keywords = {Credit derivatives; hedging; robustness.; credit derivatives; robustness},

language = {eng},

month = {3},

pages = {23-34},

publisher = {EDP Sciences},

title = {Some short elements on hedging credit derivatives},

url = {http://eudml.org/doc/250117},

volume = {11},

year = {2007},

}

TY - JOUR

AU - Durand, Philippe

AU - Jouanin, Jean-Frédéric

TI - Some short elements on hedging credit derivatives

JO - ESAIM: Probability and Statistics

DA - 2007/3//

PB - EDP Sciences

VL - 11

SP - 23

EP - 34

AB -
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.

LA - eng

KW - Credit derivatives; hedging; robustness.; credit derivatives; robustness

UR - http://eudml.org/doc/250117

ER -

## References

top- L. Andersen and J. Sidenius, Extensions to the Gaussian copula: random recovery and random factor loadings. J. Credit Risk1 (2004) 29–70.
- T. Bielecki and M. Jeanblanc, Pricing and Hedging of credit risk: replication and mean-variance approaches. Working paper (2003). Zbl1061.60064
- B. Dupire, Pricing with a smile. Risk7 (1994) 18–20.
- N. El Karoui, M. Jeanblanc-Picqué and S.E. Shreve, Robustness of the Black and Scholes formula. Math. Fin.8 (1998) 93–126. Zbl0910.90008
- M. Jeanblanc and M. Rutkowski, Hedging of credit derivatives within the reduced-form framework. Working paper (2003).
- D. Lando, On Cox processes and credit-risky securities. Rev. Derivatives Res.2 (1998) 99–120. Zbl1274.91459
- P. Schönbucher and D. Schubert, Copula-dependent default risk in intensity models. ETH Zurich, working paper (2001).

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.