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

Abstract

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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.

How to cite

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Durand, 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

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

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