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Locally Risk-Minimizing Hedging of Counterparty Risk for Portfolio of Credit Derivatives

  • Lijun Bo
  • Claudia CeciEmail author
Article
  • 23 Downloads

Abstract

We discuss dynamic hedging of counterparty risk for a portfolio of credit derivatives by the local risk-minimization approach. We study the problem from the perspective of an investor who, trading with credit default swaps (CDS) referencing the counterparty, wants to protect herself/himself against the loss incurred at the default of the counterparty. We propose a credit risk intensity-based model consisting of interacting default intensities by taking into account direct contagion effects. The portfolio of defaultable claims is of generic type, including CDS portfolios, risky bond portfolios and first-to-default claims with payments allowed to depend on the default state of the reference firms and counterparty. Using the martingale representation of the conditional expectation of the counterparty risk price payment stream under the minimal martingale measure, we recover a closed-form representation for the locally risk minimizing strategy in terms of classical solutions to nonlinear recursive systems of Cauchy problems. We also discuss applications of our framework to the most prominent classes of credit derivatives.

Keywords

Local risk-minimization Counterparty risk Recursive system of Cauchy problems 

AMS 2000 subject classifications

60J25 60J75 60H30 91B28 

Notes

Acknowledgements

The authors would like to thank two anonymous referees for the careful reading and helpful comments to improve the presentation of this paper. The research of L. Bo is supported by Natural Science Foundation of China under Grant 11471254.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXidian UniversityXi’anPeople’s Republic of China
  2. 2.Department of EconomicsUniversity “G. d’Annunzio” of Chieti-PescaraPescaraItaly

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