## Abstract

We evaluate the par spread for a single-name credit default swap with a random recovery rate. It is carried out under the framework of a structural default model in which the asset-value process is of infinite activity but finite variation. The recovery rate is assumed to depend on the undershoot of the asset value below the default threshold when default occurs. The key part is to evaluate a generalized expected discounted penalty function, which is a special case of the so-called Gerber-Shiu function in actuarial ruin theory. We first obtain its double Laplace transform in time and in spatial variable, and then implement a numerical Fourier inversion integration. Numerical experiments show that our algorithm gives accurate results within reasonable time and different shapes of spread curve can be obtained.

Original language | English (US) |
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Pages (from-to) | 103-110 |

Number of pages | 8 |

Journal | Insurance: Mathematics and Economics |

Volume | 65 |

DOIs | |

State | Published - Nov 1 2015 |

### Bibliographical note

Funding Information:Hao acknowledges support of the Natural Sciences and Engineering Research Council of Canada (grant no. 386552-2010 ).

Publisher Copyright:

© 2015 Elsevier B.V..

## Keywords

- Credit default swap
- Infinite activity
- Lévy process
- Random recovery rate
- Structural model