Pricing credit default swaps with a random recovery rate by a double inverse Fourier transform

Xuemiao Hao, Xuan Li

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 languageEnglish (US)
Pages (from-to)103-110
Number of pages8
JournalInsurance: Mathematics and Economics
Volume65
DOIs
StatePublished - 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

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