### Abstract

We study the first-passage time over a fixed threshold for a pure-jump subordinator with negative drift. We obtain a closed-form formula for its survival function in terms of marginal density functions of the subordinator. We then use this formula to calculate finite-time survival probabilities in a structural model for credit risk, and thus obtain a closed-form pricing formula for a single-name credit default swap (CDS). This pricing formula is well calibrated on market CDS quotes. In particular, it explains why the par CDS credit spread is not negligible when the maturity becomes short.

Original language | English |
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Pages (from-to) | 14-23 |

Number of pages | 10 |

Journal | Insurance: Mathematics and Economics |

Volume | 53 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2013 Jul |

Externally published | Yes |

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### Keywords

- Credit default swap
- Finite-time survival probability
- First-passage time
- Lévy process
- Structural model

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Economics and Econometrics
- Statistics and Probability