Finite-time survival probability and credit default swaps pricing under geometric Lévy markets

Xuemiao Hao, Xuan Li, Yasutaka Shimizu

Research output: Contribution to journalArticle

5 Citations (Scopus)


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 languageEnglish
Pages (from-to)14-23
Number of pages10
JournalInsurance: Mathematics and Economics
Issue number1
Publication statusPublished - 2013 Jul
Externally publishedYes



  • 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

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