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.
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The authors would like to thank the anonymous reviewer for a number of valuable comments, which helped us improve the paper greatly. XH acknowledges support of the Natural Sciences and Engineering Research Council of Canada (grant no. 386552-2010 ) and the Start-up Research Fund from the University of Manitoba . XL acknowledges support of the Start-up Funds from the University of Minnesota Duluth . YS acknowledges support of JSPS KAKENHI grant no. 24740061 and JST CREST .
- Credit default swap
- Finite-time survival probability
- First-passage time
- Lévy process
- Structural model