Local volatility enhanced by a jump to default

Peter Carr, Dilip B. Madan

Research output: Contribution to journalArticlepeer-review


A local volatility model is enhanced by the possibility of a single jump to default. The jump has a hazard rate that is the product of the stock price raised to a prespecified negative power and a deterministic function of time. The empirical work uses a power of -1.5. It is shown how one may simultaneously recover from the prices of credit default swap contracts and equity option prices both the deterministic component of the hazard rate function and revised local volatility. The procedure is implemented on prices of credit default swaps and equity options for General Motors and the Ford Motor Company over the period October 2004 to September 2007.

Original languageEnglish (US)
Pages (from-to)2-15
Number of pages14
JournalSIAM Journal on Financial Mathematics
Issue number1
StatePublished - 2010


  • Default adjusted drifts
  • Recovering default free option prices
  • Truncated power prices
  • Weibull distribution

ASJC Scopus subject areas

  • Numerical Analysis
  • Finance
  • Applied Mathematics


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