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Hitting time and time change


  • Victor Vaugirard


This paper determines first-passage time distributions with a twofold emphasis on the dynamics of the state variables and interest rate uncertainty. Underlyings follow two-dimensional geometric Brownian motions, Ornstein-Uhlenbeck processes or Poisson jump-diffusion processes, and boundaries are either fixed or indexed on risk-free bonds. Forward-neutral changes of numeraire enable one to derive generic valuation expressions, while changing time allows one to determine closed-form solutions for geometric Brownian motions and moving barriers. In turn, the latter formulas are used to reduce the variance of Monte Carlo simulations in the case of jump-diffusion processes, by means of the control variate method.

Suggested Citation

  • Victor Vaugirard, 2004. "Hitting time and time change," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(1), pages 77-94.
  • Handle: RePEc:taf:apmtfi:v:11:y:2004:i:1:p:77-94 DOI: 10.1080/1350486042000190340

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    References listed on IDEAS

    1. Lucas, Andre & Klaassen, Pieter & Spreij, Peter & Straetmans, Stefan, 2001. "An analytic approach to credit risk of large corporate bond and loan portfolios," Journal of Banking & Finance, Elsevier, vol. 25(9), pages 1635-1664, September.
    2. Bangia, Anil & Diebold, Francis X. & Kronimus, Andre & Schagen, Christian & Schuermann, Til, 2002. "Ratings migration and the business cycle, with application to credit portfolio stress testing," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 445-474, March.
    3. Gordy, Michael B., 2000. "A comparative anatomy of credit risk models," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 119-149, January.
    4. Mark Carey, 1998. "Credit Risk in Private Debt Portfolios," Journal of Finance, American Finance Association, vol. 53(4), pages 1363-1387, August.
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