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Hitting time and time change

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  • Victor Vaugirard

Abstract

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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