Hitting time and time change

Victor Vaugirard

Applied Mathematical Finance, 2004, vol. 11, issue 1, 77-94

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.

Keywords: digital option; soft barrier; forward-neutral measure; time change; jump-diffusion process (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1080/1350486042000190340

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