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On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function

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  • Tristan Guillaume

Abstract

This paper provides explicit formulae for the probability that an arithmetic or a geometric Brownian motion will not cross an absorbing boundary defined as a step function during a finite time interval. Various combinations of downward and upward steps are handled. Numerical computation of the survival probability is done quasi-instantaneously and with utmost precision. The sensitivity of the survival probability to the number and the ordering of the steps in the boundary is analyzed.

Suggested Citation

  • Tristan Guillaume, 2015. "On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function," Journal of Probability and Statistics, Hindawi, vol. 2015, pages 1-22, September.
    • Handle: RePEc:hin:jnljps:391681
    DOI: 10.1155/2015/391681
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    Cited by:

    1. Lee, Hangsuck & Lee, Gaeun & Song, Seongjoo, 2023. "Min–max multi-step barrier options and their variants," The North American Journal of Economics and Finance, Elsevier, vol. 67(C).
    2. Hangsuck Lee & Gaeun Lee & Seongjoo Song, 2022. "Multi‐step reflection principle and barrier options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(4), pages 692-721, April.
    3. Tristan Guillaume, 2024. "Rainbow Step Barrier Options," JRFM, MDPI, vol. 17(8), pages 1-32, August.

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