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Sensitivity of boundary crossing probabilities of the Brownian motion

Author

Listed:
  • Gür Sercan

    (Institute for Statistics and Mathematics, WU Vienna University of Economics and Business, Vienna, Austria)

  • Pötzelberger Klaus

    (Institute for Statistics and Mathematics, WU Vienna University of Economics and Business, Vienna, Austria)

Abstract

The paper analyzes the sensitivity of boundary crossing probabilities of the Brownian motion to perturbations of the boundary. The first- and second-order sensitivities, i.e. the directional derivatives of the probability, are derived. Except in cases where boundary crossing probabilities for the Brownian bridge are given in closed form, the sensitivities have to be computed numerically. We propose an efficient Monte Carlo procedure.

Suggested Citation

  • Gür Sercan & Pötzelberger Klaus, 2019. "Sensitivity of boundary crossing probabilities of the Brownian motion," Monte Carlo Methods and Applications, De Gruyter, vol. 25(1), pages 75-83, March.
    • Handle: RePEc:bpj:mcmeap:v:25:y:2019:i:1:p:75-83:n:4
    DOI: 10.1515/mcma-2019-2031
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    References listed on IDEAS

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    1. Achim Zeileis, 2004. "Alternative boundaries for CUSUM tests," Statistical Papers, Springer, vol. 45(1), pages 123-131, January.
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