Sensitivity of boundary crossing probabilities of the Brownian motion

Gür Sercan () and Pötzelberger Klaus ()
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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

Monte Carlo Methods and Applications, 2019, vol. 25, issue 1, 75-83

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.

Keywords: Boundary crossing probability; first exit time; sensitivity; perturbation of boundary; adaptive control variable (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1515/mcma-2019-2031

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