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Explicit Bounds for Approximation Rates of Boundary Crossing Probabilities for the Wiener Process

Part of: Stochastic processes Markov processes Probabilistic methods, simulation and stochastic differential equations Mathematical economics

Published online by Cambridge University Press:  14 July 2016

K. Borovkov  and
A. Novikov
K. Borovkov*
Affiliation:
University of Melbourne
A. Novikov*
Affiliation:
University of Technology, Sydney
*
∗Postal address: Department of Mathematics and Statistics, University of Melbourne, Parkville 3010, Australia. Email address: [email protected]
∗∗Postal address: Department of Mathematical Sciences, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia.
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Abstract

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We give explicit upper bounds for convergence rates when approximating both one- and two-sided general curvilinear boundary crossing probabilities for the Wiener process by similar probabilities for close boundaries of simpler form, for which computation of the boundary crossing probabilities is feasible. In particular, we partially generalize and improve results obtained by Pötzelberger and Wang in the case when the approximating boundaries are piecewise linear. Applications to barrier option pricing are also discussed.

Keywords

Wiener processboundary crossing probabilitybarrier option

MSC classification

Secondary: 60J65: Brownian motion 65C50: Other computational problems in probability 91B70: Stochastic models 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 1 , March 2005 , pp. 82 - 92
Copyright
© Applied Probability Trust 2005 

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