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

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  • K. Borovkov
  • Alexander Novikov
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    Abstract

    We give explicit upper bounds for convergence rates when approximating (both one- and two-sided general curvlinear) boundary crossing probabilities for the Wiener process by similar probabilities for close boundaries (of simpler form for which computing the possibility is feasible). In particular, we generalize and improve results obtained by Potzelberger and Wang [13] for the case when approximating boundaries are piecewise linear. Applications to barrier option pricing are discussed as well.

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    File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp115.pdf
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    Bibliographic Info

    Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 115.

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    Date of creation: 01 Jan 2004
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    Handle: RePEc:uts:rpaper:115

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    Keywords: wiener process; boundary crossing probabilities; barrier options;

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    1. G. O. Roberts & C. F. Shortland, 1997. "Pricing Barrier Options with Time-Dependent Coefficients," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 83-93.
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