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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

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.

Suggested Citation

  • K. Borovkov & Alexander Novikov, 2004. "Explicit Bounds for Approximation Rates for Boundary Crossing Probabilities for the Wiener Process," Research Paper Series 115, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:115
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    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-02/QFR-rp115.pdf
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    References listed on IDEAS

    as
    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, January.
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    Cited by:

    1. Thorsten Schmidt & Alexander Novikov, 2008. "A Structural Model with Unobserved Default Boundary," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 183-203.
    2. Dimitrina S. Dimitrova & Zvetan G. Ignatov & Vladimir K. Kaishev, 2017. "On the First Crossing of Two Boundaries by an Order Statistics Risk Process," Risks, MDPI, vol. 5(3), pages 1-14, August.
    3. Pingjin Deng, 2016. "Asymptotic of Non-Crossings probability of Additive Wiener Fields," Papers 1610.07131, arXiv.org.
    4. Delia Coculescu & Hélyette Geman & Monique Jeanblanc, 2008. "Valuation of default-sensitive claims under imperfect information," Finance and Stochastics, Springer, vol. 12(2), pages 195-218, April.
    5. Pötzelberger Klaus, 2012. "Improving the Monte Carlo estimation of boundary crossing probabilities by control variables," Monte Carlo Methods and Applications, De Gruyter, vol. 18(4), pages 353-377, December.

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    More about this item

    Keywords

    wiener process; boundary crossing probabilities; barrier options;
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