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Binomial approximation of Brownian motion and its maximum

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  • Carbone, Raffaella

Abstract

Motivated by some typical option pricing problems, we study how to estimate quantities of the form by replacing the Brownian motion (Bt)t[greater-or-equal, slanted]0 with a binomial random walk. The approximating term can be explicitly computed, without using any simulation. We investigate the rate of convergence of this approximation method and we study some applications, in particular the case of barrier options.

Suggested Citation

  • Carbone, Raffaella, 2004. "Binomial approximation of Brownian motion and its maximum," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 271-285, September.
    • Handle: RePEc:eee:stapro:v:69:y:2004:i:3:p:271-285
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    References listed on IDEAS

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    1. Gobet, Emmanuel, 2000. "Weak approximation of killed diffusion using Euler schemes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 167-197, June.
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    Cited by:

    1. Guillaume Leduc & Merima Nurkanovic Hot, 2020. "Joshi’s Split Tree for Option Pricing," Risks, MDPI, vol. 8(3), pages 1-26, August.
    2. Leduc, Guillaume, 2012. "European Option General First Order Error Formula," MPRA Paper 42015, University Library of Munich, Germany, revised 01 Oct 2012.

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