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On strong binomial approximation for stochastic processes and applications for financial modelling

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  • Nikolai Dokuchaev

Abstract

This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial processes, i.e., by processes with fixed size binary increments at sampling points. Moreover, this approximation can be causal, i.e., at every time it requires only past historical values of the underlying process. In addition, possibility of approximation of solutions of stochastic differential equations by solutions of ordinary equations with binary noise is established. Some consequences for the financial modelling and options pricing models are discussed.

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  • Nikolai Dokuchaev, 2013. "On strong binomial approximation for stochastic processes and applications for financial modelling," Papers 1311.0675, arXiv.org, revised Feb 2015.
    • Handle: RePEc:arx:papers:1311.0675
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    1. Heath, David & Jarrow, Robert & Morton, Andrew, 1990. "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(4), pages 419-440, December.
    2. Ciprian Tudor & Soledad Torres, 2007. "Donsker theorem for the Rosenblatt process and a binary market model," Papers math/0703085, arXiv.org.
    3. Amin, Kaushik I., 1991. "On the Computation of Continuous Time Option Prices Using Discrete Approximations," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(4), pages 477-495, December.
    4. Nikolai Dokuchaev, 2012. "On statistical indistinguishability of the complete and incomplete markets," Papers 1209.4695, arXiv.org, revised May 2013.
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