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

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  • Nikolai Dokuchaev
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    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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    File URL: http://arxiv.org/pdf/1311.0675
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1311.0675.

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    Date of creation: Nov 2013
    Date of revision: Apr 2014
    Publication status: Published in Discrete and Continuous Dynamical Systems -- Series B (DCDS-B) 20 (2014), No.6, 1549--1562
    Handle: RePEc:arx:papers:1311.0675

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    1. Nikolai Dokuchaev, 2012. "On statistical indistinguishability of the complete and incomplete markets," Papers 1209.4695, arXiv.org, revised May 2013.
    2. 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(04), pages 419-440, December.
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