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Fractional Brownian motion, random walks and binary market models

Author

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  • Tommi Sottinen

    () (Department of Mathematics, University of Helsinki, P.O. Box 4, 00014 Helsinki, Finland Manuscript)

Abstract

We prove a Donsker type approximation theorem for the fractional Brownian motion in the case $H>1/2.$ Using this approximation we construct an elementary market model that converges weakly to the fractional analogue of the Black-Scholes model. We show that there exist arbitrage opportunities in this model. One such opportunity is constructed explicitly.

Suggested Citation

  • Tommi Sottinen, 2001. "Fractional Brownian motion, random walks and binary market models," Finance and Stochastics, Springer, vol. 5(3), pages 343-355.
  • Handle: RePEc:spr:finsto:v:5:y:2001:i:3:p:343-355
    Note: received: October 1999; final version received: August 2000
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    More about this item

    Keywords

    Fractional Brownian motion; random walk; stock price model; binary market model;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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