Finance and Stochastics

, Volume 5, Issue 3, pp 343–355 | Cite as

Fractional Brownian motion, random walks and binary market models

  • Tommi Sottinen
Original Paper

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.

Key words: Fractional Brownian motion, random walk, stock price model, binary market model 
JEL Classification: C60, G10 
Mathematics Subject Classification (1991): 60F17, 60G15, 90A09 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Tommi Sottinen
    • 1
  1. 1.Department of Mathematics, University of Helsinki, P.O. Box 4, 00014 Helsinki, Finland (e-mail: FI

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