Abstract. We prove a Donsker type approximation theorem for the fractional Brownian motion in the case
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
Manuscript received: October 1999; final version received: August 2000