Fractional Brownian motion, random walks and binary market models
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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.
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