Fractional Brownian motion, random walks and binary market models
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.
Volume (Year): 5 (2001)
Issue (Month): 3 ()
|Note:||received: October 1999; final version received: August 2000|
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