Arbitrage in a discrete version of the Wick-Fractional Black Scholes model

Abstract

We consider binary market models based on the discrete Wick product instead of the pathwise product and provide a sufficient criterion for the existence of an arbitrage. This arbitrage is explicitly constructed in the class of self-financing one-step buy-and-hold strategies, (i.e., the investor holds shares of the stock only at one time step). Using coefficients obtained from an approximation of a fractional Brownian motion with Hurst parameter ½ < H < 1 the result is applied to a discrete version of the (Wick-)fractional Black-Scholes market.