On hedging European options in geometric fractional Brownian motion market model

Abstract

We work with fractional Brownian motion with Hurst index H > 1/2. We show that the pricing model based on geometric fractional Brownian motion behaves to certain extend as a process with bounded variation. This observation is based on a new change of variables formula for a convex function composed with fractional Brownian motion. The stochastic integral in the change of variables formula is a Riemann–Stieltjes integral. We apply the change of variables formula to hedging of convex payoffs in this pricing model. It turns out that the hedging strategy is as if the pricing model was driven by a continuous process with bounded variation. This in turn allows us to construct new arbitrage strategies in this model. On the other hand our findings may be useful in connection to the corresponding pricing model with transaction costs.