Fractional processes as models in stochastic finance

Abstract

We survey some new progress on the pricing models driven by fractional Brownian motion \cb{or} mixed fractional Brownian motion. In particular, we give results on arbitrage opportunities, hedging, and option pricing in these models. We summarize some recent results on fractional Black & Scholes pricing model with transaction costs. We end the paper by giving some approximation results and indicating some open problems related to the paper.

To appear in Advanced Mathematical Methods for Finance (Eds. G. Di Nunno and B. Øksendal Series in Mathematical Finance, Springer)