Risk preference based option pricing in a fractional Brownian market

Abstract

We focus on a preference based approach when pricing options in a market driven by fractional Brownian motion. Within this framework we derive formulae for fractional European options using the traditional idea of conditional expectation. The obtained formulae - as well as further results - accord with classical Brownian theory and con?rm economic intuition towards fractional Brownian motion. Furthermore the in?uence of the Hurst parameter H on the price of a European option will be analyzed. --Fractional Brownian motion,Conditional expectation,Risk preference based option pricing,Fractional option pricing,Fractional Greeks