Option Pricing in a Fractional Brownian Motion Environment

Abstract

In this paper it is developed a framework for evaluating derivatives if the underlying of the derivative contract is supposed to be driven by a fractional Brownian motion with Hurst parameter greater than 0.5. For this purpose we first prove some results regarding the quasi-conditional expectation, especially the behavior to a Girsanov transform. We obtain the risk-neutral valuation formula, the fundamental evaluation equation of a contingent claim, and the formula for the price of a European call option in the case of the fractional Black-Scholes market.

Keywords: fractional Brownian motion, fractional Black-Scholes market, mathematical finance, options

JEL Classification: C02, C60, G12, G13