A Framework for Derivative Pricing in the Fractional Black-Scholes Market

Abstract

The aim of this paper is to develop 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 and the fundamental evaluation equation in the case of the fractional Black-Scholes market.

Keywords: fractional Brownian motion, fractional Black-Scholes market, quasiconditional expectation, mathematical finance, contingent claim

JEL Classification: C02, C60, G12, G13