Pricing European and Barrier Options in the Fractional Black-Scholes Market

Abstract

The aim of this paper is to obtain the valuation formulas for European and barrier options if the underlying of the option contract is supposed to be driven by a fractional Brownian motion with Hurst parameter greater than 0.5. The paper is build upon the framework developed in Necula (2007) for the valuation of derivative products in the fractional Black-Scholes market. We also obtain a reflection principle for the fractional Brownian motion.

Keywords: fractional Brownian motion, fractional Black-Scholes market, the reflection principle for the fractional Brownian motion, mathematical finance, European option, barrier option

JEL Classification: C02, C60, G12, G13