Option Pricing in a Fractional Brownian Motion Environment
19 Pages Posted: 20 Oct 2008
Date Written: February 12, 2002
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
Suggested Citation: Suggested Citation