Option Pricing in a Fractional Brownian Motion Environment

19 Pages Posted: 20 Oct 2008

See all articles by Ciprian Necula

Ciprian Necula

University of Zurich - Department of Banking and Finance; Bucharest University of Economic Studies, Department of Money and Banking

Date Written: February 12, 2002

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

Suggested Citation

Necula, Ciprian, Option Pricing in a Fractional Brownian Motion Environment (February 12, 2002). Available at SSRN: https://ssrn.com/abstract=1286833 or http://dx.doi.org/10.2139/ssrn.1286833

Ciprian Necula (Contact Author)

University of Zurich - Department of Banking and Finance ( email )

Plattenstrasse 14
Z├╝rich, 8032
Switzerland

Bucharest University of Economic Studies, Department of Money and Banking ( email )

6, Romana Square, District 1
Bucharest, 010374
Romania

HOME PAGE: http://www.dofin.ase.ro/cipnec

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