Table of Contents
International Scholarly Research Notices
Volume 2014 (2014), Article ID 746196, 7 pages
http://dx.doi.org/10.1155/2014/746196
Research Article

Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion

College of Sciences, China University of Mining and Technology, Xuzhou 221116, China

Received 22 May 2014; Revised 14 September 2014; Accepted 14 September 2014; Published 3 November 2014

Academic Editor: Francesco Zirilli

Copyright © 2014 Jiao-Jiao Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland’s hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, the effectiveness of the proposed form is verified through a numerical example. Meanwhile, the impact of transaction cost rate and volatility on lookback option value is discussed.