Table of Contents
ISRN Mathematical Analysis
Volume 2013, Article ID 567071, 5 pages
http://dx.doi.org/10.1155/2013/567071
Research Article

On Option Pricing in Illiquid Markets with Jumps

1Department of Mathematical Sciences, UAE University, P.O. Box 17551, Al-Ain, UAE
2Department of Economics and Finance, UAE University, P.O. Box 17555, Al-Ain, UAE

Received 30 April 2013; Accepted 26 May 2013

Academic Editors: G. Gripenberg, M. Winter, and C. Zhu

Copyright © 2013 Youssef El-Khatib and Abdulnasser Hatemi-J. 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

One of the shortcomings of the Black-Scholes model on option pricing is the assumption that trading of the underlying asset does not affect the price of that asset. This assumption can be fulfilled only in perfectly liquid markets. Since most markets are illiquid, this assumption might be too restrictive. Thus, taking into account the price impact on option pricing is an important issue. This issue has been dealt with, to some extent, for illiquid markets by assuming a continuous process, mainly based on the Brownian motion. However, the recent financial crisis and its effects on the global stock markets have propagated the urgent need for more realistic models where the stochastic process describing the price trajectories involves random jumps. Nonetheless, works related to markets with jumps are scant compared to the continuous ones. In addition, those previous studies do not deal with illiquid markets. The contribution of this paper is to tackle the pricing problem for options in illiquid markets with jumps as well as the hedging strategy within this context, which is the first of its kind to the authors’ best knowledge.