About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 513496, 6 pages
http://dx.doi.org/10.1155/2014/513496
Research Article

European Option Pricing with Transaction Costs in Lévy Jump Environment

1School of Science, Donghua University, Shanghai 200051, China
2College of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China

Received 25 January 2014; Accepted 20 February 2014; Published 27 March 2014

Academic Editor: Bo Shen

Copyright © 2014 Jiayin Li 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 European option pricing problem with transaction costs is investigated for a risky asset price model with Lévy jump. By the aid of arbitrage pricing theory and the generalized Itô formula (which includes Poisson jump), the explicit solution to the risk asset price model is given. According to arbitrage-free principle, we first discretize the continuous-time model. Then, in each small time interval, the transaction costs are introduced. By using the -hedging strategy, the explicit solutions of the European options pricing formula with transaction costs are given for the risky asset price model with Lévy jump.