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International Journal of Stochastic Analysis
Volume 2015 (2015), Article ID 258217, 15 pages
http://dx.doi.org/10.1155/2015/258217
Research Article

Pricing FX Options in the Heston/CIR Jump-Diffusion Model with Log-Normal and Log-Uniform Jump Amplitudes

1School of Computing and Mathematics, University of Western Sydney, South Penrith NSW 1797, Australia
2School of Computing Engineering and Mathematics, University of Western Sydney, Sydney, NSW 1797, Australia

Received 26 November 2014; Accepted 7 May 2015

Academic Editor: Enzo Orsingher

Copyright © 2015 Rehez Ahlip and Ante Prodan. 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

We examine foreign exchange options in the jump-diffusion version of the Heston stochastic volatility model for the exchange rate with log-normal jump amplitudes and the volatility model with log-uniformly distributed jump amplitudes. We assume that the domestic and foreign stochastic interest rates are governed by the CIR dynamics. The instantaneous volatility is correlated with the dynamics of the exchange rate return, whereas the domestic and foreign short-term rates are assumed to be independent of the dynamics of the exchange rate and its volatility. The main result furnishes a semianalytical formula for the price of the foreign exchange European call option.