Currency Derivatives Pricing for Markov-Modulated Merton Jump-Diffusion Spot Forex Rate

Anatoliy Swishchuk, Maksym Tertychnyi, Winsor Hoang

CTS Forex, Calgary, Canada.
Department of Mathematics and Statistics, University of Calgary, Calgary, Canada.

DOI: 10.4236/jmf.2014.44024                

Abstract

We derive results similar to Bo et al. (2010), but in the case of dynamics of the FX rate driven by a general Merton jump-diffusion process. The main results of our paper are as follows: 1) formulas for the Esscher transform parameters which ensure that the martingale condition for the discounted foreign exchange rate is a martingale for a general Merton jump-diffusion process are derived; using the values of these parameters we proceed to a risk-neural measure and provide new formulas for the distribution of jumps, the mean jump size, and the Poisson Process intensity with respect to the measure; pricing formulas for European foreign exchange call options have been given as well; 2) obtained formulas are applied to the case of the exponential processes; 3) numerical simulations of European call foreign exchange option prices for different parameters are also provided.

Keywords

Foreign Exchange Rate, Esscher Transform, Risk-Neutral Measure, European Call Option, Markov Processes

Conflicts of Interest

The authors declare no conflicts of interest.

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