TITLE:
Currency Derivatives Pricing for Markov-Modulated Merton Jump-Diffusion Spot Forex Rate
AUTHORS:
Anatoliy Swishchuk, Maksym Tertychnyi, Winsor Hoang
KEYWORDS:
Foreign Exchange Rate, Esscher Transform, Risk-Neutral Measure, European Call Option, Markov Processes
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.4 No.4,
August
28,
2014
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.