Currency Derivatives Pricing for Markov-Modulated Merton Jump-Diffusion Spot Forex Rate ()
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.
Share and Cite:
Swishchuk, A. , Tertychnyi, M. and Hoang, W. (2014) Currency Derivatives Pricing for Markov-Modulated Merton Jump-Diffusion Spot Forex Rate.
Journal of Mathematical Finance,
4, 265-278. doi:
10.4236/jmf.2014.44024.