Takahashi, A., Takehara, K. and Yamazaki, A. (2006) Pricing Currency Options with a Market Model of Interest Rates under Jump-Diffusion Stochastic Volatility processes of Spot Exchange rates. CIRJE-F-451, Working Paper.

has been cited by the following article:

• 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.