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Currency Derivatives Pricing for Markov-modulated Merton Jump-diffusion Spot Forex Rate

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  • Anatoliy Swishchuk
  • Maksym Tertychnyi
  • Winsor Hoang

Abstract

We derived similar to Bo et al. (2010) results but in the case when the dynamics of the FX rate is 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 proceeded 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 call foreign exchange 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; 4) codes for Matlab functions used in numerical simulations of option prices are given.

Suggested Citation

  • Anatoliy Swishchuk & Maksym Tertychnyi & Winsor Hoang, 2014. "Currency Derivatives Pricing for Markov-modulated Merton Jump-diffusion Spot Forex Rate," Papers 1402.2273, arXiv.org.
    • Handle: RePEc:arx:papers:1402.2273
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    References listed on IDEAS

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