Pricing Currency Derivatives with Markov-modulated Levy Dynamics

Anatoliy Swishchuk, Maksym Tertychnyi and Robert Elliott

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Abstract: Using a Levy process we generalize formulas in Bo et al.(2010) for the Esscher transform parameters for the log-normal distribution which ensure the martingale condition holds for the discounted foreign exchange rate. Using these values of the parameters we find 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 to this measure. The formulas for a European call foreign exchange option are also derived. We apply these formulas to the case of the log-double exponential distribution of jumps. We provide numerical simulations for the European call foreign exchange option prices with different parameters.

Date: 2014-02
New Economics Papers: this item is included in nep-sog
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Citations: View citations in EconPapers (14)

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