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# Pricing currency derivatives with Markov-modulated Lévy dynamics

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<title>Pricing currency derivatives with Markov-modulated Lévy dynamics</title>
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<namePart>Swishchuk, Anatoliy</namePart>
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<abstract displayLabel="Summary">Using a Lévy process we generalize formulas in Bo et al. (2010) for the Esscher transform parameters for the log-normal distribution which ensure that 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 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.</abstract>
<note type="statement of responsibility">Anatoliy Swishchuk, Maksym Tertychnyi,  Robert Elliott</note>
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<title>Insurance : mathematics and economics</title>
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<publisher>Oxford : Elsevier, 1990-</publisher>
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<identifier type="issn">0167-6687</identifier>
<identifier type="local">MAP20077100574</identifier>
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<text>07/07/2014 Volumen 57 Número 1 - julio 2014 </text>
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