Pricing currency derivatives with Markov-modulated Lévy dynamics

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      <subfield code="a">Swishchuk, Anatoliy</subfield>
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      <subfield code="a">Pricing currency derivatives with Markov-modulated Lévy dynamics</subfield>
      <subfield code="c">Anatoliy Swishchuk, Maksym Tertychnyi,  Robert Elliott</subfield>
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      <subfield code="a">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.</subfield>
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      <subfield code="t">Insurance : mathematics and economics</subfield>
      <subfield code="d">Oxford : Elsevier, 1990-</subfield>
      <subfield code="x">0167-6687</subfield>
      <subfield code="g">07/07/2014 Volumen 57 Número 1 - julio 2014 </subfield>
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