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Pricing currency derivatives with Markov-modulated Lévy dynamics |
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| Institution: | 1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;2. Department of Mathematics, University of New Orleans, New Orleans 70148, USA;3. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;1. École Normale Supérieure, Group for Neural Theory, Paris, France;2. INRIA team Carmen, INRIA Bordeaux Sud-Ouest, 33405 Talence cedex, France;3. Intersdisciplinary Research Department - Field Sciences, Alexandru Ioan Cuza University of Ia?i, Lasc?r Catargi nr. 54, Ia?i, Romania |
| Abstract: | 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. |
| Keywords: | Foreign exchange rate Esscher transform Risk-neutral measure European call option Lévy processes Markov processes |
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