Markov-modulated jump-diffusions for currency option pricing |
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Authors: | Lijun Bo Xuewei Yang |
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Affiliation: | a Department of Mathematics, Xidian University, Xi’an 710071, PR China b School of Mathematical Sciences, Nankai University, Tianjin 300071, PR China c School of Business, Nankai University, Tianjin 300071, PR China d TEDA Institute of Computational Finance, Nankai University, Tianjin 300071, PR China |
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Abstract: | This paper introduces dynamic models for the spot foreign exchange rate with capturing both the rare events and the time-inhomogeneity in the fluctuating currency market. For the rare events, we use a compound Poisson process with log-normal jump amplitude to describe the jumps. As for the time-inhomogeneity in the market dynamics, we particularly stress the strong dependence of the domestic/foreign interest rates, the appreciation rate and the volatility of the foreign currency on the time-varying sovereign ratings in the currency market. The time-varying ratings are formulated by a continuous-time finite-state Markov chain. Based on such a spot foreign exchange rate dynamics, we then study the pricing of some currency options. Here we will adopt a so-called regime-switching Esscher transform to identify a risk-neutral martingale measure. By determining the regime-switching Esscher parameters we then get an integral expression on the prices of European-style currency options. Finally, numerical illustrations are given. |
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Keywords: | C13 C15 F31 |
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