Markov-modulated jump-diffusions for currency option pricing
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.
Year of publication: |
2010
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Authors: | Bo, Lijun ; Wang, Yongjin ; Yang, Xuewei |
Published in: |
Insurance: Mathematics and Economics. - Elsevier, ISSN 0167-6687. - Vol. 46.2010, 3, p. 461-469
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Publisher: |
Elsevier |
Keywords: | Spot foreign exchange rate Rare event Time-inhomogeneity Esscher transform Currency option |
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