Journal
INSURANCE MATHEMATICS & ECONOMICS
Volume 43, Issue 3, Pages 295-302Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.insmatheco.2008.05.002
Keywords
Currency options; Two-factor stochastic volatility; Regime switching; Esscher transform; Decomposition
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This article investigates the valuation of currency options when the dynamic of the spot Foreign Exchange (FX) rate is governed by a two-factor Markov-modulated stochastic volatility model, with the first stochastic volatility component driven by a lognormal diffusion process and the second independent stochastic volatility component driven by a continuous-time finite-state Markov chain model. The states of the Markov chain can be interpreted as the states of an economy. We employ the regime-switching Esscher transform to determine a martingale pricing measure for valuing Currency options under the incomplete market setting. We consider the valuation of the European-style and American-style currency options. In the case of American options, we provide a decomposition result for the American option price into the sum of its European Counterpart and the early exercise premium. Numerical results are included. (C) 2008 Elsevier B.V. All rights reserved.
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