Option pricing with exchange rate risk under regime-switching multi-scale jump-diffusion models

In this article, the foreign equity price and the foreign exchange rate are supposed to follow the regime-switching multi-scale jump-diffusion processes. In addition, the correlations of the two processes are not only manifested in the diffusion parts but also in the jump components. First, the Esscher transform is used to identify an equivalent martingale measure since the financial market is incomplete. Then, some pricing problems of foreign equity options are studied and the analytic solutions of pricing formulae are derived by using Fourier transform method. Numerical results are given by the fast Fourier transform algorithm and analysis are also presented. Moreover, the numerical result shows that the economic states and model’s parameters have significant effects on the values of these different kinds of foreign equity options. Finally, empirical studies are provided to illustrate the practical implementation of the proposed pricing model.