Pricing foreign equity options with regime-switching

•The valuation of FX equity options is considered in a regime-switching environment.•The impacts of economic conditions on both the FX rate and the equity price are considered.•A FFT approach is used to evaluate the options.•Numerical results are used to illustrate the practicality of our proposed method.

In this paper, we investigate the valuation of two types of foreign equity options under a Markovian regime-switching mean-reversion lognormal model, where some key model parameters in the dynamics of the foreign equity price and the foreign exchange rate are modulated by a continuous-time, finite-state Markov chain. A fast Fourier transform (FFT) approach is applied to provide an efficient way to evaluate the option prices. Numerical analysis and empirical studies are provided to illustrate the practical implementation of the proposed pricing model.