Multi-regime foreign exchange rate model: Calibration and pricing

To price exotic foreign exchange (FX) options, a model needs to be selected for FX spot rate dynamics. The classic approach of modelling spot rates with Black–Scholes framework makes inappropriate assumptions of constant drift and volatility, resulting in mispricing. In this article, we investigate multi-regime Black–Scholes (MRBS) model for FX rate, with regime-switching behaviour of drift and volatility governed by a Markov chain. We derive an analytic formula for European FX call options via Fourier transform and present a Monte Carlo simulation algorithm for FX barrier option pricing. Further, we propose a calibration strategy with penalty. Finally, the empirical study shows that volatility smile can be recovered by MRBS model; calibrating MRBS with penalty gives stable calibrated parameters and small out-of-sample mean squared errors; combined use of our calibration methods and pricing algorithms provides reasonable prices for FX barrier options. Thus, MRBS model, together with proposed calibration-with-penalty strategy and pricing algorithm, provides a promising approach for FX option pricing.