Explicit Valuation of Currency Options with Regime-Switching Risk Premium: Markovian Jumps

Abstract

Spot foreign exchange (FX) rates usually exhibit volatility clustering and regime switching in a finite number of states due to change in macroeconomic factors or financial crises. We provide regime-switching evidence based on yield-curves data under the Markov-modulated diffusion (MMD) model. A MMD model is proposed to incorporate Markov chain that is capable of capturing the dynamic feature of the spot FX rate. In addition, Markovian Jumps due to change in the state of the economy is formulated by Markov chain. Markovian jumps are embedded in a pricing kernel such that regime-switching risk is priced. An explicit valuation model of currency call options under the MMD model is derived. Empirical study shows that the derived valuation model with regime-switching risk is not only more complete but also appropriate for pricing European currency options on the spot FX rate.