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ABSTRACT
This article mainly investigates risk-minimizing European currency option pricing and hedging strategy when the spot foreign exchange rate is driven by a Markov-modulated jump-diffusion model. We suppose the domestic and foreign money market floating interest rates, the drift, and the volatility of the exchange rate dynamics all depend on the state of the economy, which is modeled by a continuous-time hidden Markov chain. The model considered in this article will provide market practitioners with flexibility in characterizing the dynamics of the spot foreign exchange rate. Using the minimal martingale measure, we obtain a system of coupled partial-differential-integral equations satisfied by the currency option price and find the corresponding hedging strategies and the residual risk. According to simulation of currency option prices in the special case of double exponential jump-diffusion regime-switching model, we further discuss and show the effects of the parameters on the prices.
Acknowledgments
The authors are very grateful to the anonymous referee for his constructive comments and suggestions on the first version of the manuscript. They would also like to thank the associate editor and editor-in-chief for their helpful advice. All remaining errors are the responsibility of the authors.
Funding
This work was supported by National Natural Science Foundation of China (71561012), Key Program of National Social Science Foundation of China (13AJL008), Natural Science Foundation of Jiangxi Province (20161BAB201027), Humanity and social Science foundation of High School of Jiangxi Province (TJ1302), and Foundation of Jiangxi University of Finance and Economics.