Equilibrium valuation of currency options under a jump-diffusion model with stochastic volatility

Abstract

In this paper, we continue to investigate the model related to Bakshi and Chen (1997). In our model, both of the money supplies in the two countries are assumed to follow jump-diffusion processes with stochastic volatility. In the set of the two-country economy, we obtain the equilibrium price of the nominal exchange rate. With the help of Fourier transform to solve a partial integro-differential equation (PIDE), we get a closed-form solution to the PIDE for a European call currency option. We also do Monte Carlo simulations to verify the correctness of the derived formula. Our model contains some existing currency option models as special cases, for example the stochastic-volatility jump-diffusion (SVJD) model in Bates (1996), in which the jump of the exchange rate is driven by one Poisson process. We also provide some numerical analysis to show that our model is effective to the foreign currency option market.