The valuation of currency options for alternate stochastic processes

This paper compares the ability of four valuation models – the Pure Diffusion model of Black‐Scholes‐Merton, the Absolute Diffusion and Pure Jump models of Cox‐Ross, and the mixed Jump‐Diffusion model of Merton – to explain the observed behavior of market prices of foreign currency options. The empirical tests are based on a comparison of the pattern of implied volatilities obtained from option market prices and the Black‐Scholes‐Merton model with those expected theoretically if exchange rates follow the four stochastic processes specified above. The results of the comparison show that the pattern of implied volatilities is most consistent with the mixed Jump‐Diffusion model.