Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options

An efficient method is developed for pricing American options on stochastic volatility/jump-diffusion processes under systematic jump and volatility risk. The parameters implicit in deutsche mark (DM) options of the model and various submodels are estimated over the period 1984 to 1991 via nonlinear generalized least squares, and are tested for consistency with $/DM futures prices and the implicit volatility sample path. The stochastic volatility submodel cannot explain the “volatility smile” evidence of implicit excess kurtosis, except under parameters implausible given the time series properties of implicit volatilities. Jump fears can explain the smile, and are consistent with one 8 percent DM appreciation “outlier” observed over the period 1984 to 1991.