Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in PHLX Deutschemark OptionsAn efficient method is developed for pricing American options on combination stochastic volatility/jump-diffusion processes when jump risk and volatility risk are systematic and nondiversifiable, thereby nesting two major option pricing models. The parameters implicit in PHLX-traded Deutschemark options of the stochastic volatility/jump- diffusion model and various submodels are estimated over 1984-91, and are tested for consistency with the $/DM futures process and the implicit volatility sample path. The parameters implicit in options are found to be inconsistent with the time series properties of implicit volatilities, but qualitatively consistent with log- differenced futures prices. No economically significant implicit expectations of exchange rate jumps were found in full-sample estimation, which is consistent with the reduced leptokurtosis of $/DM weekly exchange rate changes over 1984-91 relative to earlier periods. |
Common terms and phrases
American option asset price Bates Bureau of Economic call and put constrained data set Deterministic volatility evaluated excess kurtosis F₁ F₂ foreign currency options function futures price process Gaussian quadrature geometric Brownian geometric Brownian motion hypothesis implicit in option implicit skewness implicit variances implicit volatilities instantaneous conditional variance interest rates joint transition density Jorion jump component Jump parameters jump risk JUMPS AND STOCHASTIC Kathleen McGarry leptokurtosis log-likelihood lognormal maturity moment generating function moneyness option pricing models P-value P₁ parameters implicit Philadelphia Stock Exchange PHLX price tick pricing options properties of implicit put options rejected risk-neutral probability sample path series properties series studies spot exchange rate stochastic volatility model Stochastic volatility parameters stochastic volatility/jump-diffusion model stochastic volatility/jump-diffusion process strike prices structure of implicit subscription substantial SV model SVJD model term structure traded unconstrained volatility of variance volatility risk premium