Volatility and Price Jumps in Agricultural Futures Prices—Evidence from Wheat Options

Evidence suggests that agricultural futures price movements have fat-tailed distributions and exhibit sudden and unexpected price jumps. There is also evidence that the volatility of futures prices is time-dependent both as a function of calendar-time (seasonal effect) and time to maturity (maturity effect). This article extends Bates' (1991) jump-diffusion option pricing model by including both seasonal and maturity effects in the volatility specification. Both in-sample and out-of-sample procedures to fit market option prices on wheat futures show that the suggested model outperforms previous published models. A numerical example shows the magnitude of pricing errors for option valuation.