Forecasting options prices using discrete time volatility models estimated at mixed timescales

Option pricing models traditionally have utilized continuous-time frameworks to derive solutions or Monte Carlo schemes to price the contingent claim. Typically these models were calibrated to discrete-time data using a variety of approaches. Recent work on GARCH based option pricing models have introduced a set of models that easily can be estimated via MLE or GMM directly from discrete time spot data. This paper provides a series of extensions to the standard discrete-time options pricing setup and then implements a set of various pricing approaches for a very large cross-section of equity and index options against the forward-looking traded market price of these options, out-of-sample. Our analysis provides two significant findings. First, we provide clear evidence that including autoregressive jumps in the options model is critical in determining the correct price of heavily out-of-the money and in-the-money options relatively close to maturity. Second, for longer maturity options, we show that the anticipated performance of the popular component GARCH models, which exhibit long persistence in volatility, does not materialize. We ascribe this result in part to the inherent instability of the numerical solution to the option price in the presence of component volatility. Taken together, our results suggest that when pricing options, the first best approach is to include jumps directly in the model, preferably using jumps calibrated from intraday data.