Testing Option Pricing Models with Stochastic Volatility, Random Jumps and Stochastic Interest Rates

Abstract

In this paper, we propose a parsimonious GMM estimation and testing procedure for continuous‐time option pricing models with stochastic volatility, random jump and stochastic interest rate. Statistical tests are performed on both the underlying asset return model and the risk‐neutral option pricing model. Firstly, the underlying asset return models are estimated using GMM with valid statistical tests for model specification. Secondly, the preference related parameters in the risk‐neutral distribution are estimated from observed option prices. Our findings confirm that the implied risk premiums for stochastic volatility, random jump and interest rate are overall positive and varying over time. However, the estimated risk‐neutral processes are not unique, suggesting a segmented option market. In particular, the deep ITM call (or deep OTM put) options are clearly priced with higher risk premiums than the deep OTM call (or deep ITM put) options. Finally, while stochastic volatility tends to better price long‐term options, random jump tends to price the short‐term options better, and option pricing based on multiple risk‐neutral distributions significantly outperforms that based on a single risk‐neutral distribution.