Conditional Volatility and the GARCH Option Pricing Model with Non-Normal Innovations

Based on the theory of a wedge between the physical and risk-neutral conditional volatilities in Christoffersen, Elkamhi, Feunou, and Jacobs (2009), we develop a modification on the GARCH option pricing model with the filtered historical simulation proposed in Barone-Adesi, Engle, and Mancini (2008). The current conditional volatilities under the physical and risk-neutral measures are the same in the previous model, but should have been allowed to be different. Using an extensive data on S&P 500 index options, our approach, which employs the current risk-neutral conditional volatility estimated from the cross-section of the option prices (in contrast to the existing GARCH option pricing models), maintains theoretical consistency under conditional non-normality as well as improves the empirical performances. Remarkably, the risk-neutral volatility dynamics are stable over time under this model. In addition, the comparison between the VIX index and the risk-neutral integrated volatility validates our approach economically