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

On the basis of the theory of a wedge between the physical and risk‐neutral conditional volatilities in Christoffersen, P., Elkamhi, R., Feunou, B., & Jacobs, K. (2010), we develop a modification of the GARCH option pricing model with the filtered historical simulation proposed in Barone‐Adesi, G., Engle, R. F., & Mancini, L. (2008). The one‐day‐ahead conditional volatilities under physical and risk‐neutral measures are the same in the previous model, but should have been allowed to be different. Using extensive data on S&P 500 index options, our approach, which employs one‐day‐ahead 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, and improves the empirical performances. Remarkably, the risk‐neutral volatility dynamics are stable over time in this model. In addition, the comparison between the VIX index and the risk‐neutral integrated volatility economically validates our approach. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 33:1–28, 2013