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

Abstract

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. (c) 2011 Wiley Periodicals, Inc. Jrl Fut Mark 33:128, 2013