GARCH Option Pricing Models, the CBOE VIX, and Variance Risk Premium

In this article, we derive the corresponding implied VIX formulas under the locally risk-neutral valuation relationship (LRNVR) proposed by Duan (1995) when a class of square-root stochastic autoregressive volatility (SR-SARV) models are proposed for S&P 500 index. The empirical study shows that the GARCH implied VIX is consistently and significantly lower than the CBOE VIX for all kinds of GARCH model investigated when they are estimated with returns only. When jointly estimated with both returns and VIX, the parameters are distorted unreasonably, and the GARCH implied VIX still cannot fit the CBOE VIX from various statistical aspects. The source of this discrepancy is then theoretically analyzed. We conclude that the GARCH option pricing under the LRNVR fails to incorporate the price of volatility or variance risk premium. Copyright The Author, 2013. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com, Oxford University Press.