Abstract
In this study, we modify the classical generalized autoregressive conditional heteroskedastic (GARCH) process by introducing a new uncertainty into the volatility process. We then change probability measures from physical to risk-neutral ones by extending Duan’s (1995) locally risk-neutral valuation relationship (LRNVR). With the information of both daily index returns and the Chicago Board Options Exchange (CBOE) Volatility Index (VIX), we estimate daily variances and model parameters by using the maximum likelihood method. The new modified GARCH process solves the problem of variance risk premium in the GARCH option models completely.