Pricing CBOE VIX in non-affine GARCH models with variance risk premium

The commonly used local risk-neutral valuation relationship (LRNVR) for non-affine GARCH models only compensates for the equity risk premium. In this paper, we propose a direct approach to bridge the physical and risk-neutral measures for non-affine GARCH models, explicitly accounting for the variance risk premium. This method avoids the need to specify a particular form of pricing kernel when it is potentially complex. The closed-form CBOE VIX pricing formulas can be easily derived for several popular non-affine GARCH models, including EGARCH, GJR-GARCH, and NGARCH. Empirical results demonstrate that the newly proposed framework yields superior pricing performance for CBOE VIX.