This article develops a nonmonotonic pricing kernel with long-run and short-run variance risk premiums for option valuation, with a proposed pricing kernel retaining a U-shaped pattern that significantly improves the fitting ability for index options pricing and implied volatility. The estimation results show that the long-run volatility component is critical in generating the negative risk premium. In the in-sample and out-of-sample tests, the model with the new pricing kernel has more accurate predictions, especially the year around the financial crisis, wherein there is a decrease of an average of 35% root mean square error relative to the benchmark. Considering the bull and bear market states, our model improves implied volatility root mean square error by 23% on average.
