We develop a discrete-time option pricing model using a variance-dependent pricing kernel of Christoffersen, Heston and Jacobs (2013) under an economic framework allowing for dynamic volatility and dynamic jump intensity. Using this model, we examine the role of the variance premium and jump risk premium in explaining S&P 500 index option returns. Our results stress the importance of the variance premium in explaining the stylized characteristics of index option returns, including short-term option returns, which are insufficiently explained by extant option pricing models. In particular, the variance premium can explain both 1-month holding period returns of 2-month maturity straddles, which are significantly negative, and call returns, which decrease according to moneyness. Even though the jump risk premium emphasized in the previous literature is able to well fit the option prices, it does not improve the explanatory power for the above two stylized option returns. The outperformance of the variance premium stems from its ability to capture the wedge between physical and risk-neutral volatilities.