This paper examines the joint time series of the S&P 500 index and near-the-money short-dated option prices with an arbitrage-free model, capturing both stochastic volatility and jumps. Jump-risk premia uncovered from the joint data respond quickly to market volatility, becoming more prominent during volatile markets. This form of jump-risk premia is important not only in reconciling the dynamics implied by the joint data, but also in explaining the volatility "smirks" of cross-sectional options data. Further diagnostic tests suggest a stochastic-volatility model with two factors --- one strongly persistent, the other quickly mean-reverting and highly volatile.