The Jump-Risk Premia Implicit in Options: Evidence from an Integrated Time-Series Study

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. ∗MIT Sloan School of Management, 50 Memorial Drive, Cambridge, MA 02142. Email: [email protected]. I benefited from discussions with professors and doctoral students in the finance program at Stanford. I am especially grateful to my advisers, Darrell Duffie and Ken Singleton, who inspired me to take on this project, and helped with their insightful comments and warm encouragement. I also benefited from extensive discussions with Jun Liu, as well as comments from two anonymous referees, Andrew Ang, David Bates, Joe Chen, Mark Ferguson, Peter Glynn, Harrison Hong, Ming Huang, Mike Johannes, George Papanicolaou, Monika Piazzesi, Tom Sargent, and seminar participants at Stanford, Berkeley, MIT, UCLA, HBS, Rochester, Wisconsin Madison, Michigan, Duke, Kellogg, Chicago, Columbia, the Stanford Financial Engineering Workshop, Cornell, Minnesota, the Conference on Risk Neutral and Objective Probability Distributions, Boston College, and the 2001 AFA meetings. This paper was previously circulated as “Integrated Time-Series Analysis of Spot and Option Prices.” It can be downloaded from www.mit.edu/~junpan/.