Option-Implied Correlations and the Price of Correlation Risk∗

We provide evidence that the risk of changes in equity correlations is priced, using data on S&P100 options and options on all the stocks in the index. We develop a model for equity prices with priced correlation risk, which generates (i) option-implied correlations that exceed realized correlations, (ii) a zero difference between implied and realized equity variances, (iii) endogenous stochastic index volatility with a positive difference between implied and realized index variance, and (iv) expected index option returns that are well below individual option returns. Empirically, we find a negative correlation risk premium, and show that all four model implications are matched by the data. We also show that standard models with priced jumps or stochastic volatility for individual equity returns fail to explain these empirical features of index and individual options.