We use prices of equity index options to quantify the impact of extreme events on asset returns. We define extreme events as departures from normality of the log of the pricing kernel and summarize their impact with high-order cumulants: skewness, kurtosis, and so on. We show that high-order...

Identification problems arise naturally in forward-looking models when agents observe more than economists. We illustrate the problem in several New Keynesian and macro-finance models in which the Taylor rule includes a shock unseen by economists. We show that identification of the rule's...

We propose two metrics for asset pricing models and apply them to representative agent models with recursive preferences, habits, and jumps. The metrics describe the pricing kernel's dispersion (the entropy of the title) and dynamics (time dependence, a measure of how entropy varies over...