This paper examines the properties of the variance risk premium (VRP). We propose a flexible asset pricing model that captures co-jumps in prices and volatility, and self-exciting jump clustering. We estimate the model on equity returns and variance swap rates at different horizons. The total VRP is negative and has a downward-sloping term structure, while its jump component displays an upward-sloping term structure. The abrupt and persistent response of the short-term jump VRP to extreme events makes this specific premium a proxy for investors' fear of a market crash. Furthermore, the use of the VRP level and slope, and of its components, helps improve the short-run predictability of equity excess returns.

I extend the evidence on the basic stylized facts documented for the U.S. variance risk premium (VP) and show that, while VPs in other countries are also positive and time varying, they do not have predictive power for domestic stock returns, in contrast to the implications of existing single-country models. I also provide new empirical evidence that the U.S. VP has predictive power for international stock returns. To rationalize these results, I propose a two-country general equilibrium model and show that my model explains the predictive power of U.S. VP for international stock returns and the domestic predictability puzzle.