We show that the compensation for rare events accounts for a large fraction of the equity and variance risk premia in the S&P 500 market index. The probability of rare events vary significantly over time, increasing in periods of high market volatility, but the risk premium for tail events...

We show that the compensation for rare events accounts for a large fraction of the average equity and variance risk premia. Exploiting the special structure of the jump tails and the pricing thereof we identify and estimate a new Investor Fears index. The index suggests both large and...

Stock market volatility clusters in time, appears fractionally integrated, carries a risk premium, and exhibits asymmetric leverage effects relative to returns. At the same time, the volatility risk premium, defined by the difference between the risk-neutral and objective expectations of the...

Recent empirical evidence suggests that the variance risk premium predicts aggregate stock market returns. We demonstrate that statistical finite sample biases cannot “explain” this apparent predictability. Further corroborating the existing evidence of the U.S., we show that country...

Stock market volatility clusters in time, appears fractionally integrated, carries a risk premium, and exhibits asymmetric leverage effects relative to returns. At the same time, the volatility risk premium, defined by the difference between the risk-neutral and objective expectations of the...

We propose new refined measures of the local covariation between the return on an asset and a risk factor. Our proposed "granular betas" generalize the notion of up- and down-side betas to multi-factor functional measures of covariation. We then show how the resulting granular beta functions may...

Jumps in asset prices are ubiquitous, yet the apparent high price of jump risk observed empirically is widely viewed as puzzling. Importantly however, in addition to direct price risks, jumps may also trigger simultaneous changes in other distributional features of asset returns. We develop...

Recent empirical evidence suggests that the variance risk premium predicts aggregate stock market returns. We demonstrate that statistical finite sample biases cannot “explain” this apparent predictability. Further corroborating the existing evidence of the U.S., we show that country...