We find that firm-level variance risk premium, estimated as the difference between option-implied and expected variances, has a prominent explanatory power for credit spreads in the presence of market- and firm-level risk control variables identified in the existing literature. Such a...

We develop two novel approaches to solving for the Laplace transform of a time-changed stochastic process. We discard the standard assumption that the background process (X_t) is Levy. Maintaining the assumption that the business clock (T_t) and the background process are independent, we develop...

This paper reports on tail risk premiums in two tail risk hedging strategies: the S&P 500 puts and the VIX calls. As a new measure of tail risk, we suggest using a model-free, risk-neutral measure of the volatility of volatility implied by a cross section of the VIX options, which we call the...

We derive an option-pricing formula from recursive preference and estimate rare disaster probability. The new options-pricing formula applies to far-out-of-the money put options on the stock market when disaster risk dominates, the size distribution of disasters follows a power law, and the...