The conditional covariance between the market return and its variance, which we refer to as the leverage effect, is positively related to the variance risk premium. It contains incremental information about the variance risk premium after controlling for other return moments and additional variables suggested by the literature as determinants of the variance risk premium. This empirical finding is supported by theory: the pricing of volatility risk is the economic channel behind the strong positive relation between the two variables. We use this relation to construct a time series of the variance risk premium dating back to 1926. (JEL G12, G13) Received February 7, 2020; editorial decision September 01, 2021.

We develop a model that generates slowly unfolding disasters not only in the macroeconomy but also in financial markets. In our model, investors cannot exactly distinguish whether the economy is experiencing a mild/temporary downturn or is on the verge of a severe/prolonged disaster. Due to imperfect information, disaster periods are not fully identified by investors ex ante. Bayesian learning induces equity prices to gradually react to persistent consumption declines, which plays a critical role in explaining the VIX, variance risk premium, and put-protected portfolio returns. We show that our model can rationalize the market patterns of recent major crises, such as the dot-com bubble burst, Great Recession, and COVID-19 crisis, through investors' belief channel.

The identification of disaster risk has remained a significant challenge due to the rarity of macroeconomic disasters. We show that the interbank market can help characterize the time variation in disaster risk. We propose a risk-based model in which macroeconomic disasters are likely to coincide with interbank market failure. Using interbank rates and their options, we estimate our model via maximum likelihood estimation (MLE) and filter the short-run and long-run components of disaster risk. Our estimation results are independent of the stock market and serve as an external validity test of rare disaster models, which are typically calibrated to match stock moments.

We investigate whether a model with time‐varying probability of economic disaster can explain prices of collateralized debt obligations. We focus on senior tranches of the CDX, an index of credit default swaps on investment grade firms. These assets do not incur losses until a large fraction of previously stable firms default, and thus are deep out‐of‐the money put options on the overall economy. When calibrated to consumption data and to the equity premium, the model explains the spreads on CDX tranches prior to and during the 2008 to 2009 crisis.

We synthetically create option contracts on a corporate bond index using CDX swaptions, overcoming the limitations that stem from the lack of traded corporate bond options. Our approach allows us to estimate forward-looking moments concerning the corporate bond market in a model-free manner. By constructing an aggregate volatility measure and the associated variance risk premium, we examine the role of volatility risk in the corporate bond market. We highlight that the ex ante conditional second and higher moments we estimate from synthetic corporate bond options carry important implications for credit risk models, providing an extra basis for testing their validity.

We develop a structural credit risk model, which allows us to price equity/credit indices and their options through the asset dynamics of index constituents. We estimate the model via MLE and find that equity and credit index option prices are well explained out-of-sample. Contrary to recent empirical findings, the two option markets are not inconsistently priced through the lens of our model. Returns on both options, while extreme, do not indicate any evidence of mispricing. Our analysis suggests that jointly addressing the pricing of various instruments requires properly attributing three different sources of systematic risk: asset, variance, and jump risks.