This paper investigates Euler equations involving security prices and household‐level consumption data. It provides a useful complement to many existing studies of consumption‐based asset pricing models that use a representative‐agent framework, because the Euler equations under investigation hold even if markets are incomplete. It also provides a useful complement to simulation‐based studies of market incompleteness. The empirical evidence indicates that the theory is rejected by the data along several dimensions. The results therefore indicate that some well‐documented asset‐pricing puzzles do not result from aggregation problems for the preferences under investigation.

Expected returns on market volatility, which can be obtained from VIX futures prices in closed form using standard models, positively predict subsequent realized volatility returns. Volatility returns are negative on average. Following increases in volatility, expected volatility returns and subsequent realized volatility returns become more negative. Because realized volatility returns are negatively correlated with index returns, expected volatility returns also negatively predict S&P 500 index returns, but these results are less significant. The results are robust to a wide range of variations in the empirical setup and to small-sample biases.

Rather than assuming a fixed recovery rate in estimation, we estimate recovery rates from credit default swap spreads, using 3 years of daily data on 152 corporations. We use a quadratic pricing model, which ensures nonnegative default probabilities and recovery rates. The estimated cross section of recovery rates is plausible, with an average recovery rate of 54% and substantial cross-sectional variation. Estimated 5-year default probabilities are on average 67% higher than default probabilities obtained using the standard 40% recovery assumption. This finding critically impacts the valuation of structured credit products. Larger firms and firms with more tangible assets have higher recovery rates.

This paper investigates the importance of idiosyncratic consumption risk for the cross‐sectional variation in asset returns. We find that besides the rate of aggregate consumption growth, the cross‐sectional variance of consumption growth is also a priced factor. This suggests that consumers are not fully insured against idiosyncratic consumption risk, and that asset returns reflect their attempts to reduce their exposure to this risk. The resulting two‐factor consumption‐based asset pricing model significantly outperforms the CAPM, and its performance compares favorably with that of the Fama–French three‐factor model.

Both large oil price increases and decreases are associated with deteriorating economic conditions. The projection of the state price density (SPD) onto oil returns estimated from oil futures and option prices displays a U-shaped pattern. Because investors assign high state prices to large negative and large positive oil returns, the U-shaped SPD may steepen in either tail when economic conditions deteriorate. The positive return region of the SPD is more closely related to economic conditions. The oil SPD contains information about economic conditions and future security returns that is distinct from the information in the stock index SPD.

We specify and estimate a no-arbitrage model for sovereign CDS contracts in which countries’ default intensities depend on economic and financial indicators. To facilitate identification and to distinguish the importance of local and global covariates, we estimate a model with three global and four local covariates using CDS spreads for five maturities and twenty-five countries. The model provides a good fit. The impact of the economic and financial variables on spreads is consistent with economic intuition, and substantially varies across countries and over time. Estimated risk premiums are highly variable and peak during the 2008 financial crisis for most countries.

We analyze the relation between expected option returns and the volatility of the underlying securities. The expected return from holding a call (put) option is a decreasing (increasing) function of the volatility of the underlying. These predictions are supported by the data. In the cross section of equity option returns, returns on call (put) option portfolios decrease (increase) with underlying stock volatility. This finding is not due to cross-sectional variation in expected stock returns. It holds in various option samples with different maturities and moneyness, and is robust to alternative measures of underlying volatility and different weighting methods.

We develop a tractable dynamic model of an index option market maker with limited capital. We solve for the variance risk premium and option prices as a function of the asset dynamics and market maker option holdings and wealth. The market maker absorbs end users’ positive demand and requires a more negative variance risk premium when she incurs losses. We estimate the model using returns, options, and inventory and find that it performs well, especially during the financial crisis. The restrictions imposed by nested existing reduced-form stochastic-volatility models are strongly rejected in favor of the model with a market maker.

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 study the ability of three-factor affine term-structure models to extract conditional volatility using interest rate swap yields for 1991–2005 and Treasury yields for 1970–2003. For the Treasury sample, the correlation between model-implied and EGARCH volatility is between 60% and 75%. For the swap sample, this correlation is rather low or negative. We find that these differences in model performance are primarily due to the timing of the swap sample, and not to institutional differences between swap and Treasury markets. We conclude that the ability of multifactor affine models to extract conditional volatility depends on the sample period, but that overall these models perform better than has been argued in the literature.