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.

Equity options display a strong factor structure. The first principal components of the equity volatility levels, skews, and term structures explain a substantial fraction of the crosssectional variation. Furthermore, these principal components are highly correlated with the S&P 500 index option volatility, skew, and term structure, respectively. We develop an equity option valuation model that captures this factor structure. The model predicts that firms with higher market betas have higher implied volatilities, steeper moneyness slopes, and a term structure that covaries more with the market. The model provides a good fit, and the equity option data support the model’s cross-sectional implications.

[We develop a GARCH option model with a new pricing kernel allowing for a variance premium. While the pricing kernel is monotonic in the stock return and in variance, its projection onto the stock return is nonmonotonic. A negative variance premium makes it U shaped. We present new semiparametric evidence to confirm this U-shaped relationship between the risk-neutral and physical probability densities. The new pricing kernel substantially improves our ability to reconcile the time-series properties of stock returns with the cross-section of option prices. It provides a unified explanation for the implied volatility puzzle, the overreaction of long-term options to changes in short-term variance, and the fat tails of the risk-neutral return distribution relative to the physical distribution.]

[Most recent empirical option valuation studies build on the affine square root (SQR) stochastic volatility model. The SQR model is a convenient choice, because it yields closed-form solutions for option prices. We investigate alternatives to the SQR model, by comparing its empirical performance with that of five different but equally parsimonious stochastic volatility models. We provide empirical evidence from three different sources: realized volatilities, S& P500 returns, and an extensive panel of option data. The three sources of data all point to the same conclusion: the best volatility specification is one with linear rather than square root diffusion for variance. This model captures the stylized facts in realized volatilities, it performs well in fitting various samples of index returns, and it has the lowest option implied volatility mean squared error in and out of sample.]

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.

Abstract 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.

Which loss function should be used when estimating and evaluating option valuation models? Many different functions have been suggested, but no standard has emerged. We emphasize that consistency in the choice of loss functions is crucial. First, for any given model, the loss function used in parameter estimation and model evaluation should be the same, otherwise suboptimal parameter estimates may be obtained. Second, when comparing models, the estimation loss function should be identical across models, otherwise inappropriate comparisons will be made. We illustrate the importance of these issues in an application of the so-called Practitioner Black-Scholes model to S&P 500 index options.

Standard option valuation models leave no room for option illiquidity premia. Yet we find the risk-adjusted return spread for illiquid over liquid equity options is 3.4% per day for at-the-money calls and 2.5% for at-the-money puts. These premia are computed using option illiquidity measures constructed from intraday effective spreads for a large panel of U.S. equities, and they are robust to different empirical implementations. Our findings are consistent with evidence that market makers in the equity options market hold large and risky net long positions, and positive illiquidity premia compensate them for the risks and costs of these positions.

[International equity markets are characterized by nonlinear dependence and asymmetries. We propose a new dynamic asymmetric copula model to capture long-run and short-run dependence, multivariate nonnormality, and asymmetries in large cross-sections. We find that correlations have increased markedly in both developed markets (DMs) and emerging markets (EMs), but they are much lower in EMs than in DMs. Tail dependence has also increased, but its level is still relatively low in EMs. We propose new measures of dynamic diversification benefits that take into account higher-order moments and nonlinear dependence. The benefits from international diversification have reduced over time, drastically so for DMs. EMs still offer significant diversification benefits, especially during large market downturns.]

[We provide results for the valuation of European-style contingent claims for a large class of specifications of the underlying asset returns. Our valuation results obtain in a discrete time, infinite state space setup using the no-arbitrage principle and an equivalent martingale measure (EMM). Our approach allows for general forms of heteroskedasticity in returns, and valuation results for homoskedastic processes can be obtained as a special case. It also allows for conditional nonnormal return innovations, which is critically important because heteroskedasticity alone does not suffice to capture the option smirk. We analyze a class of EMMs for which the resulting risk-neutral return dynamics are from the same family of distributions as the physical return dynamics. In this case, our framework nests the valuation results obtained by Duan (1995) and Heston and Nandi (2000) by allowing for a time-varying price of risk and nonnormal innovations. We provide extensions of these results to more general EMMs and to discrete-time stochastic volatility models, and we analyze the relation between our results and those obtained for continuous-time models.]