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.]

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.]

[Observable covariates are useful for predicting default, but several studies question their value for explaining credit spreads. We introduce a discrete-time no-arbitrage model with observable covariates, which allows for a closed-form solution for the value of credit default swaps (CDS). The default intensity is a quadratic function of the covariates, specified such that it is always positive. The model yields economically plausible results in terms of fit, the economic impact of the covariates, and the prices of risk. Risk premiums are large and account for a smaller percentage of spreads for firms with lower credit quality. Macroeconomic and firm-specific information can explain most of the variation in CDS spreads over time and across firms, even with a parsimonious specification. These findings resolve the existing disconnect in the literature regarding the value of observable covariates for credit risk pricing and default prediction.]

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.

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.