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. (JEL G12)

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.

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 energy futures option returns for crude oil, natural gas, heating oil, and gasoline. Average call and put returns are negative at short maturities, more so for OTM options, and increase with maturity. Put returns are less negative than call returns, but this is not the case for delta-hedged returns, indicating that the aggregate risk of the underlying energy futures is priced in the raw option returns. Moneyness patterns in raw and delta-hedged returns are similar to patterns for index option returns. Significant differences between the four commodities remain after removing the effect of the underlying futures returns, with natural gas as the main outlier. Variance risk premiums are negative and explain some maturity patterns in returns, but they cannot account for return differences across markets. Energy producers are net short the underlying through their option positions, and speculators net long. The larger the net long position of the speculators, the lower the returns on call options, which suggests that demand from speculators may affect option returns in energy markets.

We build a new class of discrete-time models that are relatively easy to estimate using returns and/or options. The distribution of returns is driven by two factors: dynamic volatility and dynamic jump intensity. Each factor has its own risk premium. The models significantly outperform standard models without jumps when estimated on S&P500 returns. We find very strong support for time-varying jump intensities. Compared to the risk premium on dynamic volatility, the risk premium on the dynamic jump intensity has a much larger impact on option prices. We confirm these findings using joint estimation on returns and large option samples.

We characterize dependence in corporate credit and equity returns for 215 firms using a new class of large-scale dynamic copula models. Copula dependence and especially tail dependence are highly variable and persistent, increase significantly in the financial crisis, and have remained high since. The most drastic increases in credit dependence occur in July/August of 2007 and in August of 2011 and the decrease in diversification potential caused by the increases in dependence and tail dependence is large. Credit default swap correlation dynamics are important determinants of credit spreads.

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 cross-sectional 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. Received December 20, 2013; editorial decision April 15, 2017 by Editor Leonid Kogan.

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. The Author 2013. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: [email protected]., Oxford University Press.

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, andit has the lowest option implied volatility mean squared error in and out of sample.

The cross-section of stock returns has substantial exposure to risk captured by higher moments in market returns. We estimate these moments from daily S&P 500 index option data. The resulting time series of factors are thus genuinely conditional and forward-looking. Stocks with high sensitivities to innovations in implied market volatility and skewness exhibit low returns on average, whereas those with high sensitivities to innovations in implied market kurtosis exhibit high returns on average. The results on market skewness risk are extremely robust to various permutations of the empirical setup. The estimated premium for bearing market skewness risk is between -6.00% and -8.40% annually. This market skewness risk premium is economically significant and cannot be explained by other common risk factors such as the market excess return or the size, book-to-market, momentum, and market volatility factors. Using ICAPM intuition, the negative price of market skewness risk indicates that it is a state variable that negatively affects the future investment opportunity set.