A stylized theoretical model with stochastic volatility suggests the existence of a trade-off between returns and volatility-of-volatility. Using the VVIX, a measure of the option-implied volatility of the volatility index, we confirm this prediction and detect that time-varying aggregate volatility-of-volatility commands an economically substantial and statistically significant negative risk premium. We find that a two-standard-deviation increase in aggregate volatility-of-volatility factor loadings is associated with a decrease in average annual returns of about 11%. These results are robust to controlling for aggregate volatility, jump risk, and several other characteristics and factor sensitivities, as well as various additional tests. Received September 05, 2016; accepted June 21, 2017 by Editor Raman Uppal

In this paper, we identify the most suitable low-frequency proxies for analyzing commodity market quality. We use an 11-year sample of millisecond time-stamped order book data and examine the correlation of high-frequency liquidity and price efficiency measures with their low-frequency proxies measured with daily or 5-min Time-and-Sales (TAS) data. We find that for liquidity, the volatility-over-volume measures are the best proxies for bid–ask spread and price impact. The correlation of price efficiency measures with their daily-frequency counterparts is low. Moderately correlated proxies can be achieved by using 5-min data.

In this paper, we develop a continuous time factor model of commodity prices that allows for higher-order autoregressive and moving average components. We document the need for these components by analyzing the convenience yield’s time series dynamics. The model we propose is analytically tractable and allows us to derive closed-form pricing formulas for futures and options. Empirically, we estimate a parsimonious version of the general model for the crude oil futures market and demonstrate the model’s superior performance in pricing nearby futures contracts in- and out-of-sample. Most notably, the model substantially improves the pricing of long-horizon contracts with information from the short end of the futures curve.

In this paper, we study the role of the volatility risk premium for the forecasting performance of implied volatility. We introduce a non-parametric and parsimonious approach to adjust the model-free implied volatility for the volatility risk premium and implement this methodology using more than 20years of options and futures data on three major energy markets. Using regression models and statistical loss functions, we find compelling evidence to suggest that the risk premium adjusted implied volatility significantly outperforms other models, including its unadjusted counterpart. Our main finding holds for different choices of volatility estimators and competing time-series models, underlying the robustness of our results.

We propose a momentum strategy that operates within commodity futures curves. The diversified curve momentum strategy generates a significantly positive average excess return and a (annualized) Sharpe ratio of 1.28. The profitability of the strategy has increased markedly in the more recent years. These excess returns are difficult to reconcile with risk based explanations, as evidenced by the significantly positive alpha after controlling for exposure to several well-known risk factors. The average excess return on the diversified curve momentum strategy remains significantly positive even after accounting for transaction costs.

We analyze the risk premia embedded in the S&P 500 spot index and option markets. We use a long time-series of spot prices and a large panel of option prices to jointly estimate the diffusive stock risk premium, the price jump risk premium, the diffusive variance risk premium and the variance jump risk premium. The risk premia are statistically and economically significant and move over time. Investigating the economic drivers of the risk premia, we are able to explain up to 63% of these variations.

We conduct a comprehensive comparison of market beta estimation techniques. We study the performance of several historical, time-series model, and option-implied estimators for estimating realized market beta. Thereby, we find the hybrid methodology of Buss and Vilkov to consistently outperform all other approaches. In addition, all other approaches, including fully implied and dynamic conditional beta, based on generalized autoregressive conditional heteroskedasticity (GARCH) models, are dominated by a simple beta estimate based on historical (co-)variances and an approach based on the Kalman filter. Our conclusions remain unchanged after performing several robustness checks.

The standard full-sample time-series asset pricing test suffers from poor statistical properties, look-ahead bias, constant-beta assumptions, and rejects models when average factor returns deviate from risk premia. We therefore confront prominent equity pricing models with the classical Fama and MacBeth (1973) cross-sectional test. For all models, we uncover three main findings: (i) the intercept coefficients are economically large and highly statistically significant; (ii) cross-sectional factor risk premium estimates are generally far below the average factor excess returns; and (iii) they are usually not statistically significant. Overall, all new factor models are inconsistent with no-arbitrage pricing and cannot accurately explain the cross-section of stock returns.

Factors related to carry, duration, equity momentum, and the term structure are the most important risk factors in corporate bond markets. From a large set of factor candidates, we condense an optimal model with a two-step approach. First, we filter out factors that do not systematically move bond prices. Second, we use a Bayesian model selection approach to determine the optimal, parsimonious model. Many prominent factors do not move prices or are redundant. We document the new model’s good performance compared to that of existing models in time-series and cross-sectional tests and analyze the economic drivers of the factors.

Price movements in many commodity markets exhibit significant seasonal patterns. However, given an observed futures price, a deterministic seasonal component at the price level is not relevant for the pricing of commodity options. In contrast, this is not true for the seasonal pattern observed in the volatility of the commodity price. Analyzing an extensive sample of soybean, corn, heating oil and natural gas options, we find that seasonality in volatility is an important aspect to consider when valuing these contracts. The inclusion of an appropriate seasonality adjustment significantly reduces pricing errors in these markets and yields more improvement in valuation accuracy than increasing the number of stochastic factors.