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.

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.

Many commodity markets contain a strong seasonal component not only at the price level, but also in volatility. In this paper, the importance of seasonal behavior in the volatility for the pricing of commodity options is analyzed. We propose a seasonally varying long-run mean variance process that is capable of capturing empirically observed patterns. Semi-closed-form option valuation formulas are derived. We then empirically study the impact of the proposed Seasonal Stochastic Volatility Model on the pricing accuracy of natural gas futures options traded at the New York Mercantile Exchange (NYMEX) and corn futures options traded at the Chicago Board of Trade (CBOT). Our results demonstrate that allowing stochastic volatility to fluctuate seasonally significantly reduces pricing errors for these contracts.