Variance Risk Premia, Asset Predictability Puzzles, and Macroeconomic Uncertainty

Purpose The purpose of this paper is to study the variance risk premium in corn and soybean markets, where the variance risk premium is defined as the difference between the historical realized variance and the corresponding risk-neutral expected variance. Design/methodology/approach The authors compute variance risk premiums using historical derivatives data. The authors use regression analysis and time series econometrics methods, including EGARCH and the Kalman filter, to analyze variance risk premiums. Findings There are moderate commonalities in variance within the agricultural sector, but fairly weak commonalities between the agricultural and the equity sectors. Corn and soybean variance risk premia in dollar terms are time-varying and correlated with the risk-neutral expected variance. In contrast, agricultural commodity variance risk premia in log return terms are more likely to be constant and less correlated with the log risk-neutral expected variance. Variance and price (return) risk premia in agricultural markets are weakly correlated, and the correlation depends on the sign of the returns in the underlying commodity. Practical implications Commodity variance (i.e. volatility) risk cannot be hedged using futures markets. The results have practical implications for US crop insurance programs because the implied volatilities from the relevant options markets are used to estimate the price volatility factors used to generate premia for revenue insurance products such as “Revenue Protection” and “Revenue Protection with Harvest Price Exclusion.” The variance risk premia found implies that revenue insurance premia are overpriced. Originality/value The empirical results suggest that the implied volatilities in corn and soybean futures market overestimate true expected volatility by approximately 15 percent. This has implications for derivative products, such as revenue insurance, that use these implied volatilities to calculate fair premia.

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Option-Based Estimation of the Price of Coskewness and Cokurtosis Risk

Journal of Financial and Quantitative Analysis ◽

10.1017/s002210902000023x ◽

2020 ◽

pp. 1-27

Author(s):

Peter Christoffersen ◽

Mathieu Fournier ◽

Kris Jacobs ◽

Mehdi Karoui

Keyword(s):

Risk Premium ◽

Risk Premia ◽

Factor Models ◽

Option Prices ◽

Variance Risk Premium ◽

Market Return ◽

Price Of Risk ◽

Variance Risk ◽

Index Option

Abstract We show that the prices of risk for factors that are nonlinear in the market return can be obtained using index option prices. The price of coskewness risk corresponds to the market variance risk premium, and the price of cokurtosis risk corresponds to the market skewness risk premium. Option-based estimates of the prices of risk lead to reasonable values of the associated risk premia. An analysis of factor models with coskewness risk indicates that the new estimates of the price of risk improve the models’ performance compared with regression-based estimates.

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