Variance risk: A bird’s eye view

PurposeThe 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/approachThe 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.FindingsThere 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 implicationsCommodity 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/valueThe 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.

Variance risk in aggregate stock returns and time-varying return predictability

The variance risk premium defined as the difference between risk neutral variance and physical variance is one of the most crucial information recovered from option prices. It does not, however, reflect the asymmetry in upside and downside movements of underlying asset returns, and also has limitation in reflecting asymmetric preference of investors over gains and losses. In this sense, this paper decomposes variance risk premium into downside - and upside-variance risk premium, and then derives the skewness risk premium and examines its effectiveness in predicting future underlying asset returns. Using KOSPI200 option prices, we obtained the following results. First, we found out that the estimated skewness risk premium has meaningful forecasting power for future stock returns, while the estimated variance risk premium has little forecasting power. Second, by utilizing our results of skewness risk premium, we developed a profitable investment strategy, which verifies the effectiveness of skewness risk premium in predicting future stock returns. In conclusion, the empirical results of this paper can contribute to the literature in that it helps us understand why variance risk premium, in most global markets except the US market, has not been successful in forecasting future stock returns. In addition, our results showing the profitability of investment strategies based on skewness risk premium can also give important implications to practitioners.

Variance trading and market price of variance risk

Resolution of Policy Uncertainty and Sudden Declines in Volatility

Variance risk premium and equity returns

Free (Almost) Variance Insurance

Credit default swap spreads and variance risk premia

Variance Risk Premia in Energy Commodities

This article calibrates a class of jump-diffusion long-run risks models and quantifies how well they can account for both equity and variance risk premiums while generating realistic volatility dynamics. I find that jumps in the level and the volatility of long-run consumption growth rates perform equally well in explaining the variance risk premium. Moreover, compared to jump-in-growth models, jump-in-volatility models generate more realistic volatility dynamics and stronger predictability of returns by the variance risk premium. Finally, both jump-in-volatility and jump-in-growth models suggest that a nontrivial portion of the equity risk premium is due to compensation for jump risks.

The intertemporal CAPM model of Merton (Econometrica, 41:867–887, 1973) demonstrates that the aggregate market risk is determined by the uncertainty of the underlying return, quantified by the return variance. When holding the market portfolio, however, an investor is also bearing the uncertainty of the variance itself. Just like the equity premium demanded by investors is the result of fear to the uncertainty of future returns, a variance risk premium, defined as the difference between risk-neutral and physical expected variances is also required to compensate for the randomness of the unknown variance. Many recent studies document the link between risk preference and variance risk premium. In particular, Bakshi and Madan (Manag Sci, 52:1945–1956, 2006) argue that the variance risk premium is approximately determined by the risk aversion parameter and the higher order moments of underlying returns. In a similar vein, Bollerslev (J Financ Quant Anal, 2013) assume an affine version of the stochastic volatility model as in Heston (Rev Financ Stud, 6:327–343, 1993) and show that the variance risk premium is linearly related to the risk aversion parameter. Other investigations in this area includes Bekaert and Engstrom (Asset return dynamics under bad environment-good environment fundamentals, Working Paper, NBER, 2010), Todorov (Rev Financ Stud, 23:345–383, 2010), and Gabaix (Q J Econ, 127:645–700, 2012).

VIX Decomposed Tail Risk Premia and the Tail Risk Factor

Introducing the BITIX: The Bitcoin Fear Gauge

In this paper, we provide a theoretical framework justifying the existence of a correlation risk premium in a market with two traded assets. We prove that risk-neutral dependence can differ substantially from real-world dependence by characterizing the set of risk-neutral martingale measures. This implies that implied correlation can be significantly different with the realized correlation. Depending on the choice of the market regarding the pricing measure, implied correlation can be high or low. We label the difference between risk-neutral and real-world correlation the “correlation gap” and make the connection with correlation risk premium. We show how dispersion trading can be used to exploit this correlation gap and demonstrate how there can exist a negative correlation risk premium in the financial market.

The cross-sectional relation between conditional heteroskedasticity, the implied volatility smile, and the variance risk premium