Optimism and the variance risk premium

We propose methods to improve the forecasts from generalized autoregressive score (GAS) models (Creal et al., 2013; Harvey, 2013) by localizing their parameters using decision trees and random forests, which exploit information in state variables from within and possibly beyond the model. The proposed methods allow the researcher to draw on information from multiple state variables simultaneously and avoid the curse of dimensionality faced by kernel-based approaches. We apply the new models in four distinct empirical analyses, and in all applications the proposed new methods significantly outperform the baseline GAS model. In our applications to stock return volatility and density prediction, the optimal GAS tree model reveals a leverage effect and a variance risk premium effect. Our study of stock-bond dependence finds evidence of a flight-to-quality effect in the optimal GAS forest forecasts, while our analysis of high-frequency trade durations uncovers a volume-volatility effect.

The predictive power of Gold Variance Risk Premium on the Uncovered Interest Parity

Variance risk premia under volatility models

PRICING THE UNKNOWN: EVIDENCE FROM DERIVATIVES MARKETS ON CORPORATE ENVIRONMENTAL TARGETS

ABSTRACTWe examine skew premiums in equity options around earnings announcements. We use the realized returns to delta‐neutral risk reversal option spreads as a proxy for the skew premiums. We find skew premiums are economically significant around earnings announcements and are not explained by changes in variance risk premiums. For firms with negative option‐implied skewness, negative skew premiums triple on earnings announcements. For firms with positive option‐implied skewness, positive skew premiums increase about 23%. The premiums embedded in option prices are associated with order imbalances in puts to calls and are related to both systematic and idiosyncratic risks.

ABSTRACT This paper examines the relationship between economic policy uncertainty, risk aversion, and investors' attention for 15 equity indices across Asia, Europe, and North America. Our empirical results indicate that both risk aversion and economic uncertainty significantly increase the Google Search Volume across all equity indices. Additionally, we employed a Bayesian Panel VAR Model to explore causal relationships between risk aversion and investor attention. The impulse response analysis reveals that a positive shock in variance risk premium consistently triggers an increase in Google Search Volume across stock markets over the following month. These findings suggest that during periods marked by high economic policy uncertainty and elevated risk aversion, investors intensify their internet searches to acquire more specific information about stock indices.

We investigate the degree of asymmetry in the variance risk premium (VRP) using SSE 50 ETF options in the Chinese market. Our approach decomposes the VRP into upside and downside components and quantifies the dynamic spillover asymmetry measure (SAM). This innovative methodology enables us to explore the asymmetric volatility information embedded in VRP, offering valuable insights into investor sentiments and risk perception. By analyzing the volatility spillovers of semi-VRP, we observe that downside VRP exhibits more pronounced fluctuations compared to upside VRP, indicating that risk aversion sentiments intensify during market downturns and exert a greater influence on market risk levels. Additionally, the dynamics of SAM reveal that upside and downside VRP alternately dominate in shaping market volatility, reflecting the time-varying nature of asymmetric risk transmission. Unexpected risky events, such as policy announcements or market crises, emerge as potential drivers that amplify these asymmetries, prompting shifts in investor sentiment and market behavior. These findings contribute to a deeper understanding of the role of asymmetric VRP in financial markets, emphasizing its critical impact on volatility dynamics and the broader market sentiment transition, particularly in the context of emerging markets like China.

ABSTRACTIn this paper, we decompose the variance risk premium (VRP) into overnight and intraday components using model‐free implied variance stock indices in the United States, Europe, and Asia. We find that during the nontrading overnight period, the VRP is significantly negative, whereas during the intraday trading period, the VRP becomes positive and often insignificant. We also assess the predictive ability of the overnight and intraday VRPs with respect to future equity returns. We find that the intraday component performs better at shorter prediction horizons, whereas the overnight VRP performs better at longer horizons. Our empirical results suggest that nontrading effects are an important determinant of the VRP.

The predictive power of the oil variance risk premium

Opportunities for stochastic arbitrage in an options market arise when it is possible to construct a portfolio of options which provides a positive option premium and which, when combined with a direct investment in the underlying asset, generates a payoff which stochastically dominates the payoff from the direct investment in the underlying asset. We provide linear and mixed-integer linear programs for computing the stochastic arbitrage opportunity providing the maximum option premium to an investor. We apply our programs to 18 years of data on monthly put and call options on the Standard & Poors 500 index, finding no evidence that stochastic arbitrage opportunities are systematically present. A skewed specification of the underlying market return distribution with a constant market risk premium and constant multiplicative variance risk premium is broadly consistent with the pricing of market index options at moderate strikes.

ABSTRACT This paper provides an accounting-based valuation model that predicts that cross-sectional variation in firm-level returns to investments in both stock and stock return volatility are related to cross-sectional variation in firm-level fundamentals. The model predicts that expected stock returns have a positive quadratic relation with stock return variance and a negative quadratic relation with gains to trading in stock return variance. Consistent with these predictions, firms with high model-implied expected stock returns have high future stock return variance, and the relation is roughly quadratic. In contrast, firms with high expected stock returns have low future returns to trading in stock return variance through option contracts because these firms have high option-implied variance relative to future realized variance, i.e., low variance risk premia (VRP). The study provides a framework for using fundamentals for trading in individual stocks and options. JEL Classifications: G12; G14; G17.

This paper examines the impact of intraday periodicity on forecasting realized volatility using a heterogeneous autoregressive model (HAR) framework. We show that periodicity inflates the variance of the realized volatility and biases jump estimators. This combined effect adversely affects forecasting. To account for this, we propose a periodicity-adjusted HAR model, HARP, where predictors are constructed from the periodicity-filtered data. We demonstrate empirically (using 30 stocks from various business sectors and the SPY for the period 2000–2020) and via Monte Carlo simulations that the HARP models produce significantly better forecasts across all forecasting horizons. We also show that adjusting for periodicity when estimating the variance risk premium improves return predictability.

In this article, we review recent developments in macroeconomics and finance on the relationship between financial risk and the real economy. We focus on three specific topics: (a) the term structure of uncertainty, (b) time variation—specifically, the long-term decline—in the variance risk premium, and (c) time variation in conditional skewness. We also introduce two new data series: implied volatility from one-day options on grains for the period 1906–1936 and prices of cliquet options, which provide insurance against single-day crashes on the S&P 500. Both series give some context to the recent rise in trade in extremely short-dated options. Finally, we discuss new avenues for future research.

We develop an automated system to forecast volatility by leveraging more than 100 features and five machine learning algorithms. Considering the universe of S&P 100 stocks, our system results in superior out-of-sample volatility forecasts compared with existing risk models across forecast horizons. We further demonstrate that our system remains robust to different specifications and is scalable to a broader S&P 500 stock universe via hyperparameter transfer learning. Finally, the statistical improvement in volatility forecasts translates into significant annual returns from a cross-sectional variance risk premium strategy. This paper was accepted by Lin William Cong, finance. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.01520 .

Impact of crude oil price innovations on global stock market volatility: Evidence across time and space

Time-varying risk aversion and international stock returns

Abstract We present a novel predictor for the Dollar factor: variance risk premia imbalances (VPI), defined as the difference in variance risk premium between the U.S. and non‐U.S. countries. We argue that VPI theoretically proxies the average volatility differential between the U.S. and non‐U.S. stochastic discount factors. VPI significantly predicts monthly U.S. dollar movements, explains roughly 10% of next‐month Dollar factor variation, and generates significant economic value for investors. We rationalize our findings in a simple consumption‐based asset pricing model.

ABSTRACTThe stylized fact that volatility is not priced in individual equity options does not withstand scrutiny. First, we show that the average return of heavily traded deep out‐of‐the‐money call options on stocks is −116 basis points per day. Second, Fama‐MacBeth estimates of the volatility risk premium in stock options are similar to those in S&P 500 Index call options. Third, the mean return of heavily traded delta‐hedged at‐the‐money calls (puts) is −23 (−30) basis points. Fourth, the variance risk premium in stock options is negative. Our analysis highlights the importance of microstructure biases and robustness in empirical work with options.

Variance risk premiums in emerging markets