Variance Risk Premium Research Articles

Automated Volatility Forecasting

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

This study investigates the impact of crude oil price innovations on global stock market volatility through a ripple-spreading network model, incorporating four dimensions of crude oil price changes: realized volatility, implied volatility, variance risk premium, and realized skewness volatility. Additionally, we assess the effects of three types of crude oil shocks—oil-specific, aggregate demand, and oil supply shocks. The results indicate that while all four dimensions exhibit similar temporal diffusion patterns, their spatial impacts differ. Global stock markets demonstrate heightened sensitivity to implied volatility and variance risk premium, followed by realized volatility and, lastly, realized skewness volatility. Moreover, we find that realized volatility spreads through multiple transmission pathways, albeit at a slower pace compared to implied volatility and the variance risk premium. Among the crude oil shocks, oil-specific shock induces the most rapid volatility transmission across global markets, with aggregate demand shock following and oil supply shock exerting the smallest influence.

Valuation and Returns on Stock Return Volatility

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.

Time-varying risk aversion and international stock returns

We estimate aggregate, time-varying risk aversion inferred from options, stock returns and macroeconomic data for a panel of 8 countries. We document that, for most countries, the estimated risk aversion measure is counter-cyclical. Moreover, we show that estimated risk aversion forecasts monthly stock index returns up to 12 months ahead. This effect is statistically significant in panel regressions, and it survives the inclusion of additional control variables, such as an estimated of the variance risk premium, an investors’ sentiment index, and a measure of economic uncertainty. Finally, we show that risk aversion provides useful information to an investor who aims at timing the market. An investment strategy that uses the estimated time-varying risk aversion measure to solve a mean–variance asset allocation problem, delivers significantly positive returns.

The U.S. Dollar and variance risk premia imbalances

The U.S. Dollar and variance risk premia imbalances

Very Noisy Option Prices and Inference Regarding the Volatility Risk Premium

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.

How do market volatility and risk aversion sentiment inter-influence over time? Evidence from Chinese SSE 50 ETF options

We propose to implement the TVP-VAR-SV model and the spillover index approach to investigate the dynamics of mutual influences between market volatility and risk aversion sentiment (represented by variance risk premium), from aspects of realized variance (RV) and implied variance (IV). We innovatively study the evolution of volatility information transmission mechanisms by analyzing time-varying impulse response and dynamic connectedness in the Chinese market. Upon inspecting shock effects from investor sentiment to RV and IV, we discover that investor sentiment can cause sudden shocks on realized volatility but produce expansive shocks on expected volatility. As we compare spillover effects in call and put options, we find that (i) sentiments in put option contain more volatility information and can affect market volatility, while sentiments in call option primarily perceive volatility spillovers from market volatility, and (ii) investor sentiments in call (put) option become to present more volatility information in a bullish (bearish) market. Our study provides valuable insights on behavioral finance theory and portfolio risk management.

A rational finance explanation of the stock predictability puzzle

AbstractWe address the stock predictability puzzle, a challenge in the stock market often discussed in behavioral finance. Our approach formulates a statistical model within rational finance, avoiding reliance on behavioral finance assumptions, and integrates stock return predictability into the Black–Scholes option pricing framework. Empirical analysis focuses on the predictability of stock prices by option and spot traders, introducing a forward‐looking measure we term “implied excess predictability.” Results show that option traders' predictability of stock returns positively correlates with moneyness, whereas for spot traders, this relationship is inverse. These findings suggest a potential asymmetry in stock price predictability between spot and option traders. Additionally, we demonstrate the importance of incorporating stock return predictability into option pricing formulas, particularly for options with strike prices significantly different from the stock price. Conversely, when moneyness is close to unity, predictability is not integrated into option pricing, indicating equal information among spot and option traders. Comparison of volatility measures reveals the difference between implied and realized variances or variance risk premia as potential predictors of stock returns.

Variance risk premiums in emerging markets

We provide for the first time the emerging market variance risk premium (EMVRP) from 2006 to 2023, based on nine emerging stock and option markets—Brazil, China, India, South Korea, Mexico, Poland, Russia, South Africa, and Taiwan. The EMVRP significantly predicts international stock returns and currency appreciation rates, especially for horizons longer than six months. This is in sharp contrast with the predictive pattern of the developed market variance risk premium (DMVRP), which is more important over horizons shorter than six months. These findings are consistent with an illustrative model incorporating partial market integration and heterogeneous economic uncertainty.

Recent Developments in Financial Risk and the Real Economy

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.

The asymmetry in day and night option returns: Evidence from an emerging market

AbstractDelta‐hedged option selling strategies typically yield positive returns, owing to the volatility risk premium embedded in the option price. Recent research based on S&P 500 options has found a day–night asymmetry in option returns. We find a similar disparity in the returns for short Nifty option strategies. Positive and significant overnight option returns are accompanied by negative intraday returns. The day–night asymmetry is robust across option categories and subsamples but weaker on days with significant jumps in the underlying. We confirm that the variance risk premium earned by option sellers is mainly a reward for overnight risk.

Predictability Puzzles

Abstract Dynamic equilibrium models based on present value computation not only imply that returns are predictable but also generate particular short-term patterns of predictability in asset returns. I take advantage of this to construct a set of tests of equilibrium generated predictability (EGP). I apply the tests to document two puzzles: First, option-implied or realized measures of volatility ought to predict returns but do not; and second, the variance risk premium (VRP) predicts returns but only at long horizons. VRP fails the tests of EGP as the term structure of predictable variation is inconsistent with an equilibrium interpretation.

Instantaneous volatility of the yield curve, variance risk premium and bond return predictability

This paper proposes a new way of estimating the instantaneous volatility of fixed income securities using derivatives data, which can further be used to construct the corresponding yield curve variance risk premium (VRP). We show that this VRP measure exhibits strong long-horizon predictive power for bond excess returns. After controlling for the shape of the yield curve, the VRP strongly predicts 1-year holding period excess returns for 2-year to 10-year zero coupon bonds. The marginal R2 of VRP is as high as 12.6%. One standard deviation increase in the VRP is associated with 2.224% increase in the bond excess return. This result is robust when we include various other bond return predictors, such as the Cochrane–Piazzesi “tent-shaped” factor. The out-of-sample analysis suggests that this predictability is not only statistically significant, but also can be translated into economic gains. Additional tests suggest that this predictability varies with economic conditions.

Modeling Conditional Factor Risk Premia Implied by Index Option Returns

ABSTRACTWe propose a novel factor model for option returns. Option exposures are estimated nonparametrically, and factor risk premia can vary nonlinearly with states. The model is estimated using regressions with minimal assumptions on factor and option return dynamics. We estimate the model using index options to characterize the conditional risk premia for factors of interest, such as the market return, market variance, tail and intermediary risk factors, higher moments, and the VIX term structure slope. Together, market return and variance explain more than 90% of option return variation. Unconditionally, the magnitude of the variance risk premium is plausible. It displays pronounced time variation, spikes during crises, and always has the expected sign.

The daily rise and fall of the VIX1D: Causes and solutions of its overnight bias

This paper explores the unique intraday dynamics of the VIX1D. We identify a distinct overnight bias, that causes the index to consistently rise during trading hours and to fall overnight. This bias stems from the index’s calculation methodology, particularly the use of business time and dynamic weighting of next-term options, which include overnight variance risk premiums. It overlaps with and is more pronounced than the day-of-the-week effect. To mitigate this bias, we propose data filtering and revising the calculation method to a forward-starting variance. These solutions aim to enhance the VIX1D’s interpretability and reliability for risk assessment in financial markets.

Monetary policy and currency variance risk premia

I analyze how the stance of monetary policy predicts variance risk premia in the currency market. The stance of monetary policy is measured using the shadow short rate, and two year and ten year bond yields. The stance of U.S. monetary policy predicts currency variance risk premia, after controlling for the stance of the foreign currency’s monetary policy. Contractionary U.S. monetary policy predicts lower currency variance risk premia, consistent with an increase in investor risk aversion. In contrast, the stance of the foreign currency’s monetary policy does not predict currency variance risk premia, after controlling for the stance of U.S. monetary policy.

Pricing CBOE VIX in non-affine GARCH models with variance risk premium

The commonly used local risk-neutral valuation relationship (LRNVR) for non-affine GARCH models only compensates for the equity risk premium. In this paper, we propose a direct approach to bridge the physical and risk-neutral measures for non-affine GARCH models, explicitly accounting for the variance risk premium. This method avoids the need to specify a particular form of pricing kernel when it is potentially complex. The closed-form CBOE VIX pricing formulas can be easily derived for several popular non-affine GARCH models, including EGARCH, GJR-GARCH, and NGARCH. Empirical results demonstrate that the newly proposed framework yields superior pricing performance for CBOE VIX.

A Decomposition of Conditional Risk Premia and Implications for Representative Agent Models

We develop a methodology to decompose the conditional market risk premium and risk premia on higher-order moments of excess market returns into risk premia related to contingent claims on down, up, and moderate market returns. The decomposition exploits information about the risk-neutral market return distribution embedded in option prices, but does not depend on assumptions about the functional form of investor preferences or about the market return distribution. The total market risk premium is highly time-varying, as are the contributions from downside, upside, and central risk. Time-series variation in risk premia associated with each region is primarily driven by variation in risk prices associated with the probability of entering each region at short horizons, but it is primarily driven by variation in risk quantities at longer horizons. Analogous decompositions implied by prominent representative agent models generally fail to match the dynamic risk premium behavior implied by the data. Our results provide a set of new empirical facts regarding the drivers of conditional risk premia and identify new challenges for representative agent models. This paper was accepted by Lukas Schmid, finance. Supplemental Material: The internet appendix and data files are available at https://doi.org/10.1287/mnsc.2022.01663 .

The cash-secured put-write strategy and the variance risk premium

The cash-secured put-write strategy and the variance risk premium

The Global Determinants of International Equity Risk Premiums

We examine the commonalities in international equity risk premiums by linking empirical evidence for the ability of U.S. downside and upside variance risk premiums (DVP and UVP, respectively) to predict international stock returns with implications from an empirical model featuring asymmetric economic uncertainty and risk aversion. We find that DVP and UVP predict international stock returns through U.S. bad and good macroeconomic uncertainties, respectively. Sixty percent to 80% of the dynamics of the global equity risk premium for horizons under seven months are driven by economic uncertainty, whereas risk aversion appears more relevant for longer horizons. The predictability patterns of DVP and UVP vary across countries depending on those countries’ financial and economic exposure to global shocks. In those with higher economic exposure, investors demand higher compensation for bad macroeconomic uncertainty but lower compensation for good macroeconomic uncertainty, whereas the compensation for bad macroeconomic uncertainty is lower for countries with high financial exposure. This paper was accepted by Lukas Schmid, finance. Supplemental Material: The data and online appendices are available at https://doi.org/10.1287/mnsc.2023.4958 .