Volatility Risk Premium Research Articles

Quantitative Easing and Direct Lending in Response to the COVID‐19 Crisis

AbstractThis paper develops a dynamic general equilibrium model to study quantitative easing (QE) and direct lending to firms. QE works through three channels: expanding bank reserves raises liquidity and lowers the liquidity premium, purchasing assets withdraws risk and lowers the volatility risk premium, and the resulting economic stimulus lowers the credit risk premium. When bank reserves are higher, the liquidity premium channel is weaker, and QE is less expansionary. Direct lending is more expansionary than QE because it substitutes bank lending and mitigates the credit risk frictions associated with bank lending, while QE stimulates bank lending and worsens the frictions.

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.

Volatility risk premium, good volatility and bad volatility: Evidence from SSE 50 ETF options

This paper studies the impact of volatility risk premium of SSE 50 ETF options on the price volatility of the underlying securities. After dividing options into different attributes including different types, market conditions and moneyness, we find that options contain implicit volatility information for the underlying securities and volatility risk premium has a significantly positive impact on the realized volatility. We further discuss the effect of options with different attributes on good and bad volatilities. The empirical results show that volatility risk premium has significant influence on both of them. In particular, the impact of volatility risk premium on good volatility is significantly stronger than that of bad volatility. In addition, we investigate the out-of-sample forecast performance of the volatility risk premium on realized volatility. The results show that the implied information content of deep out-of-the-money options has the highest prediction accuracy for weekly good realized volatility.

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.

The Common Factor in Volatility Risk Premia

The Common Factor in Volatility Risk Premia

Forecasting day-ahead expected shortfall on the EUR/USD exchange rate: The (I)relevance of implied volatility

The existing literature provides mixed results on the usefulness of implied volatility for managing risky assets, while evidence for expected shortfall predictions is almost nonexistent. Given its forward-looking nature, implied volatility might be more valuable than backward-looking measures of realized price fluctuations. Conversely, the volatility risk premium embedded in implied volatility leads to overestimating the observed price variation. This paper explores the benefits of augmenting econometric models used in forecasting the expected shortfall, a risk measured endorsed in the Basel III Accord, with information on implied volatility obtained from EUR/USD option contracts. The day-ahead forecasts are obtained from several classes of econometric models: historical simulation, EGARCH, quantile regression-based HAR, joint VaR and ES model, and combination forecasts. We verify whether the resulting expected shortfall forecasts are well-specified and test the models’ accuracy. Our results provide evidence that the information provided by forward-looking implied volatility is more valuable than that in backward-looking realized measures. These results hold across multiple model specifications, are stable over time, hold under alternative loss functions, and are more pronounced during periods of higher market uncertainty when risk modeling matters most.

Can Volatility Risk Premia Improve Fama-French Three-Factor Model in the Explanation of Stock Index Returns? — Evidence from US Industrial Stock Indices

Can Volatility Risk Premia Improve Fama-French Three-Factor Model in the Explanation of Stock Index Returns? — Evidence from US Industrial Stock Indices

The volatility index and volatility risk premium in China

We introduce the China Volatility Index (CNVIX), a model-free volatility index for the Chinese equity market based on ETF options. To construct the CNVIX, we extend the Chicago Board Options Exchange (CBOE) methodology in the emerging Chinese options market. We examine the leverage effect and volatility feedback effect between the CNVIX and the underlying asset, as well as the CNVIX’s return forecastability. Our findings indicate a significant negative asymmetric leverage effect, insignificant volatility feedback effect in the CNVIX, and a positive mean volatility risk premium (VRP), which can forecast the underlying asset’s returns over various horizons.

Dynamic Relationship between Volatility Risk Premia of Stock and Oil Returns

This study investigates the relationship between the volatility risk premia (VRP) of stock and oil returns. Using daily data on VRP from 10 May 2007 to 16 May 2017, VAR analyses on the stock and oil VRP are conducted, and it is found that the effects of the stock VRP on the oil VRP are limited and, if any, short-lived. In contrast, the VRP of oil has significantly positive and long-lasting effects on the stock VRP after the financial crisis. These results suggest that investors’ sentiments (measured by VRP) are transmitted from the oil to the stock market over time, but not vice versa. This is unexpected because the financialization of commodities means a massive increase in investment in commodities by investors in the traditional stock and bond markets; hence, the direction of effects is thought to be from the stock to the commodity market.

Swaption and term structures of volatility risk premiums

Swaption and term structures of volatility risk premiums

Uncertainty‐driven oil volatility risk premium and international stock market volatility forecasting

AbstractForecasting international stock market volatility using the oil volatility risk premium (OVRP) is important for asset allocation and financial risk management. In previous literature, the issue of biased OVRP has not been well addressed. The OVRP is defined as the difference between the ex ante risk‐neutral expectation of oil return variation and the oil realized variance. This is a biased estimator as argued by previous studies. In this paper, we propose a new measure of OVRP, namely, the uncertainty‐driven OVRP (UOVRP), in which the expected realized variation is the conditional variance of oil futures returns estimated by a typical GARCH‐MIDAS model, and the long‐term volatility component of conditional variance is directly determined by several uncertainty indices. Using heterogeneous autoregressive models (HAR), we find that UOVRPs significantly and positively predict most of the international stock market volatility in‐sample. Furthermore, it significantly outperforms the realized volatility, the “model‐free” OVRP, and recently proposed volatility predictors for most American, European, and Pacific markets out‐of‐sample. On average, UOVRPs driven by the world uncertainty index and the U.S. economic policy uncertainty perform the best among all UOVRPs. The predictive ability of UOVRPs is robust across a series of checks.

Realized GARCH, CBOE VIX, and the Volatility Risk Premium

Abstract We show that the realized GARCH model yields closed-form expression for both the volatility index (VIX) and the volatility risk premium (VRP). The realized GARCH model is driven by two shocks, a return shock and a volatility shock, and these are natural state variables in the stochastic discount factor (SDF). The volatility shock endows the exponentially affine SDF with compensation for volatility risk. This leads to dissimilar dynamic properties under the physical and risk-neutral measures that can explain time-variation in the VRP. In an empirical application with the S&P 500 returns, the VIX, and the VRP, we find that the realized GARCH model significantly outperforms conventional GARCH models.

Belief Dispersion and Convex Cost of Adjustment in the Stock Market and in the Real Economy

I develop a continuous-time general equilibrium model with a continuum of states of the world and a continuum of agents endowed with heterogeneous beliefs. The model permits to analyze the interactions between financial markets and production. There is a single firm that faces convex adjustment costs and maximizes its terminal value. Equivalently, the firm uses decreasing returns to scale risk-return technology. The model is tractable and matches many of the empirical regularities in aggregate output and stock prices, such as a financial volatility that is higher than the macroeconomic volatility, skewness, kurtosis, short-term momentum, and volatility risk premium during recessions. All these aspects disappear when one assumes beliefs homogeneity or constant returns to scale. In particular, the impact of beliefs heterogeneity observed in endowment economies does not pertain when introducing production unless one assumes decreasing returns to scale in the risk-return technology. This paper was accepted by David Sraer, finance. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.4495 .

Implied volatility information of Chinese SSE 50 ETF options

This paper examines the impact of the implied volatility information in SSE 50 ETF options on the underlying securities volatility. After segmenting options according to option type, moneyness, time to maturity and trading years, we confirm that options contain implied volatility information about the underlying securities, and there is a significant positive effect of the volatility risk premium on the volatility of underlying securities. As for the regression coefficient of volatility risk premium, the call option is higher than the put option due to the investors' risk aversion, and the long-term option is higher than the short-term option. With the moneyness from DOTM to DITM, the call options decrease while the put options increase for the existence of skew and kurtosis risk.

Trading the FX volatility risk premium with machine learning and alternative data

In this study, we show how both machine learning and alternative data can be successfully leveraged to improve and develop trading strategies. Starting from a trading strategy that harvests the EUR/USD volatility risk premium by selling one-week straddles every weekday, we present a machine learning approach to more skillfully time new trades and thus prevent unfavorable ones. To this end, we build probability-calibrated Random Forests on various predictors, extracted from both traditional market data and financial news, to predict the closing Sharpe ratio of short one-week delta-hedged straddles. We then demonstrate how the output of these calibrated machine learning models can be used to engineer intuitive new trading strategies. Ultimately, we show that our proposed strategies outperform the original strategy on risk-based performance measures. Moreover, the features that we derived from financial news articles significantly improve the performance of the approach.

The volatility risk premium in the oil market

This article provides a comprehensive analysis of the volatility risk premium (VRP) in the oil market. We approach the problem from the practitioner’s perspective as an investment strategy that sells and delta-hedges oil options, paying particular attention to the strategy’s risk-adjusted returns and its drawdown characteristics. The results are differentiated across options with different moneyness and expirations and presented in the form of VRP smile and VRP term structure. Strategy results are analyzed using alternative delta-hedging techniques that vary hedging frequencies, hedging thresholds, and volatilities used to calculate options’ delta. We discuss the performance under different regimes and highlight the structural break driven by the changing behavior among main participants in the oil options market.

Jump and volatility risk in the cross-section of corporate bond returns

Investigating the pricing of jump and volatility risk in the cross-section of corporate bonds, we find that bonds with high jump and volatility betas have low expected returns. The jump and volatility risk effects are economically significant, exhibit an intra-rating pattern, and increase as ratings decrease. While both jump and volatility risk effects heighten during the subprime crisis period, jump risk becomes more important than volatility risk in times of stress. The pronounced negative jump and volatility risk premiums cannot be explained by coskewness, cokurtosis, or downside risk exposure and are robust to controlling for conventional risk factors and bond characteristics.

The Pricing of Volatility and Jump Risks in the Cross-Section of Index Option Returns

AbstractExisting studies relate the puzzling low average returns on out-of-the-money (OTM) index call and put options to nonstandard preferences. We argue the low option returns are primarily due to the pricing of market volatility risk. When volatility risk is priced, expected option returns match the realized average option returns. Moreover, consistent with its theoretical effect on expected option returns, the volatility risk premium is positively related to future index option returns and this relationship is stronger for OTM options and at-the-money straddles. Finally, we find the jump risk premium contributes to some portion of OTM put option returns.

The asymmetric relationship between volatility index and volatility-of-volatility index

ABSTRACT We use the nonlinear autoregressive distributed lag model to assess the asymmetric relationship between the Chicago Board Options Exchange’s volatility index (VIX) and volatility-of-volatility index (VVIX) over the period January 2007 to March 2020. To control for potentially confounding factors, we include measures for economic policy uncertainty and the volatility risk premium. There are three key findings. First, we find that there is an asymmetric long run cointegrating positive relationship running from VVIX to VIX. In this long run relationship, VIX is more responsive to deceases in VVIX than increases in VVIX. Second, we also find an asymmetric short run relationship between VIX and VVIX. However, in contrast to the long run results, for the short run VIX is more responsive to increases in VVIX than decreases in VVIX. Third, consistent with other studies, we find that in the long run VIX rises with greater economic policy uncertainty but falls with increases in the volatility risk premium. We discuss the implications of our findings for practitioners in risk and portfolio management, derivative pricing, and trading.

Wavelet Multiscale and Spillover Analyses of Volatility and Correlation

This article investigates the dynamic empirical relationships among realized, risk-neutral, and risk premium measures of volatility and correlation of the S&P 500 stock index from January 1, 2000, to December 31, 2020. The empirical investigation runs a spillover analysis to identify the receiver and the transmitter variables and implements a wavelet local multiple correlation (WLMC) methodology to study the multiscale correlations. The results identify the implied measures as the most influential variables and also reveal that the strength of correlation is changing with time scales; moreover, the correlation between volatility risk premium and correlation risk premium is not always statistically significant through either time scales or time periods. These findings support the use of scale-based correlation metrics in derivatives studies.