Forecasting stock market volatility and information content of implied volatility index

This study investigates the incremental information content of implied volatility index relative to the GARCH family models in forecasting volatility of the three Asia-Pacific stock markets, namely India, Australia and Hong Kong. To examine the in-sample information content, the conditional variance equations of GARCH family models are augmented by incorporating implied volatility index as an explanatory variable. The return-based realized variance and the range-based realized variance constructed from 5-min data are used as proxy for latent volatility. To assess the out-of-sample forecast performance, we generate one-day-ahead rolling forecasts and employ the Mincer–Zarnowitz regression and encompassing regression. We find that the inclusion of implied volatility index in the conditional variance equation of GARCH family model reduces volatility persistence and improves model fitness. The significant and positive coefficient of implied volatility index in the augmented GARCH family models suggests that it contains relevant information in describing the volatility process. The study finds that volatility index is a biased forecast but possesses relevant information in explaining future realized volatility. The results of encompassing regression suggest that implied volatility index contains additional information relevant for forecasting stock market volatility beyond the information contained in the GARCH family model forecasts.     

Forecasting the oil futures price volatility: A new approach

This study provides a new perspective of modelling and forecasting realized range-based volatility (RRV) for crude oil futures. We are the first to improve the Heterogeneous Autoregressive model of Realized Range-based Volatility (HAR-RRV) model by considering the significant jump components, signed returns and volatility of realized range-based volatility. The empirical results show that the volatility of volatility significantly exists in the oil futures market. Moreover, our new proposed models with significant jump components, signed returns and volatility of volatility can gain higher forecast accuracy than HAR-RRV-type models. The results are robust to different forecasting windows and forecasting horizons. Our new findings are strategically important for investors making better decisions.     

Volatility forecasting: combinations of realized volatility measures and forecasting models

This article examines financial time series volatility forecasting performance. Different from other studies which either focus on combining individual realized measures or combining forecasting models, we consider both. Specifically, we construct nine important individual realized measures and consider combinations including the mean, the median and the geometric means as well as an optimal combination. We also apply a simple AR(1) model, an SV model with contemporaneous dependence, an HAR model and three linear combinations of these models. Using the robust forecasting evaluation measures including RMSE and QLIKE, our empirical evidence from both equity market indices and exchange rates suggests that combinations of both volatility measures and forecasting models improve the forecast performance significantly.     

What should the value of lambda be in the exponentially weighted moving average volatility model?

Forecasting volatility is fundamental to forecasting parametric models of value-at-risk. The exponentially weighted moving average (EWMA) volatility model is the recommended model for forecasting volatility by the Riskmetrics group. For monthly data, the lambda parameter of the EWMA model is recommended to be set to 0.97. In this study, we empirically investigate if this is the optimal value of lambda in terms of forecasting volatility. Employing monthly realized volatility as the benchmark for testing the value of lambda, it is found that a value of lambda of 0.97 is far from optimal. The tests are robust to a variety of test statistics. It is further found that the optimal value of lambda is time varying and should be based upon recent historical data. The article offers a practical method to increase the reliability and accuracy of value-at-risk forecasts that can be easily implemented within an Excel spreadsheet.     

Forecasting realized volatility of crude oil futures with equity market uncertainty

This paper examines whether the equity market uncertainty (EMU) index contains incremental information for forecasting the realized volatility of crude oil futures. We use 5-min high-frequency transaction data for WTI crude oil futures and develop six heterogeneous autoregressive (HAR) models based on classical HAR-type models. The empirical results suggest that EMU contains more incremental information than the economic policy uncertainty (EPU) for forecasting the realized volatility of crude oil futures. More importantly, we argue that EMU is a non negligible additional predictive variable that can significantly improve the 1-day ahead predictive accuracy of all six HAR-type models, and improve the 1-week ahead forecasting performance of the HAR-RV, HAR-RV-J, HAR-RSV, HAR-RV-SJ models. These findings highlight a strong short-term and a weak mid-term predictive ability of EMU in the crude oil futures market.     

Which types of commodity price information are more useful for predicting US stock market volatility?

This study aims to investigate which types of commodity price information are more useful for predicting US stock market realized volatility (RV) in a data-rich word. The standard predictive regression framework and monthly RV data are used to explore the RV predictability of commodity futures for the next-month RV on S&P 500 spot index. We utilize principal component analysis (PCA) and factor analysis (FA) to extract the common factors for each type and all types of commodity futures. Our results indicate that the futures volatility information of grains and softs has a significant predictive ability in forecasting the RV of the S&P 500. In addition, the FA method can yield better forecasts than the PCA and average methods in most cases. Further analysis shows that the volatility information of grains and softs exhibits higher informativeness during recessions and pre-crises. Finally, the forecasts of the five combination methods and different out-of-sample periods confirm our results are robust.     

Prediction of volatility based on realized-GARCH-kernel-type models: Evidence from China and the U.S.

We propose three Realized-GARCH-Kernel-type models which do not make the distribution assumptions on the return disturbance terms. We use this type of model to predict the return volatilities of the 50ETF in China and the S&P500 index in the U.S. The semiparametric kernel density estimator of our models, which captures the skewness, asymmetry and fat-tail of financial assets, performs well both statistically and economically. Our models have more predictive power than other eight comparable volatility models that need to pre-specify the distribution of the disturbance terms. Our results are robust to eight measures of realized volatility. Using option straddle strategies, we show that our models generate larger trading profits and greater Sharpe ratios than the other competing models.     

ALLOWING FOR JUMP MEASUREMENTS IN VOLATILITY: A HIGH‐FREQUENCY FINANCIAL DATA ANALYSIS OF INDIVIDUAL STOCKS

Following recent advances in the non‐parametric realized volatility approach, we separately measure the discontinuous jump part of the quadratic variation process for individual stocks and incorporate it into heterogeneous autoregressive volatility models. We analyse the distributional properties of the jump measures vis‐à‐vis the corresponding realized volatility ones, and compare them to those of aggregate US market index series. We also demonstrate important gains in the forecasting accuracy of high‐frequency volatility models.     

Volatility forecasting: long memory,regime switching and heteroscedasticity

In this article, we account for the first time for long memory, regime switching and the conditional time-varying volatility of volatility (heteroscedasticity) to model and forecast market volatility using the heterogeneous autoregressive model of realized volatility (HAR-RV) and its extensions. We present several interesting and notable findings. First, existing models exhibit significant nonlinearity and clustering, which provide empirical evidence on the benefit of introducing regime switching and heteroscedasticity. Second, out-of-sample results indicate that combining regime switching and heteroscedasticity can substantially improve predictive power from a statistical viewpoint. More specifically, our proposed models generally exhibit higher forecasting accuracy. Third, these results are widely consistent across a variety of robustness tests such as different forecasting windows, forecasting models, realized measures, and stock markets. Consequently, this study sheds new light on forecasting future volatility.     

Realized volatility models and alternative Value-at-Risk prediction strategies

We assess the Value-at-Risk (VaR) forecasting performance of recently proposed realized volatility (RV) models combined with alternative parametric and semi-parametric quantile estimation methods. A benchmark inter-daily GJR-GARCH model is also employed. Based on four asset classes, i.e. equity, FOREX, fixed income and commodity, and a turbulent six year out-of-sample period (2007–2013), we find that statistical accuracy and regulatory compliance is essentially improved when we use quantile methods which account for the fat tails and the asymmetry of the innovations distribution. In particular, empirical analysis gives evidence in favor of the skewed student distribution and the Extreme Value Theory (EVT) method. Nonetheless, efficiency of VaR estimates, as defined by the minimization of Basel II capital requirements and its opportunity costs, is reassured only with the use of realized volatility models. Overall, empirical evidence support the use of an asymmetric HAR realized volatility model coupled with the EVT method since it produces statistically accurate VaR forecasts which comply with Basel II accuracy mandates and allows for more efficient capital allocations.     

Can asymmetric conditional volatility imply asymmetric tail dependence?

In this article, we investigate two types of asymmetries, that is, the asymmetry of conditional volatility and the asymmetry of tail dependence in the crude oil markets. We employ the two different sample datasets in which each dataset covers the time period of stable and unstable oil prices, individually. A variety of different copulas and three asymmetric GARCH regression models are used in order to capture the two types of asymmetries. In particular, we extend the TBL-GARCH model proposed by Choi et al. (2012) to the asymmetric GARCH regression type model. The findings from the two different approaches are congruent, in that there is no asymmetry of tail dependence and no asymmetric conditional volatility in crude oil returns over the two different sample periods. Our study reconfirms the findings of Aboura and Wagner (2016) by showing that asymmetric conditional volatility relates to asymmetric tail dependence.     

Volatility forecasting using related markets’ information for the Tokyo stock exchange

Due to lack of information, volatility cannot be estimated via a high-frequency approach when markets are non-trading. In this paper, we focus on volatility forecasting for the Tokyo Stock Exchange (TSE) using high-frequency data of related assets traded in international markets when TSE is closed. We use the heterogenous autoregressive model to identify an optimal approach of this additional information for the ten largest TSE-listed stocks, TOPIX and Nikkei 225. The usefulness of harnessing global and neighbour market information in forecasting the TSE market volatility is confirmed through in-depth empirical analysis. Our findings have important implications for investors and policy makers.     

Forecasting the realized volatility in the Chinese stock market: further evidence

In this study, the impact of noise and jump on the forecasting ability of volatility models with high-frequency data is investigated. A signed jump variation is added as an additional explanatory variable in the volatility equation according to the sign of return. These forecasting performances of models with jumps are compared with those without jumps. Being applied to the Chinese stock market, we find that the jump variation has a significant in-sample predictive power to volatility and the predictive power of the negative one is greater than the positive one. Furthermore, out-of-sample evidence based on the fresh model confidence set (MCS) test indicates that the incorporation of singed jumps in volatility models can significantly improve their forecasting ability. In particular, among the realized variance (RV)-based volatility models and generalized autoregressive conditional heteroscedasticity (GARCH) class models, the heterogeneous autoregressive model of realized volatility (HAR-RV) model with the jump test and a decomposed signed jump variation have better out-of-sample forecasting performance. Finally, the use of the decomposed signed jump variations in predictive regressions can improve the economic value of realized volatility forecasts.     

Forecasting the aggregate stock market volatility in a data-rich world

ABSTRACT

In this article, we utilize the basic lasso and elastic net models to revisit the predictive performance of aggregate stock market volatility in a data-rich world. Motivated by the existing literature, we determine several candidate predictors that have 22 technical indicators and 14 macroeconomic and financial variables. Our out-of-sample results reveal several noteworthy findings. First, few macroeconomic and financial variables and most of technical indicators have superior performance relative to the benchmark model. Second, combination forecasts are able to significantly beat the benchmark and some signal predictors Third, the lasso and elastic models with all predictors can generate more accurate forecasts than the benchmark and some other predictors in both the statistical and economic sense. Fourth, the lasso and elastic models exhibit higher forecast accuracy during periods of expansions and recessions. Finally, our findings are robust to several tests, such as different forecasting windows, forecasting models, and forecasting evaluations.     

Linear time-varying regression with a DCC-GARCH model for volatility

This article provides a new linear state space model with time-varying parameters for forecasting financial volatility. The volatility estimates obtained from the model by using the US stock market data almost exactly match the realized volatility. We further compare our model with traditional volatility models in the ex post volatility forecast evaluations. In particular, we use the superior predictive ability and the reality check for data snooping. Evidence can be found supporting that our simple but powerful regression model provides superior forecasts for volatility.     

Do misalignments predict aggregated stock-market volatility?

This paper considers forecasting regressions of “realized volatility” on a misalignment measure. Results show that this misalignment measure is useful to predict in and out-of-sample stock-market volatility at monthly horizons. The analysis also suggests a threshold effect.     

Evaluating and improving GARCH-based volatility forecasts with range-based estimators

This article investigates the feasibility of using range-based estimators to evaluate and improve Generalized Autoregressive Conditional Heteroscedasticity (GARCH)-based volatility forecasts due to their computational simplicity and readily availability. The empirical results show that daily range-based estimators are sound alternatives for true volatility proxies when using Superior Predictive Ability (SPA) test of Hansen (2005) to assess GARCH-based volatility forecasts. In addition, the inclusion of the range-based estimator of Garman and Klass (1980) can significantly improve the forecasting performance of GARCH-t model.     

Further empirical evidence on the forecasting of volatility with smooth transition exponential smoothing

Smooth transition exponential smoothing (STES) uses a logistic function of a user-specified transition variable as adaptive time varying smoothing parameter. This paper empirically addresses three aspects of the use of STES for volatility forecasting. Previous empirical results showed the method performing well in comparison with fixed parameter exponential smoothing and a variety of GARCH models. However, those results related only to forecasting weekly volatility. In this paper, we address the use of STES for forecasting daily volatility. A second issue that we evaluate is the robustness of STES in the presence of extreme outlying observations. The third aspect that we consider is the use of trading volume within a transition variable in the STES method. Our simulation results suggest that STES performs well in terms of robustness, when compared with standard methods and several alternative robust methods. Analysis using stock return data shows that STES has the potential to outperform standard and robust forms of fixed parameter exponential smoothing and GARCH models. The results suggest the use of the sign and size of past shocks as STES transition variables, and provide no clear support for the incorporation of trading volume in a transition variable.     

Uncertainty and crude oil market volatility: new evidence

ABSTRACT

The main goal of this paper is to investigate the predictability of five economic uncertainty indices for oil price volatility in a changing world. We employ the standard predictive regression framework, several model combination approaches, as well as two prevailing model shrinkage methods to evaluate the performances of the uncertainty indices. The empirical results based on simple autoregression models including only one index suggest that global economic policy uncertainty (GEPU) and US equity market volatility (EMV) indices have significant predictive power for crude oil market volatility. In addition, the model combination approaches adopted in this paper can improve slightly the performances of individual autoregressive models. Lastly, the two model shrinkage methods, namely Elastin net and Lasso, outperform other individual AR-type model and combination models in most forecasting cases. Other empirical results based on alternative forecasting methods, estimation window sizes, high/low volatility and economic expansion/recession time periods further make sure the robustness of our major conclusions. The findings in this paper also have several important economic implications for oil investors.     

Forecasting the volatility of crude oil futures using high-frequency data: further evidence

We forecast the realized volatility of crude oil futures market using the heterogeneous autoregressive model for realized volatility and its various extensions. Out-of-sample findings indicate that the inclusion of jumps does not improve the forecasting accuracy of the volatility models, whereas the “leverage effect” pertaining to the difference between positive and negative realized semi-variances can significantly improve the forecasting accuracy in predicting the short- and medium-term volatility. However, the signed jump variations and its decomposition couldn’t significantly enhance the models’ forecasting accuracy on the long-term volatility.