Predictive ability of asymmetric volatility models at medium-term horizons

Using realized volatility to estimate conditional variance of financial returns, we compare forecasts of volatility from linear GARCH models with asymmetric ones. We consider horizons extending to 30 days. Forecasts are compared using three different evaluation tests. With data from an equity index and two foreign exchange returns, we show that asymmetric models provide statistically significant forecast improvements upon the GARCH model for two of the datasets and improve forecasts for all datasets by means of forecasts combinations. These results extend to about 10 days in the future, beyond which the forecasts are statistically inseparable from each other.     

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.     

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.     

The risk-return relation and VIX: evidence from the S&P 500

A significantly positive risk-return relation for the S&P 500 market index is detected if the squared implied volatility index (VIX) is allowed for as an exogenous variable in the conditional variance equation of the parsimonious GARCH(1,1) model. This result holds for both daily and weekly observations, for extended conditional mean and variance specifications, and is robust to sub-samples. We show that the conditional variance obtained from the GARCH model with VIX has better predictive ability for realized volatility than the conditional variance from GARCH without VIX and VIX itself, thereby documenting an important information content of VIX for conditional variance. The results are interpreted as evidence that adding VIX squared in the conditional variance equation yields a better measure of conditional variance which, subsequently, uncovers a strong risk-return relation.     

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.     

On the predictive power of ARJI volatility forecasts for Bitcoin

Motivated by the recent literature on cryptocurrency volatility dynamics, this paper adopts the ARJI, GARCH, EGARCH, and CGARCH models to explore their capabilities to make out-of-sample volatility forecasts for Bitcoin returns over a daily horizon from 2013 to 2018. The empirical results indicate that the ARJI jump model can cope with the extreme price movements of Bitcoin, showing comparatively superior in-sample goodness-of-fit, as well as out-of-sample predictive performance. However, due to the excessive volatility swings on the cryptocurrency market, the realized volatility of Bitcoin prices is only marginally explained by the GARCH genre of employed models.     

Improving GARCH volatility forecasts with regime-switching GARCH

Many researchers use GARCH models to generate volatility forecasts. Using data on three major U.S. dollar exchange rates we show that such forecasts are too high in volatile periods. We argue that this is due to the high persistence of shocks in GARCH forecasts. To obtain more flexibility regarding volatility persistence, this paper generalizes the GARCH model by distinguishing two regimes with different volatility levels; GARCH effects are allowed within each regime. The resulting Markov regime-switching GARCH model improves on existing variants, for instance by making multi-period-ahead volatility forecasting a convenient recursive procedure. The empirical analysis demonstrates that the model resolves the problem with the high single-regime GARCH forecasts and that it yields significantly better out-of-sample volatility forecasts. First Version Received: November 2000/Final Version Received: August 2001     

The information content of implied volatility in developed versus developing FX markets

This article predicts the daily movement of monthly foreign exchange (FX) rate volatility using a linear combination of a time-series model and implied volatilities from options. The focus is on analysing the FX volatilities in three developing economies (the Brazilian real (BRL), the Indian rupee (INR) and the Russian ruble (RUB)) against the US dollar (USD). The empirical exercise utilizes two time-series models, mixed data sampling (MIDAS) and GARCH. The analysis indicates that for both developed and developing economies the predictive power of MIDAS and that of GARCH is comparable. Further on in this article, we will ascertain whether the relationship between realized and implied volatility is fundamentally different in the case of developing economies from that among developed economies. Thus, we compare the pairs USD/BRL, USD/INR and USD/RUB against EURO/USD and USD/Japanese yen to determine the information content and predictive power of implied volatilities. Plots of the MIDAS coefficients show that the volatility is more persistent in developing economies than in developed economies.     

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.     

Structural breaks and GARCH models of stock return volatility: The case of South Africa

This paper investigates the empirical relevance of structural breaks in forecasting stock return volatility using both in-sample and out-of-sample tests applied to daily returns of the Johannesburg Stock Exchange (JSE) All Share Index from 07/02/1995 to 08/25/2010. We find evidence of structural breaks in the unconditional variance of the stock returns series over the period, with high levels of persistence and variability in the parameter estimates of the GARCH(1,1) model across the sub-samples defined by the structural breaks. This indicates that structural breaks are empirically relevant to stock return volatility in South Africa. However, based on the out-of-sample forecasting exercise, we find that even though there structural breaks in the volatility, there are no statistical gains from using competing models that explicitly accounts for structural breaks, relative to a GARCH(1,1) model with expanding window. This could be because of the fact that the two identified structural breaks occurred in our out-of-sample, and recursive estimation of the GARCH(1,1) model is perhaps sufficient to account for the effect of the breaks on the parameter estimates. Finally, we highlight that, given the point of the breaks, perhaps what seems more important in South Africa, is accounting for leverage effects, especially in terms of long-horizon forecasting of stock return volatility.     

Revisiting the long memory dynamics of the implied–realized volatility relationship: New evidence from the wavelet regression

The literature studying stock index options confirms severe biases and inefficiencies in using implied volatility as a forecast of future volatility. In this paper, we revisit the implied–realized volatility relationship with wavelet band least squares (WBLS) exploring the long memory of volatility, a possible cause of the bias. Using the S&P 500 and DAX monthly and bi-weekly option prices covering the recent financial crisis, we conclude that the implied–realized volatility relation is driven solely by the lower frequencies of the spectra representing long investment horizons. The findings enable improvement of future volatility forecasts as they support unbiasedness of implied volatility as a good proxy for future volatility in the long run.     

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.     

Value at risk forecasting for volatility index

Forecasts of values at risk (VaRs) are made for volatility indices such as the VIX for the US S&P 500 index, the VKOSPI for the KOSPI (Korea Stock Price Index) and the OVX (oil volatility index) for crude oil funds, which is the first in the literature. In the forecasts, dominant features of the volatility indices are addressed: long memory, conditional heteroscedasticity, asymmetry and fat-tails. An out-of-sample comparison of the VaR forecasts is made in terms of violation probabilities, showing better performance of the proposed method than several competing methods which consider the features differently from ours. The proposed method is composed of heterogeneous autoregressive model for the mean, GARCH model for the volatility and skew-t distribution for the error.     

Forecasting volatility in the Chinese stock market under model uncertainty

Volatility forecasting is an important issue in empirical finance. In this paper, the main purpose is to apply the model averaging techniques to reduce volatility model uncertainty and improve volatility forecasting. Six GARCH-type models are considered as candidate models for model averaging. As to the Chinese stock market, the largest emerging market in the world, the empirical study shows that forecast combination using model averaging can be a better approach than the individual forecasts.     

Does VIX or volume improve GARCH volatility forecasts?

This article considers whether the inclusion of two additional variables can improve volatility forecasts over a standard GARCH-based model. We consider three alternative ways of incorporating the volatility index (VIX) and trading volume as exogenous variables within a selection of GARCH models. We are particularly interested in whether these variables have additional incremental forecast power over and above the baseline GARCH specification. Our results suggest that both the VIX and volume do provide some additional forecast power, and this is generally improved when considering both of these series jointly in the model. However, while the results may be statistically significant the gain is marginal and the coefficient values small. Moreover, in a horse race exercise VIX does not outperform the GARCH approach. In answering the question of whether VIX produces better forecasts than the GARCH model, then the answer is no, but the informational content of VIX cannot be ignored and should be incorporated into forecast regressions.     

Value at risk estimation by threshold stochastic volatility model

This article proposes a threshold stochastic volatility model that generates volatility forecasts specifically designed for value at risk (VaR) estimation. The method incorporates extreme downside shocks by modelling left-tail returns separately from other returns. Left-tail returns are generated with a t-distributional process based on the historically observed conditional excess kurtosis. This specification allows VaR estimates to be generated with extreme downside impacts, yet remains empirically widely applicable. This article applies the model to daily returns of seven major stock indices over a 22-year period and compares its forecasts to those of several other forecasting methods. Based on back-testing outcomes and likelihood ratio tests, the new model provides reliable estimates and outperforms others.     

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.     

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.     

Predicting stock realized variance based on an asymmetric robust regression approach

This paper introduces an asymmetric robust weighted least squares (ARLS) approach to improve the forecasting performance of the heterogeneous autoregressive model for realized volatility. The ARLS approach down-weights extreme observations to limit the bad influence of outliers on the estimated parameters. Compared with existing robust regression methods, our model further takes into account the asymmetry of outliers using a class of kernel functions. Out-of-sample results show the ARLS approach can generate more accurate forecasts of the S&P 500 index realized volatility in the statistical and economic senses. The model that considers the asymmetry of outliers gains superior performance among various robust regression competitors. The forecasting improvements also hold in other international stock markets. More importantly, the source of the predictive ability of the ARLS model comes from the less biased and more efficient parameter estimation.     

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.