Trading and non-trading period realized market volatility: Does it matter for forecasting the volatility of US stocks?

We study the potential merits of using trading and non-trading period market volatilities to model and forecast the stock volatility over the next one to 22 days. We demonstrate the role of overnight volatility information by estimating heterogeneous autoregressive (HAR) model specifications with and without a trading period market risk factor using ten years of high-frequency data for the 431 constituents of the S&P 500 index. The stocks’ own overnight squared returns perform poorly across stocks and forecast horizons, as well as in the asset allocation exercise. In contrast, we find overwhelming evidence that the market-level volatility, proxied by S&P Mini futures, matters significantly for improving the model fit and volatility forecasting accuracy. The greatest model fit and forecast improvements are found for short-term forecast horizons of up to five trading days, and for the non-trading period market-level volatility. The documented increase in forecast accuracy is found to be associated with the stocks’ sensitivity to the market risk factor. Finally, we show that both the trading and non-trading period market realized volatilities are relevant in an asset allocation context, as they increase the average returns, Sharpe ratios and certainty equivalent returns of a mean–variance investor.     

Forecast on silver futures linked with structural breaks and day-of-the-week effect

Silver future is crucial to global financial markets. However, the existing literature rarely considers the impacts of structural breaks and day-of-the-week effect simultaneously on the volatility of silver future price. Based on heterogeneous autoregressive (HAR) theory, we establish six new type heterogeneous autoregressive (HAR) models by incorporating structural breaks and day-of-the-week effect to forecast the volatility. The empirical results indicate that new models’ accuracy is better than the original HAR model. We find that structural breaks and the day-of-the-week effect contain much forecasting information on silver forecasting. In addition, structural breaks have a positive effect on the silver futures’ volatility. Day-of-the-week effect has a significantly negative influence on silver futures’ price volatility, especially in the mid-term and the long-term. Our works is the first to combine the structural breaks and day-of-the-week effect to identify more market information. This paper provides a better forecasting method to predict silver future volatility.     

Macroeconomic Forecasting Performance under Alternative Specifications of Time‐Varying Volatility

This paper compares alternative models of time‐varying volatility on the basis of the accuracy of real‐time point and density forecasts of key macroeconomic time series for the USA. We consider Bayesian autoregressive and vector autoregressive models that incorporate some form of time‐varying volatility, precisely random walk stochastic volatility, stochastic volatility following a stationary AR process, stochastic volatility coupled with fat tails, GARCH and mixture of innovation models. The results show that the AR and VAR specifications with conventional stochastic volatility dominate other volatility specifications, in terms of point forecasting to some degree and density forecasting to a greater degree. Copyright © 2014 John Wiley & Sons, Ltd.     

Volatility forecasting in the Bitcoin market: A new proposed measure based on the VS-ACARR approach

This paper proposes a new volatility-spillover-asymmetric conditional autoregressive range (VS-ACARR) approach that takes into account the intraday information, the volatility spillover from crude oil as well as the volatility asymmetry (leverage effect) to model/forecast Bitcoin volatility (price range). An empirical application to Bitcoin and crude oil (WTI) price ranges shows the existence of strong volatility spillover from crude oil to the Bitcoin market and a weak leverage effect in the Bitcoin market. The VS-ACARR model yields higher forecasting accuracy than the GARCH, CARR, and VS-CARR models regarding out-of-sample forecast performance, suggesting that accounting for the volatility spillover and asymmetry can significantly improve the forecasting accuracy of Bitcoin volatility. The superior forecast performance of the VS-ACARR model is robust to alternative out-of-sample forecast windows. Our findings highlight the importance of accommodating intraday information, spillover from crude oil, and volatility asymmetry in forecasting Bitcoin volatility.     

Stock volatility and trading

Both, rational and behavioral models predict that stock and market volatility affect trading by investors. Tax-induced trading hypothesis predicts that investors increase realization of capital losses short term and capital gains only long term as volatility increases. Behavioral models predict that disposition biases of holding on to losers and disposing of winners intensifies with volatility. We document that market and stock volatility influence stock trading. Evidence on trading in response to rise in market volatility supports tax-loss harvesting hypothesis – abnormal trading of losers increases and winners decreases. However, evidence on trading patterns conditional on individual stock volatility is in support of both tax-loss-harvesting and behavioral models: trading in both losing stocks (tax-loss-harvesting hypothesis) and winning stocks (disposition effect hypothesis) increases with rise in stock volatility.     

Time-varying risk aversion and renminbi exchange rate volatility: Evidence from CARR-MIDAS model

In this paper, we investigate the relation between time-varying risk aversion and renminbi exchange rate volatility using the conditional autoregressive range-mixed-data sampling (CARR-MIDAS) model. The CARR-MIDAS model is a range-based volatility model, which exploits intraday information regarding the intraday trajectory of the price. Moreover, the model features a MIDAS structure allowing for time-varying risk aversion to drive the long-run volatility dynamics. Our empirical results show that time-varying risk aversion has a significantly negative effect on the long-run volatility of renminbi exchange rate. Moreover, we observe that both intraday ranges and time-varying risk aversion contain important information for forecasting renminbi exchange rate volatility. The range-based CARR-MIDAS model incorporating time-varying risk aversion provides more accurate out-of-sample forecasts of renminbi exchange rate volatility compared to a variety of competing models, including the return-based GARCH, GARCH-MIDAS and GARCH-MIDAS incorporating time-varying risk aversion as well as range-based CARR, CARR-MIDAS and heterogeneous autoregressive (HAR), for forecast horizons of 1 day up to 3 months. This result is robust to alternative risk aversion measure, alternative MIDAS lags as well as alternative out-of-sample periods. Overall, our findings highlight the value of incorporating intraday information and time-varying risk aversion for forecasting the renminbi exchange rate volatility.     

Forecasting the Chinese stock market volatility with international market volatilities: The role of regime switching

The purpose of this paper is to investigate the role of regime switching in the prediction of the Chinese stock market volatility with international market volatilities. Our work is based on the heterogeneous autoregressive (HAR) model and we further extend this simple benchmark model by incorporating an individual volatility measure from 27 international stock markets. The in-sample estimation results show that the transition probabilities are significant and the high volatility regime exhibits substantially higher volatility level than the low volatility regime. The out-of-sample forecasting results based on the Diebold-Mariano (DM) test suggest that the regime switching models consistently outperform their original counterparts with respect to not only the HAR and its extended models but also the five used combination approaches. In addition to point accuracy, the regime switching models also exhibit substantially higher directional accuracy. Furthermore, compared to time-varying parameter, Markov regime switching is found to be a more efficient way to process the volatility information in the changing world. Our results are also robust to alternative evaluation methods, various loss functions, alternative volatility estimators, various sample periods, and various settings of Markov regime switching. Finally, we provide an extension of forecasting aggregate market volatility on monthly frequency and observe mixed results.     

Modeling and forecasting of stock index volatility with APARCH models under ordered restriction

This article examines volatility models for modeling and forecasting the Standard & Poor 500 (S&P 500) daily stock index returns, including the autoregressive moving average, the Taylor and Schwert generalized autoregressive conditional heteroscedasticity (GARCH), the Glosten, Jagannathan and Runkle GARCH and asymmetric power ARCH (APARCH) with the following conditional distributions: normal, Student's t and skewed Student's t‐distributions. In addition, we undertake unit root (augmented Dickey–Fuller and Phillip–Perron) tests, co‐integration test and error correction model. We study the stationary APARCH (p) model with parameters, and the uniform convergence, strong consistency and asymptotic normality are prove under simple ordered restriction. In fitting these models to S&P 500 daily stock index return data over the period 1 January 2002 to 31 December 2012, we found that the APARCH model using a skewed Student's t‐distribution is the most effective and successful for modeling and forecasting the daily stock index returns series. The results of this study would be of great value to policy makers and investors in managing risk in stock markets trading.     

Overnight stock returns and realized volatility

The information flow in modern financial markets is continuous, but major stock exchanges are open for trading for only a limited number of hours. No consensus has yet emerged on how to deal with overnight returns when calculating and forecasting realized volatility in markets where trading does not take place 24 hours a day. Based on a recently introduced formal testing procedure, we find that for the S&P 500 index, a realized volatility estimator that optimally incorporates overnight information is more accurate in-sample. In contrast, estimators that do not incorporate overnight information are more accurate for individual stocks. We also show that accounting for overnight returns may affect the conclusions drawn in an out-of-sample horserace of forecasting models. Finally, there is considerably less variation in the selection of the best out-of-sample forecasting model when only the most accurate in-sample RV estimators are considered.     

Forecasting stock market volatility: Can the risk aversion measure exert an important role?

In this paper, we predict realized volatility of stock return by utilizing time-varying risk aversion based on a simple linear autoregressive model. Our in-sample results suggest that time-varying risk aversion have significant impact for stock return volatility. In terms of out-of-sample forecasting performance, the empirical results indicate that the incorporation of time-varying risk aversion in the benchmark model can yield more accurate stock return volatility forecasts. Notably, the out-of-sample forecasting results confirm that our conclusions are robust when we apply alternative lag orders and alternative prediction evaluation periods. Finally, we study links between the prediction ability of time-varying risk aversion and the volatility of other stock indices and two kinds of crude oil, and find that the new predictor can effectively strengthen forecasting performance in most case. In view of the importance of volatility risk in the asset pricing process, our research is of great significance for financial asset participants.     

Modeling dynamic conditional correlations with leverage effects and volatility spillover effects: Evidence from the Chinese and US stock markets affected by the recent trade friction

In this article, we investigate the dynamic conditional correlations (DCCs) with leverage effects and volatility spillover effects that consider time difference and long memory of returns, between the Chinese and US stock markets, in the Sino-US trade friction and previous stable periods. The widespread belief that the developed markets dominate the emerging markets in stock market interactions is challenged by our findings that both the mean and volatility spillovers are bidirectional. We do find that most of the shocks to these DCCs between the two stock markets are symmetric, and all the symmetric shocks to these DCCs are highly persistent between Shanghai’s trading return and S&P 500′s trading or overnight return, however all the shocks to these DCCs are short-lived between S&P 500′s trading return and Shanghai’s trading or overnight return. We also find clear evidence that the DCC between Shanghai’s trading return and S&P 500′s overnight return has a downward trend with a structural break, perhaps due to the “America First” policy, after which it rebounds and fluctuates sharply in the middle and later periods of trade friction. These findings have important implications for investors to pursue profits.     

Forecasting risk measures using intraday data in a generalized autoregressive score framework

A new framework for the joint estimation and forecasting of dynamic value at risk (VaR) and expected shortfall (ES) is proposed by our incorporating intraday information into a generalized autoregressive score (GAS) model introduced by Patton et al., 2019 to estimate risk measures in a quantile regression set-up. We consider four intraday measures: the realized volatility at 5-min and 10-min sampling frequencies, and the overnight return incorporated into these two realized volatilities. In a forecasting study, the set of newly proposed semiparametric models are applied to four international stock market indices (S&P 500, Dow Jones Industrial Average, Nikkei 225 and FTSE 100) and are compared with a range of parametric, nonparametric and semiparametric models, including historical simulations, generalized autoregressive conditional heteroscedasticity (GARCH) models and the original GAS models. VaR and ES forecasts are backtested individually, and the joint loss function is used for comparisons. Our results show that GAS models, enhanced with the realized volatility measures, outperform the benchmark models consistently across all indices and various probability levels.     

Temporal aggregation of volatility models

In this paper, we consider temporal aggregation of volatility models. We introduce semiparametric volatility models, termed square-root stochastic autoregressive volatility (SR-SARV), which are characterized by autoregressive dynamics of the stochastic variance. Our class encompasses the usual GARCH models and various asymmetric GARCH models. Moreover, our stochastic volatility models are characterized by multiperiod conditional moment restrictions in terms of observables. The SR-SARV class is a natural extension of the class of weak GARCH models. This extension has four advantages: (i) we do not assume that fourth moments are finite; (ii) we allow for asymmetries (skewness, leverage effect) that are excluded from weak GARCH models; (iii) we derive conditional moment restrictions and (iv) our framework allows us to study temporal aggregation of IGARCH models.     

Incorporating the RMB internationalization effect into its exchange rate volatility forecasting

Recently, the Chinese government has launched the renminbi (RMB) internationalization policy as an impetus to foster China’s global economic integration. The RMB internationalization effect on China’s economy and the RMB exchange rate has attracted massive attention in recent financial research. In this paper, we adopt a genetic programming (GP) method to generate new RMB exchange rate volatility forecasting models incorporating the RMB internationalization effect. Our models are proved to have significant accuracy improvement in predicting both RMB/US dollar and RMB/euro exchange rate volatilities, compared with standard GARCH volatility models, which are incapable of capturing the RMB internationalization effect. Furthermore, our models display salient practical implications for policy makers to formulate monetary policies and currency traders to design effective trading strategies.     

Open interest,volume, and volatility: evidence from Taiwan futures markets

This paper examines the relationships amongst volatility, total trading volume (TVOL) and total open interest (TOI) for three Taiwan stock index futures markets as well as the role of the latter two variables in the dynamics of GARCH modeling and forecasting. From both ex-post and ex-ante perspectives, we study this issue by using the VAR model and augmented GARCH-type models, respectively. For the GARCH-type models, we employ both symmetric and asymmetric models augmented with lagged logs in TOI and/or TVOL. We find that whether addition of these two variables helps the basic GARCH models predict future volatility depends upon the sample period examined for all three sets of futures. Nonetheless, the best three models for out-of-sample volatility forecasting in the MSE sense are generally the augmented models for all sub-intervals and all three futures contracts.     

Forecasting volatility with component conditional autoregressive range model

In this paper, we propose a component conditional autoregressive range (CCARR) model for forecasting volatility. The proposed CCARR model assumes that the price range comprises both a long-run (trend) component and a short-run (transitory) component, which has the capacity to capture the long memory property of volatility. The model is intuitive and convenient to implement by using the maximum likelihood estimation method. Empirical analysis using six stock market indices highlights the value of incorporating a second component into range (volatility) modelling and forecasting. In particular, we find that the proposed CCARR model fits the data better than the CARR model, and that it generates more accurate out-of-sample volatility forecasts and contains more information content about the true volatility than the popular GARCH, component GARCH and CARR models.     

How does inter-industry spillover improve the performance of volatility forecasting?

This study aims to investigate whether introducing inter-industry spillover information into the GARCH-MIDAS model improves out-of-sample forecasting attempts. We explore the transmission of volatility across sectors, as well as the reliance on inter-industry business links. Our findings demonstrate strong cross-industry volatility spillovers that are related to the degree of the industry-to-industry trading linkage. We compare the out-of-sample volatility forecasting performance of the spillovers-information-incorporated GARCH-MIDAS model with that of the traditional GARCH model. The empirical results show that the GARCH-MIDAS model outperforms traditional GARCH models. Notably, we discover that good (bad) news is always transferred from the back end of the production process to the front end, meaning that economic growth (decline) is driven by consumption expansion (shrinkage).     

Non-linear volatility dynamics and risk management of precious metals

In this paper, we investigate the value-at-risk predictions of four major precious metals (gold, silver, platinum, and palladium) with non-linear long memory volatility models, namely FIGARCH, FIAPARCH and HYGARCH, under normal and Student-t innovations’ distributions. For these analyses, we consider both long and short trading positions. Overall, our results reveal that long memory volatility models under Student-t distribution perform well in forecasting a one-day-ahead VaR for both long and short positions. In addition, we find that FIAPARCH model with Student-t distribution, which jointly captures long memory and asymmetry, as well as fat-tails, outperforms other models in VaR forecasting. Our results have potential implications for portfolio managers, producers, and policy makers.     

Forecasting volatility via stock return,range, trading volume and spillover effects: The case of Brazil

For the purpose of developing alternative approach for forecasting volatility, we consider heterogeneous VAR (HVAR) model which accommodates the market effects of different horizons, namely, daily, weekly and monthly effects, and examine the interdependence of stock markets in Brazil and the US, based on information of daily return, range and trading volume. To compare with the new approach, we also work with the univariate and multivariate GARCH models with asymmetric effects, trading volumes and fat-tails. The heteroskedasticity-corrected Granger causality tests based on the HVAR show the strong evidence of such spillover effects. We assess the value-at-risk thresholds for Brazil, based on the out-of-sample forecasts of the HVAR model, finding the new approach works satisfactory for the periods including the global financial crisis, without assuming heavy-tailed conditional distributions.     

Volatility forecasting in European government bond markets

In this paper we examine the predictive power of the heterogeneous autoregressive (HAR) model for the return volatility of major European government bond markets. The results from HAR-type volatility forecasting models show that past short- and medium-term volatility are significant predictors of the term structure of the intraday volatility of European bonds with maturities ranging from 1 year up to 30 years. When we decompose bond market volatility into its continuous and discontinuous (jump) component, we find that the jump component is a significant predictor. Moreover, we show that feedback from past short-term volatility to forecasts of future volatility is stronger in the days that precede monetary policy announcements.