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.     

Asymmetric Conditional Volatility and Firm Size: Evidence from Australian Equity Portfolios

This paper examines the relationship between firm size and equity volatility for two portfolios of Australian equities. Univariate and Multivariate GARCH models are used to demonstrate that conditional variance is related to firm size. There is strong evidence to suggest that the variance-covariance matrix of returns is time varying and asymmetric. A negative innovation to the return of the large firm portfolio results in higher levels of conditional volatility in the small firm portfolio than would be the case for a positive innovation of equal magnitude. News about own returns appears to determine the conditional variance of the portfolio of large firms. The conditional covariance between the two portfolios also displays evidence of asymmetry.     

我国股市波动的非对称性和杠杆效应研究

本文选取2006年1月4日到2008年12月31日期间上证综合价格指数日收益率和收益波动率的数据,建立二者变量指标的GARCH模型、AGARCH模型、EGARCH模型,对我国牛熊市轮替过程中股票市场波动的非对称性和杠杆效应进行实证分析。结果发现,股改后牛熊市期间我国股票市场的波动表现出显著的长记忆性、非对称性和杠杆效应,股票市场波动性对"利好"和"利空"消息呈现出不平衡性反应,我国股票市场出现了强市恒强、弱市恒弱现象。最后,从投资者心理预期、过度反应与反应不足、投资者构成和交易机制等方面对该结论进行了分析。     

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.     

The persistence and asymmetric volatility in the Nigerian stock bull and bear markets

This paper considers the persistence and asymmetric volatility at each market phase of the Nigerian All Share Index (ASI). The estimate of the fractional difference parameter is used as a stability measure of the degree of persistence in the level of the series and in the absolute/squared returns, which are used as proxies for the volatility. Both semi-parametric and parametric methods are applied. Forms of Generalized Autoregressive Conditionally Heteroscedastic (GARCH) models, which include fractional integration and asymmetric variants are estimated at each market phase of the stock returns. The results show that the level of persistence differs between the two market phases in both level and squared/absolute return series. Apart from general asymmetry and persistence in Nigerian stocks, each market phase still presents significant persistence and asymmetry.     

What are returns outside trading hours capturing for volatility of individual stocks?

This study is the first to harness the negative returns and squared returns outside trading hours, trading volume and leverage effects in an augmented heterogeneous autoregressive model for forecasting volatility of individual stocks. Besides significant leverage effects and trading volume impact, we find that an increase in the negative returns is associated with a decline in volatility, but an increase in the squared returns is associated with a rise in volatility. This new finding suggests that the negative returns and squared returns outside trading hours are capturing additional leverage effects and additional volatilities, respectively. Moreover, the relations display differences amongst various firm categories which arise from firm heterogeneity.     

The linkages,persistence, asymmetry in the volatility,the price discovery and efficiency,and the effect of the US subprime mortgage financial crisis on the spot and the futures market’s returns: the case of India

This article examines the effects of persistence, asymmetry and the US subprime mortgage crisis on the volatility of the returns and also the price discovery, efficiency and the linkages and causality between the spot and futures volatility by using various classes of the ARCH and GARCH models, and through the Granger’s causality. We have used two indices: one for spot and the other for futures, for the daily data from 12 June 2000 to 30 September 2013 from Nifty stock indices. We have then tested for ARCH effects, and subsequently employed various models of the ARCH and GARCH conditional volatility. The GARCH(1,1) model is found to be significant, and it implies that the returns are not autocorrelated and have ‘short memory’. It supports the hypothesis of the efficiency of the markets. The negative ‘news’ has more significant effect on volatility, corroborating the ‘leverage impact’ in finance on market volatility. We have also tested the volatility spillover effects. The two methods we employed support the spillover effects and the causality is bidirectional. We also have used the dummy variable for the US subprime mortgage financial crisis and found that they are statistically significant. Indian stock market is thus integrated to the world stock markets.     

Asymmetric effect of advertising on the Chinese stock market

In this paper, we investigate whether investor attention to advertising has an asymmetric effect on Chinese stock returns by using a multivariate Markov switching model with time-varying regime transition probabilities. Using the Chinese stock market as a setting, we obtain lagged conditional volatility from generalized autoregressive conditional heteroskedasticity (GARCH) for modelling the time-varying transition probabilities of the regime-switching process to capture changes in the market regime. Our evidence documents that the high advertising portfolio does earn higher abnormal return than the low advertising portfolio in low-volatility periods. In high-volatility periods, however, the abnormal return is insignificant when the firm increases advertising spending. Our results support the behavioural model argument that in high-volatility period, advertising information diffuses slowly due to cognitive dissonance. Thus, the effect of advertising on stock returns is asymmetric, and it shows statistical significance in low-volatility periods.     

Asymmetry and leverage in GARCH models: a News Impact Curve perspective

Models for conditional heteroskedasticity belonging to the GARCH class are now common tools in many economics and finance applications. Among the many possible competing univariate GARCH models, one of the most interesting groups allows for the presence of the so-called asymmetry or leverage effect. In our view, asymmetry and leverage are two distinct phenomena, both inspired by the seminal work of Black in 1976. We propose definitions of leverage and asymmetry that build on the News Impact Curve, allowing to easily and coherently verify if they are both present. We show that several GARCH models are asymmetric but none is allowing for a proper leverage effect. Finally, we extend the leverage definition to a local leverage effect and show that the AGARCH model is coherent with the presence of local leverage. An empirical analysis completes the paper.     

中美股市杠杆效应与波动溢出效应——基于GARCH模型的实证分析

本文基于极大似然函数值准则和赤池信息准则,从众多非对称GARCH模型中选择最优模型来研究中美股市杠杆效应和波动溢出效应。结果表明:沪市和深市都表现出显著的杠杆效应,与美国股市相比沪市和深市杠杆效应较弱;沪市和深市之间存在显著的双向波动溢出效应,且沪市对深市的波动溢出效应更显著;美国股市与中国股市之间不存在显著的波动溢出效应。     

ASYMMETRIC INFORMATION IMPACTS: EVIDENCE FROM THE AUSTRALIAN TREASURY-BOND FUTURES MARKET

Abstract.  The effect of information flows on the return volatility of Australian 3-year Treasury bond futures is examined using linear and non-linear GARCH models. Results show significant asymmetric information effects, where bad news has a greater impact on volatility than good news and a non-linear Threshold ARCH(1,1) in mean model provides the most accurate estimation of return volatility. Diagnostic tests confirm this finding and out of sample forecasting error statistics verify that the Threshold ARCH(1,1) in mean model yields the lowest forecasting error. The Threshold ARCH(1,1)-M model is best at capturing the asymmetric information impact on the Australian three-year T-Bond futures return volatility.     

基于GARCH模型对人民币汇率波动的实证研究

本文建立了人民币汇率波动的GARCH族模型,实证检验了汇率制度改革以来人民币汇率波动的特征。结果显示,2005年7月21日至今,人民币的汇率收益具有显著的左厚尾特征;汇率的波动并不服从正态分布,具有集聚性;并且人民币的波动具有记忆性,随时间变化不会衰减;通过TGARCH模型的实证结果显示,人民币的汇率波动存在一定的杠杆效应,人民币汇率还不具备浮动汇率的特征。根据分析,本文认为杠杆效应的存在源自于汇率升值的单向预期,给出以下建议：通过有节奏的汇率市场化改革,以及改善国际收支双顺差,减少对升值的单向预期;央行对汇率的波动适当控制;培育人民币汇率衍生市场,增加进出口贸易企业规避汇率风险的金融产品;增加对附加值高的出口企业非汇率贸易政策支持。     

THE DYNAMIC RELATION BETWEEN RETURNS,TRADING VOLUME,AND VOLATILITY: LESSONS FROM SPILLOVERS BETWEEN ASIA AND THE UNITED STATES

This paper investigates the dynamic relationship between index returns, return volatility, and trading volume for eight Asian markets and the US. We find cross‐border spillovers in returns to be non‐existent, spillovers in absolute returns between Asia and the US to be strong in both directions, and spillovers in volatility to run from Asia to the US. Trading volume, especially on the Asian markets, depends on shocks in domestic and foreign returns as well as on volatility, especially those shocks originating in the US. However, only weak evidence is found for trading volume influencing other variables. In the light of the theoretical models, these results suggest sequential information arrivals, with investors being overconfident and applying positive feedback strategy. Furthermore, new information causes price volatility to rise due to differences in its interpretation among traders, but the subsequent market reaction takes the form of adjustment in price level, not volatility. Lastly, the intensity of cross‐border spillovers seems to have increased following the 1997 crisis, which we interpret as evidence of increased noisiness in prices and diversity in opinions about news originating abroad. Our findings might also help to understand the nature of financial crises, to predict their further developments and consequences.     

股指期货对现货市场的信息传递效应分析

本文研究了股票指数合约的交易对现货市场的影响以及股指期货是否有助于现货市场在信息传递速度与效率方面的提升.利用了GARCH模型,修正GARCH模型,TGARCH模型及极端值模型,通过对香港恒生H股指期货合约引入前后样本的实证分析发现,在期货合约未上市前,波动性干扰反应在时间上的持续性效果较持久.反之,在股价指数期货合约推出后,可以观察到波动性干扰因子的影响会更快速的反应到经济体系中,显示此时的波动过程更趋稳定.由此推论出期货交易的进行加速了信息传递的效率.亦即开放期货合约的交易,对于其标的现货市场的信息传递以及市场波动性,皆具有正面的贡献.     

TRADING VOLUME,VOLATILITY, AND GARCH EFFECTS IN THE SOUTH KOREAN WON/US DOLLAR EXCHANGE MARKET: EVIDENCE FROM CONDITIONAL QUANTILE ESTIMATION*

Under the MDH, this paper investigates the asymmetry in the positive relationship between unexpected volume and volatility, and whether the unexpected volume series as a proxy for the rate of information arrival absorbs the GARCH effects. This is achieved by applying a quantile regression approach to the won/dollar exchange market with reliable data on trading volumes. Interestingly, the results show that in a freely floating exchange rate system, the positive relationship increases as exchange rate returns are higher. Contrary to previous studies, despite a significantly positive relationship, the inclusion of volumes alone does not reduce volatility persistence at medium or high levels of returns. In addition, the reform of the South Korean exchange rate system had an impact on the relationship, which occurred in response to a financial crisis.     

An information theoretic analysis of stock returns,volatility and trading volumes

Information theory is used to examine the dynamic relationships between stock returns, volatility and trading volumes for S&P500 stocks. This provides an alternative approach to traditional Granger causality tests when dealing with nonlinear relationships. The article highlights the dominant role played by trading volumes in all of these relationships – even in the return–volatility relation – and finds evidence of a market level feedback effect from index returns to the return–volatility relation at the stock level. The article also produces a number of stylized facts from an information theoretic perspective.     

Volatility spillover and multivariate volatility impulse response analysis of GFC news events

This article applies two measures to assess spillovers across markets: the Diebold and Yilmaz’s (2012) spillover index and the Hafner and Herwartz’s (2006) analysis of multivariate GARCH models using volatility impulse response analysis. We use two sets of data, daily realized volatility (RV) estimates taken from the Oxford-Man RV library, for the S&P500 and the FTSE, plus 10 years of daily returns series for the New York Stock Exchange Index and the FTSE 100 index. Both data sets capture both the global Financial Crisis (GFC) and the subsequent European Sovereign Debt Crisis (ESDC). The spillover index captures the transmission of volatility to and from markets, plus net spillovers. The Volatility Impulse Responses (VIRF) have to be calibrated to conditional volatility estimated at a particular point in time. We explore the impact of three different shocks, the onset of the GFC, the height of the GFC, and the impact of the ESDC. Our modelling includes leverage and asymmetric effects applying a multivariate GARCH model, and further analysis using both BEKK and diagonal BEKK (DBEKK) models. We find the impact of negative shocks is larger, but shorter in duration, in this case a difference between 3 and 6 months.     

Modeling long memory volatility using realized measures of volatility: A realized HAR GARCH model

Long memory is an important feature of the volatility of financial returns. We document that the recently developed Realized GARCH model (Hansen et al., 2012) is insufficient for capturing the long memory of underlying volatility. We develop a parsimonious variant of the Realized GARCH model by introducing the HAR specification of Corsi (2009) into the volatility dynamics. A comparison of the theoretical and sample autocorrelation functions shows that the new model specification better captures the long memory dynamics of volatility. We calculate the multi-period out-of-sample volatility forecasts for several return series and find that the new model is a significant improvement over the classic Realized GARCH model.     

FINANCIAL CRISES AND INTERNATIONAL STOCK MARKET VOLATILITY TRANSMISSION

This paper examines the interplay between stock market returns and their volatility, focusing on the Asian and global financial crises of 1997–98 and 2008–09 for Australia, Singapore, the UK, and the US. We use a multivariate generalised autoregressive conditional heteroskedasticity (MGARCH) model and weekly data (January 1992–June 2009). Based on the results obtained from the mean return equations, we could not find any significant impact on returns arising from the Asian crisis and more recent global financial crises across these four markets. However, both crises significantly increased the stock return volatilities across all of the four markets. Not surprisingly, it is also found that the US stock market is the most crucial market impacting on the volatilities of smaller economies such as Australia. Our results provide evidence of own and cross ARCH and GARCH effects among all four markets, suggesting the existence of significant volatility and cross volatility spillovers across all four markets. A high degree of time‐varying co‐volatility among these markets indicates that investors will be highly unlikely to benefit from diversifying their financial portfolio by acquiring stocks within these four countries only.     

Modelling the dynamics of Bitcoin and Litecoin: GARCH versus stochastic volatility models

We examine and compare a large number of generalized autoregressive conditional heteroskedastic (GARCH) and stochastic volatility (SV) models using series of Bitcoin and Litecoin price returns to assess the model fit for dynamics of these cryptocurrency price returns series. The various models examined include the standard GARCH(1,1) and SV with an AR(1) log-volatility process, as well as more flexible models with jumps, volatility in mean, leverage effects, t-distributed and moving average innovations. We report that the best model for Bitcoin is SV-t while it is GARCH-t for Litecoin. Overall, the t-class of models performs better than other classes for both cryptocurrencies. For Bitcoin, the SV models consistently outperform the GARCH models and the same holds true for Litecoin in most cases. Finally, the comparison of GARCH models with GARCH-GJR models reveals that the leverage effect is not significant for cryptocurrencies, suggesting that these do not behave like stock prices.