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Measuring and Testing the Impact of News on Volatility
The Journal of Finance
Abstract
This paper defines the news impact curve that measures how new information is incorporated into volatility estimates. Various new and existing ARCH models, including a partially nonparametric one, are compared and estimated with daily Japanese stock return data. New diagnostic tests are presented that emphasize the asymmetry of the volatility response to news. The authors' results suggest that the model by L. Glosten, R. Jagannathan, and D. Runkle (1989) is the best parametric model. The EGARCH also can capture most of the asymmetry; however, there is evidence that the variability of the conditional variance implied by the EGARCH is too high. Copyright 1993 by American Finance Association.
... First, it attempts to capture the asymmetric volatility return using "GARCH (generalized autoregressive conditional heteroskedasticity) family" models. Second, unlike previous studies the present study used the sign bias test of (Engle and Ng 1993) of univariate model, to capture the positive and negative news shock (or leverage effects) on ESG equity return. Third, study capture volatility persistence in long memory process in market returns of ESG Equity indices. ...
... To address this aspect of the ARCH model, Black (1976) discovers a negative correlation between current and future returns volatility. According to "Leverage effects" (Engle and Ng 1993), the hypothesis is that negative news has a more significant impact on conditional volatility than positive news. The market is more volatile when bad negative news arrives than good positive news, which is called the "leverage effect." ...
... The market is more volatile when bad negative news arrives than good positive news, which is called the "leverage effect." To account for the presence of leverage effects, (Engle and Ng 1993) propose the sign bias test explained below. ...
The aim of the study is to investigate the evidence of information asymmetry, dynamic connectedness, and volatility spillover among ESG equity indices of emerging market economies. Using Sign bias test and GARCH family models, the study finds that ESG equity indices have a leverage effect, significantly impacted by bad news over good news shock. The study has used FIGARCH model to measure the persistence of long‐memory effects across the emerging market. Further, to ensure the interconnection between ESG equity indices that may arise due to the persistence of long‐memory effects, the stusy has examined estimates of TVP‐VAR, and finds moderate interconnection between ESG equity indices. To be specific, ESG equity indices of the Philippines, Indonesia, Korea, Singapore, and India are more sensitive to receiving any sustainable innovation shocks from Brazil, South Africa, and Mexican ESG indices. The study finds significant bidirectional relationships between the ESG equity indices of “Philippines and Brazil,” “Indonesia and India,” and “South Africa and Mexico” that may lead to the spreading of market contagion in the presence of more substantial leverage effects with a long memory. This research offers insights for investors to consider sustainable equity assets for efficient portfolio diversification, mitigating environmental, social, and governance risks associated with volatility spillovers and dynamic connectedness. Policymakers may refer the findings of the study to design effective ESG regulations, for reducing risk in global financial system. Since the pandemic has produced more economic and financial instability in emerging markets, investors and regulators may pay more attention to return and volatility connectivity among ESG equity indices and financial markets to safeguard investment and restore market stability.
... Besides, the Realized Realtime GARCH model is similarly extended to the Realized Real-time GARCH-L model to capture the leverage effect of current random shock. Thirdly, a simulation experiment, the corresponding news impact curves (NIC) proposed by Engle and Ng (1993), and cumulative impact response function (CIRF) proposed by Di and Gangopadhyay (2015) are used to observe the impact of external information on future volatility. Fourthly, some important statistical properties are discussed. ...
... Besides, the news impact curve (NIC) and cumulative impact response function (CIRF) are considered to understand how current information affects future volatility. The NIC proposed by Engle and Ng (1993) is usually used to study the influence of past information on one-step ahead volatility. Considering that the information content has been enlarged, here the NIC of the Realized RT-GARCH model is redefined as where t+1 = denotes the current information at day t + 1. ...
... However, it is generally accepted that the negative information creates a greater shock to financial assets compared to the positive information of the same magnitude, which can be called the leverage effect. The well-known characteristic was found by Christie (1982) and Engle and Ng (1993). Most volatility models have been extended to incorporate this feature, see Nelson (1991), Engle and Ng (1993), Wang and Mykland (2014) among others. ...
Existing high-frequency-based volatility models usually regard the volatility process of financial returns as a function of the past daily-frequency and high-frequency information, and cannot take full advantage of the current information. This paper incorporates the Real-time information into the Realized GARCH model and proposes the Realized Real-time GARCH model. The new model retains the basic structure of the Realized GARCH model and considers the volatility process as a mixed product of past information and current information. Then some significant properties of the proposed model are discussed. Also, the variation of this model, the Realized Real-time GARCH-L model, is proposed to describe the leverage effect of the Real-time information. Our empirical results show that considering Real-time information makes the model perform better in terms of dealing with sudden jumps of volatility, improves the in-sample empirical fitting, and contributes to the improvements in forecasting multi-step ahead volatility, conditional density of returns and value at risk (VaR). Besides, the leverage effect of Real-time information also provides substantial improvements over the Realized Real-time GARCH model.
... The results in Column 1 indicate that from the 1st lag to the 36th lag, returns are statistically significant at the 1% level, suggesting the presence of serial correlation in the model. Consequently, the study investigates the appropriate autoregressive-moving average (ARMA (p, q)) structure, aligning with the studies of [17], Engel & Victor [20]). Furthermore, the result in column 2 of Table 2 reveals that squared returns exhibit statistical significance from the 1st to the 36th lag, indicating the presence of an ARCH effect. ...
... Having confirmed the existence of nonlinearity, we proceed with asymmetric modelling using the EGARCH and GJR-GARCH models; [17], Engel & Victor [20]) argue that these models are most appropriate for asymmetric GARCH analysis. The results, presented in Table 7, indicate that the coefficients for all three distributions in both the EGARCH and GJR-GARCH models are statistically significant. ...
This study models and forecasts the volatility of the Nigerian Stock Exchange (NSE) using advanced econometric techniques, focusing on examining the asymmetric volatility and the leverage effect. Daily data from the NSE All Share Index spanning from 30 th January, 2012, to 16 th October, 2024 (3,176 days) are analysed using generalized autore-gressive conditional heteroskedasticity family models, including EGARCH and GJR-GARCH, along with non-Gaussian distributions like the Student's t-distribution. The findings reveal a significant leverage effect, where negative shocks impact stock prices more than positive ones, supporting asymmetric volatility theory. The study also identifies volatility clustering, where high-volatility periods are followed by continued volatility, further highlighting the persistence of market turbulence. Among the models tested, GJR-GARCH with the Student's t-distribution performs best in forecasting volatility, providing superior fit and forecasting accuracy. These insights offer practical implications for investors and policymakers in managing risks in emerging markets, particularly during periods of high volatility.
... Volatility exhibits a series of stylized facts, including temporal clustering (Mandelbrot 1997; Kim and Shin 2023), long memory (Poon and Granger 2003), heavy tails (Cont 2001), leverage effect (McAleer and Medeiros 2008; Aıt-Sahalia 2017; Engle and Ng 1993;Tversky and Kahneman 1991;Christie 1982;Bekaert and Wu 2000), and mean reversion (Goudarzi 2013). These stylized attributes make volatility forecasting possible and are detailed in Appendix A. Nevertheless, predicting volatility remains a challenging endeavor. ...
... Additionally, the leverage effect or the Asymmetric Volatility Phenomenon (AVP) suggests a negative correlation exists between prices and volatility: as prices drop, volatility intensifies, and as prices rise, volatility diminishes, though to a lesser extent (McAleer and Medeiros 2008; Aıt-Sahalia 2017; Engle and Ng 1993). Due to the AVP, option prices exhibit a skew. ...
Volatility forecasting for financial institutions plays a pivotal role across a wide range of domains, such as risk management, option pricing, and market making. For instance, banks can incorporate volatility forecasts into stress testing frameworks to ensure they are holding sufficient capital during extreme market conditions. However, volatility forecasting is challenging because volatility can only be estimated, and different factors influence volatility, ranging from macroeconomic indicators to investor sentiments. While recent works show promising advances in machine learning and artificial intelligence for volatility forecasting, a comprehensive assessment of current statistical and learning-based methods is lacking. Thus, this paper aims to provide a comprehensive survey of the historical evolution of volatility forecasting with a comparative benchmark of key landmark models, such as implied volatility, GARCH, LSTM, and Transformer. We open-source our benchmark code to further research in learning-based methods for volatility forecasting.
... Finally, leverage effect refers to the widely documented negative correlation between observed changes in stock returns and volatility [26], see also [25,41] and references therein. It is often incorporated in models for financial price dynamics through a negative correlation between the noises driving price and volatility, see [44,34,36,50]. ...
... which readily follows from (26) and the fact that Y N is bounded up to time τ N h . The martingale component of Π N is given by, using α = f ′ (0)(1 + βγ), ...
We consider a tick-by-tick model of price formation, in which buy and sell orders are modeled as self-exciting point processes (Hawkes process), similar to the one in [El Euch, Fukasawa, Rosenbaum, The microstructural foundations of leverage effect and rough volatility, Finance and Stochastics, 2018]. We adopt an agent based approach by studying the aggregation of a large number of these point processes, mutually interacting in a mean-field sense. The financial interpretation is that of an asset on which several labeled agents place buy and sell orders following these point processes, influencing the price. The mean-field interaction introduces positive correlations between order volumes coming from different agents that reflect features of real markets such as herd behavior and contagion. When the large scale limit of the aggregated asset price is computed, if parameters are set to a critical value, a singular phenomenon occurs: the aggregated model converges to a stochastic volatility model with leverage effect and faster-than-linear mean reversion of the volatility process. The faster-than-linear mean reversion of the volatility process is supported by econometric evidence, and we have linked it in [Dai Pra, Pigato, Multi-scaling of moments in stochastic volatility models, Stochastic Processes and their Applications, 2015] to the observed multifractal behavior of assets prices and market indices. This seems connected to the Statistical Physics perspective that expects anomalous scaling properties to arise in the critical regime.
... To affirm the adequacy of our GARCH model specifications, a suite of misspecification tests, detailed in Appendix 14, was conducted. The Sign Bias test [56] was utilized to detect potential asymmetric effects, with a significant outcome advocating for the further inclusion of leverage parameters. The Q 2 (20) statistic [38] assessed the need for additional ARCH components to capture volatility dynamics effectively. ...
... Evaluation of univariate GARCH performance Significance levels are marked by ***, **, * for 1%, 5%, and 10% respectively, with corresponding p-values in parentheses; Sign Bias:Engle and Ng (1993) test; Q2(20): Weighted Portmanteau test statistics[38]; VaR: Value-at-Risk test[57]; CVaR: Conditional Value-at-Risk test[58]; VaR Dur.: Value-at-Risk Duration(Christoffersen and Pelletier, 2004). All VaR test statistics are based on the 5% quantile levelTable 15Bivariate hedge ratios: robustness test using standard GARCH(1,1) ...
Using daily data from January 5, 2012, to June 28, 2024, this study applies a novel DCC-GARCH decomposed connectedness algorithm to analyze the spillover effects between Chinese fintech assets (FNTC) and traditional financial sector assets—banking (BANK), securities (SECU), and insurance (INSR). The role of FNTC in enhancing investment strategies for these assets is also explored. The distinct distribution and significant asset correlation of FNTC provide statistical support for investment strategy optimization. FNTC is shown to effectively hedge risk exposure, with multivariate hedging strategies outperforming those of bivariate ones. Bivariate FNTC portfolios outperform single assets in Sharpe ratio, indicating more effective strategies. Multivariate portfolios don't always beat bivariate ones. Notably, the classic Minimum Variance Portfolio rival modern strategies, highlighting contextual selection's importance. This research provides strategic insights for China's finance and fintech, advancing the field from a portfolio perspective.
... Cependant, s'il est élevé, le risque est important, ce qui suggère une forte volatilité.La volatilité augmente les rendements quotidiens d'un indice boursier. L'arrivée de nouvelles informations inattendues, l'augmentation du levier financier, les changements des taux directeurs de la politique monétaire, les crises financières et les récessions économiques sont les principales causes de volatilité(Engle, R. F. & Ng, V. K. 1993 ; Black, 1976 ). Aujourd'hui,elle joue un rôle important dans de nombreuses applications économiques et financières car elle est au coeur de nombreuses décisions économiques et financières telles que la diversification des portefeuilles et la gestion des risques. ...
... Ainsi, les modèles de type GARCH sont dextres avec la distribution d'erreur généralisée (GED) est jugée appropriée dans le but de modéliser la volatilité conditionnelle. En outre, les modèles de type GARCH sont au niveau de confiner, au moins partiellement, la leptokurtose de la distribution inconditionnelle du rendement d'une composante économique ainsi que les informations importantes concernant la dépendance dans les valeurs quadratiques du rendement(Engle et Ng, 1993). Par conséquent, l'utilisation du modèle de type GARCH pour la variance conditionnelle est raisonnable pour prévoir les rendements du marché pour MASI et SPMII.Tableau 19 : Résultats des modèles estimés de la famille GARCH Source : Établi par les auteurs Nous utilisons les modèles GARCH (1.1), EGARCH (1.1) et TGARCH (1.1) pour prévoir les indices boursiers MASI et SPMII respectivement et les résultats sont donnés dans le tableau ci-dessous. ...
Notre recherche est réservé à la méthodologie et à la mise en
œuvre des deux indices à savoir : L'indice Standard and Poor Marocain Islamique (SPMII) et
l'indice Marocain Toutes Actions (MASI), en commençant, tout d'abord, par présenter leurs
statistiques descriptives, aussi que leurs représentations sont faites par des courbes expliquant
et montrant leurs variations et leurs tendances, sur cela, nous avons constaté que la courbe du
SPMII varie d'une manière presque stable contrairement à son homologue qui grimpe d'une
manière importante compte tenu de sa date de naissance considérée comme ancienne par
rapport à l'autre qui est nouvellement créé . Ensuite, nous avons testé les deux indices avec le
modèle ADF (Augmented Dickey Fuller) afin de vérifier la stationnarité de leurs séries
temporelles.
Nous avons estimé les deux indices par l'effet ARCH précisément par le test
ARCH-LM. Le tableau 18 ci-dessus montre les résultats du test ARCH-LM. Les séries de
rendement du MASI et du SPMII montrent des preuves d'effets ARCH, ce qui prouve l'impact
de l'effet d'hétéroscédasticité , c'est-à-dire le regroupement de la volatilité. Nous avons utilisé
les modèles GARCH (1.1), EGARCH (1.1) et TGARCH (1.1) pour prévoir les indices boursiers
MASI et SPMII respectivement et les résultats sont donnés dans le tableau 19 ci-dessus, qui a
révélé que de forts effets ARCH et GARCH sont évidents dans les rendements. Après
l'estimation des paramètres précités, il est déduit de l'apparition d'un effet de levier, c'est-à-dire
que la volatilité des innovations négatives est plus élevée que celle des innovations positives.
De même que le test des modèles GARCH utilisant le multiplicateur de Lagrange
(ARCH-LM) a été utilisé pour examiner la présence d'effets ARCH durables dans les résidus
standardisés, en conclusion, le test ARCH-LM pour tous les modèles GARCH indique que des
effets ARCH demeurent dans les résidus standardisés des équations de variance. Notre
recherche actuelle n'a pas été en mesure de couvrir toutes les parties du sujet en question. Bien
sûr, la période de temps était très limitée et le SPIII nouvellement créé n'a pas une longue
période de temps comme le cas de MASI.
En synthèse, le chapitre 6 explore la méthodologie et l'application des indices
SPMII et MASI. Les courbes révèlent des tendances stables pour le SPMII et une croissance
significative pour le MASI. Les tests ADF et ARCH-LM confirment l'effet d'hétéroscédasticité
dans les séries de rendement. Les modèles GARCH révèlent des effets ARCH et GARCH
marqués, illustrant une volatilité différenciée entre les innovations positives et négatives.166
Malgré des limites temporelles et la jeuneté du SPIII, notre étude révèle la persistance des effets
ARCH dans les résidus standardisés, incitant à approfondir cette analyse.
... Findings: To predict volatility in medium and high-volatility sectors, GARCH models perform better, demonstrating their ability to capture persistent volatility. Engle and Ng (1993) Methodology: GARCH and ARCH models. Findings: Volatility reacts asymmetrically to interest rate changes, with sector-specific variations. ...
... Sectoral analysis indicates that changes in interest rates negatively affect sector index returns. This result aligns with studies by Campbell and Hentschel (1992) and Engle and Ng (1993). Volatility persistence in sectors like banking, holdings, and transportation is in line with Schwert's (1989) and Bollerslev's (1986) findings. ...
This study analyses the impact of interest rate changes and past volatility on sector index returns in Borsa Istanbul using a GARCH(1,1) model. The results show that interest rate changes negatively affect sector returns, including banking, food, holdings, tourism, services, transportation, financial, industrial, and technology. Furthermore, the GARCH(1,1) model indicates persistence in volatility in sectors like banking, holdings, transportation, financial, industrial, and technology, where past volatility strongly influences future volatility. Conversely, sectors such as food, tourism, and services exhibit less volatility persistence, suggesting more stable returns during interest rate fluctuations. The GARCH (1,1) specification outperforms the ARCH model by capturing the persistence of variance, making it a more reliable measure for sectoral volatility. The results align with previous research, mainly on the sensitivity of financial sectors to interest rate changes and market volatility. This study's unique contribution lies in its focus on BIST 100 sectors, offering valuable insights for investors to optimise asset allocation. By understanding sector-specific sensitivities to interest rate changes and volatility, investors can make informed decisions to enhance returns.
... 9 With a normal Gaussian distribution AR (1)-PGARCH (1,1) meets three performances into 4, followed closely by AR (1)-TGARCH (1,1). Bitcoin price index forecasting is elaborated using five GARCH family models with a normal distribution [48,54,58,61]. ...
This study addresses the issue of modeling and forecasting Bitcoin volatility using daily closing prices from 18th July 18, 2015, to 04th September 4, 2023. This study endeavored to model the dynamics following AR (1)-GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) (1,1), AR (1)-PGARCH (1,1), AR (1)-EGARCH (1,1), AR (1)-(TGARCH) (Threshold Generalized Autoregressive Conditional Heteroscedasticity) (1,1), AR (1)-CGARCH (Component AutoRegressive Conditional Heteroskedasticity) (1,1), and AR (1)-ACGARCH (1,1) processes under a normal Gaussian distribution for errors. The results show that the AR (1)-ACGARCH (1,1) model is the best for modeling gold volatility and AR (1)-APARCH (1,1) for forecasting. Bitcoin can be an expedient tool for portfolio and risk management, and the results of this study will help investors make informed decisions.
... The role of information flow during periods of global uncertainty has been extensively studied. Engle and Ng (1993) developed models to capture asymmetric responses to news, finding that negative shocks have a more pronounced effect on volatility than positive shocks. This asymmetry may be amplified in emerging markets during periods of global uncertainty, as documented by Bekaert and Harvey (1997) ...
This study investigates the relationship between herding behavior and stock price volatility in the Vietnamese stock market, with a particular focus on the moderating role of global economic uncertainty. Using a comprehensive dataset of 756 listed companies on both the Ho Chi Minh and Hanoi Stock Exchanges from 2010 to 2016, yielding 2,268 firm-year observations, the research employs multiple methodological approaches including GARCH modeling, panel regression analysis, and System GMM estimation. Herding behavior is measured using the Cross-Sectional Absolute Deviation (CSAD) approach, while stock price volatility is captured through various measures including GARCH (1,1) and realized volatility estimates. The empirical findings reveal significant evidence of herding behavior in the Vietnamese market, with a strong positive relationship between herding and stock price volatility (β = 0.456, p < 0.01). Global economic uncertainty is found to significantly moderate this relationship, amplifying the impact of herding on volatility during periods of heightened global uncertainty. The study contributes to the existing literature by providing novel insights into the dynamics of herding behavior in emerging markets and its interaction with global economic conditions. These findings have important implications for investors, policymakers, and market regulators, particularly in the context of emerging market economies and their increasing integration with global financial markets.
... To address this issue, Dickey-Fuller proposed a parametric correction, resulting in the Augmented Dickey-Fuller test. The results of the stationarity tests indicate that all variables are stationary at an integration order of 1. Engle and Ng (1993) propose a set of tests for volatility asymmetry, known as the sign and size bias tests. These tests are used to determine whether an asymmetric model is necessary for a given series or if a symmetric GARCH model is adequate. ...
This paper investigates the impact of the Russia-Ukraine war on fluctuations in eight prominent cryptocurrencies. Given their inherent volatility, cryptocurrencies have become an important area of study for understanding how global crises affect financial markets. Using advanced dynamic and asymmetric modeling techniques, this study examines the interdependence and asymmetric volatility of these digital assets. By analyzing how cryptocurrencies respond to the uncertainty and shocks generated by the conflict, this research aims to provide insights into their behavior as alternative financial instruments during geopolitical instability. Our findings reveal a negative impact of the war on cryptocurrencies such as Cardano, Dogecoin, Tether, and XRP, while Bitcoin, Litecoin, BNB, and Ethereum experienced a positive impact. These results highlight the varying vulnerabilities of cryptocurrencies and suggest that assuming constant correlations is inadequate. This necessitates further exploration of conditional correlation dynamics to better capture contagion effects during geopolitical events. The study also discusses the implications of these findings for investors, policymakers, and regulators, emphasizing the importance of considering external factors, like geopolitical events, in investment decision-making and the development of regulatory frameworks for the cryptocurrency market.
... The analysis reveals that the asymmetric effects, as represented by the parameter ω, are significant for certain asset classes like gold, oil, and energy, indicating that negative shocks (e.g., adverse news or market downturns) have a more pronounced impact on volatility compared with positive shocks. This asymmetry aligns with the leverage effect observed in financial markets, where bad news tends to increase perceived risk and uncertainty, leading to heightened volatility [54,55]. Commodities such as gold and oil, being highly sensitive to geopolitical and macroeconomic factors, exhibit strong asymmetric volatility responses due to their role as hedging instruments and their dependency on external factors like supply disruptions or inflationary pressures. ...
This study examines the volatility and hedging effectiveness of commodities,
specifically gold and oil, on the Indian stock market, focusing on both aggregate and sectoral indices. Data have been collected from 1 January 2021 to 31 December 2024 to cover the post-COVID-19 period. Utilizing the Asymmetric Dynamic Conditional Correlation Generalized Autoregressive Conditional Heteroskedasticity (ADCC-GARCH) model, we analyze the volatility spillovers and time-varying correlations between commodity and stock market returns. The analysis of spillover connectedness reveals that both commodities exhibit limited and inconsistent hedging potential. Gold demonstrates low and stable spillovers in most sectors, indicating its diminished role as a reliable safe-haven asset in Indian markets.
Oil shows relatively higher but volatile spillover effects, particularly with sectors closely tied to energy and industrial activities, reflecting its dependence on external economic and geopolitical factors. This study contributes to the literature by providing a sector-specific perspective on commodity–stock market interactions, challenging conventional assumptions of hedging efficiency of gold and oil. It also emphasizes the need to explore alternative hedging mechanisms for risk management in the post-crisis phase.
... Three standard diagnostic tests are employed to validate model specification: the Ljung-Box test checks autocorrelation in standardized and squared residuals to ensure the model captures all temporal volatility dependencies [50]; the ARCH-LM test checks remaining ARCH effects to ensure the model adequately explains conditional variance [51]; and the sign bias test evaluates asymmetric volatility responses, confirming that negative shocks induce greater volatility than positive ones [52]. ...
Financial stability analysis requires volatility modeling, especially in emerging nations where pension fund systems are very vulnerable to macrofinancial risks. In order to examine the volatility dynamics of Romania’s private pension system, this study uses daily net asset value (NAV) data from 2012 to 2024 to evaluate four GARCH-type models: standard GARCH (sGARCH), exponential GARCH (EGARCH), Glosten–Jagannathan–Runkle GARCH (GJR-GARCH), and component GARCH (C-GARCH). The analysis includes domestic and international equity indices (BET, STOXX), government bond yields (ROMGB 10Y, ROMANI 5Y), short-term interbank rates (ROBOR ON), and exchange rate fluctuations (RON/EUR). Current findings indicate that EGARCH captures asymmetric fluctuations in pension fund performance, where positive shocks generate larger increases in volatility than negative ones, highlighting an atypical asymmetry pattern. Furthermore, the stabilizing effects of government bonds are overshadowed by stock market behavior, which becomes the primary driver of risk. Fluctuations in exchange rates further increase volatility, especially in markets vulnerable to external disturbances. The findings offer empirical evidence for the necessity of more cautious risk management approaches and highlight the importance of regulatory oversight in maintaining market confidence. The study underscores the importance of customized allocation frameworks that reduce vulnerability to disruptive events while maintaining prospects for sustained growth. This new dataset contributes to enhancing the comprehension of pension fund volatility within the context of emerging markets. These insights can assist managers and policymakers seeking to fortify retirement outcomes.
... (Han et al. 2009) further argues that stock price momentum can arise from uncertainty about the accuracy of cash flow forecasts, with momentum reflecting investors' evolving understanding of the relative reliability of information sources and their subsequent updates to expectations. Several studies, including (Ang and Bekaert 2006), (Engle and Ng 1993), (Glosten et al. 1993), and (Schwert and Seguin 1990), focus on the relationship between price changes and information flow. The most widely used models for capturing volatility dynamics in financial time series are GARCH-type models. ...
This study seeks to advance the understanding and prediction of stock market return uncertainty through the application of advanced deep learning techniques. We introduce a novel deep learning model that utilizes a Gaussian mixture distribution to capture the complex, time-varying nature of asset return distributions in the Chinese stock market. By incorporating the Gaussian mixture distribution, our approach effectively characterizes short-term fluctuations and non-traditional features of stock returns, such as skewness and heavy tails, that are often overlooked by traditional models. Compared to GARCH models and their variants, our method demonstrates superior performance in volatility estimation, particularly during periods of heightened market volatility. It provides more accurate volatility forecasts and offers unique risk insights for different assets, thereby deepening the understanding of return uncertainty. Additionally, we propose a novel use of Code embedding which utilizes a bag-of-words approach to train hidden representations of stock codes and transforms the uncertainty attributes of stocks into high-dimensional vectors. These vectors are subsequently reduced to two dimensions, allowing the observation of similarity among different stocks. This visualization facilitates the identification of asset clusters with similar risk profiles, offering valuable insights for portfolio management and risk mitigation. Since we predict the uncertainty of returns by estimating their latent distribution, it is challenging to evaluate the return distribution when the true distribution is unobservable. However, we can measure it through the CRPS to assess how well the predicted distribution matches the true returns, and through MSE and QLIKE metrics to evaluate the error between the volatility level of the predicted distribution and proxy measures of true volatility.
... The financial interpretation of the leverage effect is that in the "asymmetric" or "leverage" volatility models, good/bad news has different predictability for future volatility. To test the presence of a leverage effect, Engle and Ng (1993) developed several diagnostic tests based on the news impact curve, namely, the sign bias test, the negative size bias test and the positive size bias test. These tests determine whether the squared normalized residual can be predicted by historical variables that are not included in the volatility model. ...
Purpose
The study aimed to examine the impact of COVID-19-related governments’ interventions on the volatility in stock returns in several Asian countries following the COVID-19 outbreak.
Design/methodology/approach
Using a battery of conditional volatility models, we first investigate the dynamic behavior of the stock return volatility for selected Asian stock markets during the pandemic period. Second, we wish to find out how these volatilities overlap with a wide range of governments’ interventions related to COVID-19 and whether a relationship can be established between two types of uncertainty and the volatility of the considered stock returns.
Findings
We confirm an asymmetric pattern in the volatility of selected Asian stock markets. In addition, the result shows that the effects of governments’ interventions vary significantly across countries. The “Containment and Health” and “Economic Support” indices appear to have a significant and negative impact on the volatility of the overwhelming majority of stock markets. Further, all Asian stock markets are experiencing a significant positive effect of “Stringency measures” on the return volatilities.
Originality/value
This research could have implications for investors and policymakers in terms of portfolio diversification to maintain active and gainful investment strategies during the pandemic crisis.
... The family GARCH abbreviated fGARCH [9] is an omnibus model that subsumes some familiar asymmetric and symmetric GARCH models as sub-classes [28]. These sub-classes include the standard GARCH (sGARCH) model [25], the Threshold GARCH (TGARCH) model [29], the Nonlinear Asymmetric GARCH (NAGARCH) model [30], the Absolute Value GARCH (AVGARCH) model [31,32], the Nonlinear ARCH (NGARCH) model [33], the Exponential GARCH (EGARCH) model [34], the GJR GARCH (GJRGARCH) model [35], and the Asymmetric Power ARCH (apARCH) model [36]. The fGARCH(p, q) model can be stated as: ...
This study utilised the dynamics of five time-varying models to estimate six essential features of financial return volatility that are relevant for robust risk management. These features include pronounced persistence, mean reversion, leverage effect or volatility asymmetry, conditional skewness, conditional fat-tailedness, and the long memory behaviour of volatility decomposition into long-term and short-term components. Both simulation and empirical evidence are provided. Through the applications of these models using the S&P Indian index, the study shows that the market returns are characterised by these volatility features. Our findings from the long-memory behaviour revealed that although the response to shocks is greater in the short-term component, it is however short-lived. On the contrary, despite a high degree of persistence in the long-term component, market information or unexpected news arrival only has a low long-run impact on the market. Based on this, the long-run investment risks within the Indian stock market seem to be under control. Hence, our findings suggest that rational investors should try to stay calm with the arrival of unexpected news in the market because the long-run effect of such news will not be severe, and the market will eventually return to its normal state.
... Average value-at-risk is also known as expected shortfall (ES). 2 The GARCH model has been extended to incorporate volatility and return leverage effects, such as the GJR-GARCH model byGlosten et al. (1993) and the N-GARCH model byEngle and Ng (1993). ...
This paper applies the Lévy-GJR-GARCH model to explore the empirical dynamics of Bitcoin, Ethereum, and Ripple. It highlights volatility clustering, pronounced skewness, and high kurtosis in cryptocurrency markets. The study finds that models integrating innovation distributions more accurately capture and explain the volatility processes and tail risks in these assets. Advanced models, especially those accounting for extreme tail-end and asymmetric jump effects, are better suited for adapting to market changes and providing precise risk indicators, effectively identifying potential losses.
... According to this theory, asynchronous information spreads more quickly, and the market is more efficient (Li et al., 2023). Engle and Ng (1993) applied this concept to financial markets, arguing that price moves and volatility asymmetrically to news reflect information transmission from one market segment to another. This theory is particularly applicable to Sri Lanka's dual financial system, which consists of conventional and Islamic indices. ...
Purpose
This study aims to investigate the co-movement and information transmission between conventional and Islamic equity indices in Sri Lanka.
Design/methodology/approach
This study uses daily data of All Share Price Index and Dow Jones Islamic Market Sri Lanka Index from 2013 to 2023 for conventional and Islamic proxies. Descriptive statistics, cross-correlation, dynamic conditional correlation (DCC)-GARCH and wavelet analysis were used for the investigation.
Findings
Analyses reveal synchronous correlation yet lead-lag dynamics between the indices. The Islamic index has lower volatility, clustering and persistence than the conventional index. Localized volatility patches and scale-dependent synchronicity suggest diversification opportunities to optimize risk-adjusted returns.
Research limitations/implications
The insights from this study are important for investors to optimize diversified portfolios by exploiting time-varying correlations. The identified lead-lag dynamics, bidirectional information flows and scale-dependent synchronization between the indices enable both investors to predict market movements for effective asset allocation and regulators to monitor market efficiency and stability and implement shock mitigation measures.
Originality/value
This study uniquely integrates DCC-generalized autoregressive conditional heteroskedasticity (GARCH) and wavelet analysis to examine the dynamic, time-varying relationships between Islamic and conventional equity markets in Sri Lanka’s dual financial system. This approach helps embrace both short-run changes and long-run movements to gain in-depth co-movement and spillovers, as well as potential diversification gains within an emerging financial market.
... Conditional variance from GARCH models can be used to compute VaR estimates dynamically, adjusting for periods of high or low volatility. Studies have shown that GARCH-based VaR models outperform static models, especially during turbulent market conditions (Engle & Ng, 1993). An alternative framework to incorporate time varying volatility in VaR estimation is through stochastic volatility model, which allow for greater flexibility in capturing complex volatility dynamics (Taylor, 1994). ...
This study examines the cryptocurrency market by introducing novel multivariate risk measures rooted in optimal transport theory to estimate Vectors-at-Risk (VaR) and Conditional Vectors-at-Risk (CVaR). We compare these measures against traditional univariate and copula-based methods for estimating Value-at-Risk and Conditional Value-at-Risk, focusing on factors such as magnitude, computational efficiency, and backtesting performance. The findings reveal that, while the proposed method incurs significantly higher computational costs, it effectively captures the correlation structure among assets’ risks, resulting in more conservative tail risk estimates compared to conventional techniques. As financial markets continue to evolve, the implications of adopting advanced tail risk measures such as those based on Optimal Coupling will be crucial for maintaining financial stability and mitigating systemic risk. Therefore, we believe that this study can be very useful in the context of regulatory frameworks, economic stability, risk management, and portfolio selection.
... There are three prevalent types of volatility models: (1) the ARCH/GARCH-family models (Bollerslev 1986;Engle 1982;Engle and Ng 1993), (2) stochastic volatility (SV) models (e.g., the autoregressive stochastic volatility (ARSV) model (Taylor 1982), the Hull-White model (Hull and White 1987), and the multi-factor model (Dahlen and Solibakke 2012)), and (3) realized volatility (RV) models (Andersen et al. 2001). RV models depend on high-frequency intra-daily data which are not always available. ...
In this paper, we carry out a comprehensive comparison of Gaussian generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive stochastic volatility (ARSV) models for volatility forecasting using the S&P 500 Index. In particular, we investigate their performance using the physical measure (also known as the real-world probability measure) for risk management purposes and risk-neutral measures for derivative pricing purposes. Under the physical measure, after fitting the historical return sequence, we calculate the likelihoods and test the normality for the error terms of these two models. In addition, two robust loss functions, the MSE and QLIKE, are adopted for a comparison of the one-step-ahead volatility forecasts. The empirical results show that the ARSV(1) model outperforms the GARCH(1, 1) model in terms of the in-sample and out-of-sample performance under the physical measure. Under the risk-neutral measure, we explore the in-sample and out-of-sample average option pricing errors of the two models. The results indicate that these two models are considerably close when pricing call options, while the ARSV(1) model is significantly superior to the GARCH(1, 1) model regarding fitting and predicting put option prices. Another finding is that the implied versions of the two models, which parameterize the initial volatility, are not robust for out-of-sample option price predictions.
... Studies have shown that GARCH-type models outperform traditional time series models in capturing the volatility dynamics in stock markets (Poon and Granger, 2003). The GARCH modeling is confirmed by Engle's ARCH test, 2 which shows a strong ARCH effect in the residuals of the first difference of the logged cryptocurrency price (Engle and Ng, 1993). ...
The sudden volatility in cryptocurrency prices, especially Dogecoin and Bitcoin, owed
to Elon Musk's public statements during COVID-19 has triggered a debate to study the
impact of Musk’s endorsement on cryptocurrencies and examine the hedging
capabilities and leverage effect on cryptocurrencies during uncertainties. Observation
of the market capitalization of Bitcoin and Dogecoin shows that the price of these
cryptocurrencies is disturbed due to positive and negative comments by Musk and
other public icons. Therefore, these cryptocurrencies are often looked at with suspicion
by participants in the cryptocurrency market. This research aims to analyze the impact
of favorable and unfavorable Musk’s remarks on Bitcoin and Dogecoin and further
examine the hedging capabilities and leverage effect of Dogecoin and Bitcoin against
stocks, gold, Treasury yields, the Euro, and the Pound exchange rate, particularly
during the COVID-19 pandemic. The research collects daily observations from Jan
2018 to Dec 2022 from Yahoo Finance, yielding 1226 observations, and uses
statistical tests to analyze the significance of Musk's tweets on cryptocurrencies.
Further, this research applies the GARCH model to understand the impact of Musk's
remarks on the hedging capabilities and leverage effect on Dogecoin and Bitcoin
during COVID-19. The findings indicate that Musk's comments had no lasting impact
on cryptocurrency prices. However, his unfavorable remarks significantly affected
Bitcoin's and Dogecoin's hedging capabilities during the pandemic. The study also
revealed a pronounced leverage effect in Dogecoin, contrasting with a moderate
impact on Bitcoin. Dogecoin strongly responded to positive news or Musk’s favorable
tweets, while Musk’s unfavorable tweets influenced Bitcoin's leverage effect. The study
suggested the importance of information in the cryptocurrency market. The study also
focused on the significance of long-term perspectives and correlations between
traditional assets like stocks and cryptocurrency yields, which can be instrumental in
guiding investment decisions and aiding in risk management during uncertainties.
... The distribution of equity return rates exhibits high peaks and fat tails [2]. A negative correlation exists between share prices and volatility [6]. Lastly, mean reversion in return rates is observed [7]. ...
This paper proposes an options pricing model that incorporates stochastic volatility, stochastic interest rates, and stochastic jump intensity. Market shocks are modeled using a jump process, with each jump governed by an asymmetric double-exponential distribution. The model also integrates a Markov regime-switching framework for volatility and the risk-free rate, allowing the market to alternate between a finite number of distinct economic states. A closed-form solution for European option pricing is derived. To demonstrate the significance of the proposed model, a comparison with various other models is performed, and the sensitivity of the various model parameters is illustrated.
... For more information on the development of forecasting methods, see [37]. More advanced models and associated statistical tests are now being employed as well (see [38][39][40]). ...
Forecasting using historical time series data has become increasingly important in today’s world. This paper aims to assess the potential for stable positive development within the wholesale and retail trade sector (SK NACE Section G) and the operations of HORTI, Ltd.( Košice, Slovakia), a company within this industry (SK NACE 46.31—wholesale of fruit and vegetables) by predicting three financial indicators: costs, revenues, and earnings before taxes (EBT) (or earnings after taxes (EAT)). We analyze quarterly data from Q1 2009 to Q4 2023 taken from the sector and monthly data from January 2013 to December 2022 for HORTI, Ltd. Through time series analysis, we aim to identify the most suitable model for forecasting the trends in these financial indicators. The study demonstrates that simple legacy forecasting methods, such as exponential smoothing and Box–Jenkins methodology, are sufficient for accurately predicting financial indicators. These models were selected for their simplicity, interpretability, and efficiency in capturing stable trends, and seasonality, especially in sectors with relatively stable financial behavior. The results confirm that traditional Holt–Winters’ and Autoregressive Integrated Moving Average (ARIMA) models can provide reliable forecasts without the need for more complex approaches. While advanced methods, such as GARCH or machine learning, could improve predictions in volatile conditions, the traditional models offer robust, interpretable results that support managerial decision-making. The findings can help managers estimate the financial health of the company and assess risks such as bankruptcy or insolvency, while also acknowledging the limitations of these models in predicting large shifts due to external factors or market disruptions.
... Our choice is motivated by the fact that volatility in financial markets often exhibits significantly asymmetric effects, where negative shocks tend to trigger greater volatility than positive shocks. Existing research has demonstrated that asymmetric GARCH-type models, such as the GJR-GARCH model, significantly outperform symmetric GARCH models in capturing various asymmetric characteristics (Engle and Ng 1993;Pan and Liu 2018;Wang et al. 2020). In this study, we extend the basic GJR-GARCH model to a multi-country model to better capture the asymmetric effects across countries, as well as within a country. ...
In behavioral economics, it has widely been documented that there might be a close relationship between overall market sentiment and economic performance, such as GDP per capita. In this paper, we investigate the effects of market sentiment on stock market volatility, which has widely been recognized as an important factor for economic sustainability. In particular, we aim to identify the existence of spillover effects of market sentiments on global stock market volatility. As a first attempt, we chose ten countries from major economic regions over the world (including America, Asia, Europe, and Oceania), and analyzed their interdependence and interconnectedness using a GJR-GARCH-MIDAS model. The results highlight that an individual country’s stock market volatility is significantly influenced not only by its own market sentiment (proxied by the consumer confidence index) but also by the overall market sentiments of other countries across the world. The results also highlight significant country-by-country heterogeneity in the time lags of the global spillover effects, which indicates substantial heterogeneity in the behavioral dynamics of individual countries.
The non-stationarity, non-linearity, and time-varying fluctuations of streamflow have increased with changes in the environment, challenging accurate streamflow prediction. Furthermore, the overlook of long-term memory features could lead to biases in model parameter estimation and testing of time series properties. The classical linear Autoregressive-Generalized Autoregressive Conditional Heteroskedasticity (AR-GARCH) model has a narrow parameter range, and the moment conditional requirements for parameter estimation are relatively strict, limiting its applicability and prediction accuracy in modelling and predicting daily streamflow. Under the premise of long-term memory, a dual-threshold double autoregressive (DTDAR) model is proposed to capture the non-linear patterns in streamflow series. Using 15 hydrological stations in the Yellow River basin in China as an example, DAR models are compared with AR-GARCH models to assess their applicability and predictive ability. The results indicate that the DAR-type models have a stronger predictive ability for daily streamflow than the AR-GARCH-type models. The threshold models (DTDAR, TAR-GARCH) convert non-linear transformations into several linear problems, improving the prediction accuracy of single linear structural models (DAR and FDAR, AR-GARCH and FAR-HARCH), among which the R2 value is improved by 29.15 % and 15.06 %, 25.53 % and 15.53 %, and the NSE value is increased by 0.29 and 0.16, 0.24 and 0.15. Compared to the normal distribution, the student's t distribution for residuals is a better choice for predicting daily streamflow time series in the study area. This study enriches the stochastic hydrological models and improves the accuracy of streamflow prediction.
This paper explores if the crossproduct of return and realized volatility measure contributes to volatility forecasting. We find there is an asymmetric crossproduct effect in volatility and propose a realized asymmetric GARCH (henceforth RealAGARCH) model. The RealAGARCH model is a generalization to the absolute GARCH and the asymmetric GARCH. Moreover, the RealAGARCH model has a news impact surface instead of a news impact curve, which makes it different from other GARCH‐like models. Empirical performance of the RealAGARCH model is evaluated on a variety of stock indices, and the results show dominance of RealAGARCH over the benchmark RealGARCH judging by either in‐sample or out‐of‐sample forecasting performance. A battery of checks confirm the robustness of our findings and thus the importance of incorporating crossproduct effect into volatility forecasting.
Purpose
This study aims to investigate the impact of volatility asymmetries and external shocks, including the global financial crisis of 2007 and the COVID-19 pandemic, on the returns and volatility of the stock market in the Indian context.
Design/methodology/approach
The data used is extensive, covering around 24 years of stock market activity in terms of prices and subsequent returns. To achieve the objectives, variants of conditional models that incorporate the effect of volatility asymmetries and external shocks have been estimated.
Findings
This study found that the asymmetric effect is significant, and due to both the global financial crisis and the COVID-19 pandemic, volatility has increased significantly. The inclusion of the asymmetric effect of volatility, global financial crisis and COVID-19 into volatility modeling reveals that the effect of both past innovation or shocks and past volatility has increased, which is evident from the change in lag length structure found in different conditional models of volatility.
Research limitations/implications
This study has important implications for understanding the dynamics of stock market volatility across various economic phases. It provides insights into how stock markets evolve in terms of volatility swings and the subsequent price formation. Moreover, this study provides insights for policymakers to devise efficient mechanisms to control the possible effects of such shocks on the financial system.
Originality/value
This study contributes toward a comparative study of events based on their likelihood of occurrence and thereupon impact on stock market performance.
This study investigates the relationship between government interventions aimed at curbing the spread of the novel coronavirus (COVID-19) and stock market volatility across 67 countries. Using panel regression analysis, we examine how various non-pharmaceutical interventions influence financial market uncertainty. Using panel regression analysis, we examine how various non-pharmaceutical interventions influence financial market uncertainty. Our findings reveal that stringent policy responses significantly increase stock market volatility, independent of the direct impact of the pandemic itself. Specifically, information campaigns and public event cancellations are identified as major contributors to this phenomenon. These results highlight the dual role of government actions: mitigating health risks while simultaneously amplifying financial instability.
In numerous domains of finance and economics, modelling and predicting stock market volatility is essential. Predicting stock market volatility is widely used in the management of portfolios, analysis of risk, and determination of option prices. This study is about volatility modelling of the daily Johannesburg Stock Exchange All Share Index (JSE ALSI) stock price data between 1 January 2014 and 29 December 2023. The modelling process incorporated daily log returns derived from the JSE ALSI. The following volatility models were presented for the period: sGARCH(1,1) and fGARCH(1,1). The models for volatility were fitted using five unique error distribution assumptions, including Student’s t, its skewed version, the generalized error and skewed generalized error distributions, and the generalized hyperbolic distribution. Based on information criteria such as Akaike, Bayesian, and Hannan–Quinn, the ARMA(0,0)-fGARCH(1,1) model with a skewed generalized error distribution emerged as the best fit. The chosen model revealed that the JSE ALSI prices are highly persistent with the leverage effect. JSE ALSI price volatility was notably influenced during the COVID-19 pandemic. The forecast over the next 10 days shows a rise in volatility. A comparative study was then carried out with the JSE Top 40 and the S&P500 indices. Comparison of the FTSE/JSE Top 40, S&P 500, and JSE ALLSI return indices over the COVID-19 pandemic indicated higher initial volatility in the FTSE/JSE Top 40 and S&P 500, with the JSE ALLSI following a similar trend later. The S&P 500 showed long-term reliability and high rolling returns in spite of short-run volatility, the FTSE/JSE Top 40 showed more pre-pandemic risk and volatility but reduced levels of rolling volatility after the pandemic, similar in magnitude for each index with low correlations among them. These results provide important insights for risk managers and investors navigating the South African equity market.
Cryptocurrency (CRP) has grown in popularity over the last decade. Since there is no central body to control the Bitcoin (BTC) markets, they are extremely volatile. However, several similar variables that cause price volatility in traditional markets also affect cryptocurrencies. Several bubble phases have taken place in BTC prices, mostly during the years 2013 and 2017. Other digital currencies of primary importance, such as Ethereum and Litecoin, also exhibited several bubble phases. Among traditional methods of analysis for this volatile market, only a small number of studies focused on Machine Learning (ML) techniques. The present study objective is to get an in-depth knowledge of the time series properties of CRP data and combine volatility models with ML models. In the hybrid method, we first apply the Nonlinear Generalized Autoregressive Conditional Heteroskedasticity (NGARCH) model with asymmetric distribution to calculate standardized returns, then forecast the UP and DOWN movement of standardized returns through ML models such as Logistic Regression (LR), Linear Discrimination Analysis (LDA), Quadratic Discrimination Analysis (QDA), Artificial Neural Networks (ANNs), K-Nearest Neighbors (KNN), and Support Vector Machine (SVM). The findings show that the proposed hybrid approach of time series models and ML accurately predicts prices; specifically, the KNN model reveals that the scheme can be applicable to CRP market prediction. It is deduced that ML methods combined with volatility models have the tendency to better forecast this volatile market.
Purpose – Based on weekly data from 2012 to 2024, this paper aims to evaluate empirically the integration and contagion properties of some emerging stock markets from North Africa including Morocco, Tunisia and Egypt, and to deepen the understanding of the linkage between them during stable and turmoil periods (Covid 19, Ukrainian war and Gazza war).
Design/methodology/approach – Besides traditional Granger causality (GC) test (Granger, 1969), the (Shi, Hurn, & Phillips, 2020)’ time-varying (TV) GC test, the (Song & Taamouti, 2020)’ quantiles GC test, and the (Breitung-Candelon, 2006)’ frequency domain (FD) GC tests are used for the contagion (diversification) check between market volatility (returns). Then, the returns DCC- GARCH specifications are used for the integration investigations. Then, based on the returns DCC dynamic regressions, the contagion analysis between considered markets that are related to the unexpected events is done.
Findings – As the results from the standard GC, all considered tests reveal that in mean, Tunisian returns R_T and Egyptian R_E are predictable by Moroccan R_M. Only Tunisian and Egyptian return can play then the role of diversifier. Results from these causality tests detect some contagion in variance between markets, which was denied from dynamic DDC regression regressions in returns. From dynamic DCC-GARCH model, our empirical results show a weak integration between returns.
Originality/value – Via the dynamic DCC ARCH and the DCC quantile regression, the time varying GC, the quantile GC, and the spectral GC tests, this paper provides a deeper understanding of North African marginal stock market behavior and linkage.
We propose a novel multiplicative factor multi‐frequency GARCH (MF2‐GARCH) model, which exploits the empirical fact that the daily standardized forecast errors of one‐component GARCH models are predictable by a moving average of past standardized forecast errors. In contrast to other multiplicative component GARCH models, the MF2‐GARCH features stationary returns, and long‐term volatility forecasts are mean‐reverting. When applied to the S&P 500, the new component model significantly outperforms the one‐component GJR‐GARCH, the GARCH‐MIDAS‐RV, and the log‐HAR model in long‐term out‐of‐sample forecasting. We illustrate the MF2‐GARCH's scalability by applying the new model to more than 2100 individual stocks in the Volatility Lab at NYU Stern.
This study investigates the impact of macroeconomic variables on stock market performance in Nigeria from 1985 to 2023, focusing on the relationships between stock market returns (SMR), gross domestic product (GDP), inflation rate (INFR), and exchange rate (EXR). Utilizing data sourced from reputable financial and economic databases, the research employs the Autoregressive Distributed Lag (ARDL) approach to analyze both short-run dynamics among the variables. Stationarity tests reveal that GDP and EXR are stationary at levels (I(0)), while INFR is stationary at first difference (I(1)), indicating a mixed order of integration. The ARDL Bounds co-integration test confirms a long-run relationship among the variables, justifying the application of ARDL analyses. The findings indicate that GDP has a significant positive effect on SMR in both the short and long run, suggesting that economic growth enhances investor confidence and market performance. Conversely, INFR exhibits a negative impact on SMR, highlighting the detrimental effects of rising inflation on stock market dynamics. Additionally, EXR positively influences SMR in the long run, although its short-run impact is less pronounced. The study concludes that effective economic policies aimed at promoting GDP growth, controlling inflation, and stabilizing exchange rates are essential for fostering a robust stock market environment in Nigeria. These insights contribute to the understanding of the interplay between macroeconomic factors and stock market performance, providing valuable implications for policymakers and investors alike.
Purpose
This paper aims to investigate the impact of the COVID-19 pandemic and the Russian−Ukrainian war on the volatility of several cryptocurrencies.
Design/methodology/approach
To do this, the study uses the GJR-GARCH and dynamic conditional correlation (DCC)-GJR-GARCH models, which allow the author to estimate the conditional variance of the cryptocurrencies’ returns and assess their dependence structure over time.
Findings
The results show that the health crisis had a negative impact on all cryptocurrencies studied, except for Bitcoin, which experienced a positive impact. Additionally, the study finds that the Russian-Ukrainian war had a mixed impact on the cryptocurrencies studied, with some experiencing positive impacts (BNB, Dogecoin, Ethereum and Tether) and others experiencing negative impacts (Bitcoin, BUSD, Coin and XRP). Moreover, the author analyzes the spillover effects among the cryptocurrencies and observe significant interdependence during the periods under study.
Originality/value
Finally, the study discusses the implications of the findings for investors, policymakers and regulators, highlighting the importance of considering external factors when making investment decisions or designing regulatory frameworks for the cryptocurrency market.
Volatilitas pada pasar keuangan merupakan salah satu fenomena yang sangat menarik karena dampaknya terhadap eksistensi pasar finansial global. Keberadaan volatilitas berhubungan dengan risiko sebuah. Tulisan ini bertujuan menentukan model terbaik dalam memodelkan volatilitas return saham pada empat negara di Asia dengan menggunakan model simetris GARCH dan berbagai macam model asimetris GARCH. Hasil dari fitting model terbaik untuk keempat pasar saham menunjukkan bahwa model asimetris GARCH menunjukkan estimasi yang lebih baik dalam menggambarkan volatilitas return saham. Lebih jauh lagi, model tersebut mengungkapkan keberadaan efek asimetris pada keempat pasar saham.
Purpose
The purpose of this study is to achieve a comprehensive understanding of how the intricate interconnections between oil price fluctuations, supply chain disruptions and shifting demand patterns collectively shape inflation dynamics within the Chinese economy, especially during critical periods such as the Covid-19 pandemic and geopolitical events like the Russia–Ukraine conflict. The importance of assessing the impact of oil price volatility on China’s inflation becomes particularly pronounced amidst these challenging circumstances.
Design/methodology/approach
This study uses the Markov Regime-Switching generalized autoregressive conditional heteroskedasticity (MRS-GARCH) family of models under student’s t-distributions to measure the uncertainty of oil prices and the inflation rate during the period spanning from 1994 to 2023 in China.
Findings
The results indicate that the MRS-GJR-GARCH-in-mean (MRS-GARCH-M) models, when used under student’s t-distributions, exhibit superior performance in modeling the volatility of both oil prices and the inflation rate. This finding underscores the effectiveness of these models in capturing the intricacies of volatility dynamics in the context of oil prices and inflation. The study has identified compelling evidence of regime-switching behavior within the oil price market. Subsequently, the author conducted an analysis by extracting the forecastable component, which represents the expected variation, from the best-fitted models. This allowed us to isolate the time series of oil price uncertainty, representing the unforecastable component. With this unforecastable component in hand, the author proceeded to estimate the impact of oil price fluctuations on the inflation rate. To accomplish this, the author used an autoregressive distributed lag model, which enables us to explore the dynamic relationships and lags between these crucial economic variables. The study further reveals that fluctuations in oil prices exert a noteworthy and discernible influence on the inflation rate, with distinct patterns observed across different economic regimes. The findings indicate a consistent positive impact of oil prices on inflation rate uncertainty, particularly within export-oriented and import-oriented industries, under both of these economic regimes.
Originality/value
This study offers original value by analyzing the impact of crude oil price volatility on inflation in China. It provides unique insights into the relationship between energy market fluctuations and macroeconomic stability in one of the world’s largest economies. By focusing on crude oil – a critical but often overlooked component – this research enhances understanding of how energy price dynamics influence inflationary trends. The findings can inform policymakers and stakeholders about the significance of energy market stability for maintaining economic stability and guiding inflation control measures in China.
This paper investigates the impact of FOMC announcements on cryptocurrency risk spillovers under different market conditions and their mechanisms of action. We calculate the high-frequency RGARCH volatilities of four major dirty cryptocurrencies and six major clean currencies, and apply the quantile-expanded joint-network approach to test their risk spillovers under different market conditions, and then investigate their impact and mechanism of action by monetary shocks. The results show that: (i) the total spillover in the extreme volatility market is larger than the total spillover in the normal market, and there is a tail asymmetry. (ii) The total cryptocurrency risk spillover in the highly volatile market, the normal market, and the smooth volatility market are all positively affected by monetary shocks. (iii) Mechanism analysis shows that the FOMC announcement will have an impact on the total cryptocurrency market risk spillover through two channels, which are changing the market expectations and hedging demand. Heterogeneity analysis shows that clean cryptocurrencies have positive net spillovers to dirty cryptocurrencies, and the mutual spillovers between the two are significantly affected by monetary shocks in extremely volatile markets.
Most of nonparametric GARCH models typically employ daily frequency data to forecast the returns, correlations, and risk indicators of financial assets, without incorporating alternative frequency data. As a result, valuable financial market information may remain underutilized during the estimation process. To partially mitigate this issue, we introduce the intraday high-frequency data to enhance the estimation of the volatility function in a nonparametric GARCH model. To achieve this objective, we introduce a nonparametric proxy model for volatility. Under mild assumptions, we derive the asymptotic bias and variance of the estimator and further investigate the impact of various volatility proxies on estimation accuracy. Our findings from both simulations and empirical analysis indicate a considerable improvement in the estimation of the volatility function through the introduction of high-frequency data.
Previous studies of the information content of the implied volatilities from the prices of call options have used a cross-sectional regression approach. This paper compares the information content of the implied volatilities from call options on the S&P 100 index to GARCH (Generalized Autoregressive Conditional Heteroscedasticity) and Exponential GARCH models of conditional volatility. By adding the implied volatility to GARCH and EGARCH models as an exogenous variable, the within-sample incremental information content of implied volatilities can be examined using a likelihood ratio test of several nested models for conditional volatility. The out-of-sample predictive content of these models is also examined by regressing ex post volatility on the implied volatilities and the forecasts from GARCH and EGARCH models.
The short-run interdependence of prices and price volatility across three major international stock markets is studied. Daily opening and closing prices of major stock indexes for the Tokyo, London, and New York stock markets are examined. The analysis utilizes the autoregressive conditionally heteroskedastic (ARCH) family of statistical models to explore these pricing relationships. Evidence of price volatility spillovers from New York to Tokyo, London to Tokyo, and New York to London is observed, but no price volatility spillover effects in other directions are found for the pre-October 1987 period. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.
An appropriate metric for the success of an algorithm to forecast the variance of the rate of return on a capital asset could be the incremental profit from substituting it for the next best alternative. We propose a framework to assess incremental profits for competing algorithms to forecast the variance of a prespecified asset. The test is based on the return history of the asset in question. A hypothetical insurance market is set up, where competing forecasting algorithms are used. One algorithm is used by each hypothetical agent in an "ex post ante" forecasting exercise, using the available history of the asset returns. The profit differentials across agents (in various groupings) reflect incremental values of the forecasting algorithms. The technique is demonstrated with the NYSE portfolio, over the period of July 22, 1966 to December 31, 1985. For the limited set of alternative specifications, we find that GARCH(1,1) yields better profits than the 3 competing specifications. The profit from pricing one-day options on the NYSE portfolio significant. The evidence also suggests that using a limited estimation period may be preferable to estimating specification parameters from all available observations. Finally, the hedging activity that requires a variance determined hedge ratio is an important component of the success of a variance forecast-algorithm.
The use of increasingly complex statistical models has led to heavy reliance on maximum likelihood methods for both estimation and testing. In such a setting, only asymptotic properties can be expected for estimators or tests. Often there are asymptotically equivalent procedures that differ substantially in computational difficulty and finite sample performance. In a maximum likelihood framework, the Wald, Likelihood Ratio, and Lagrange Multiplier (LM) tests are a natural trio. They all share the property of being asymptotically locally the most powerful invariant tests, and in fact all are asymptotically equivalent. However, in practice, there are substantial differences in the way the tests look at particular models. Frequently when one is very complex, another will be much simpler. Furthermore, this formulation guides the intuition as to what is testable and how best to formulate a model to test it. In terms of forming diagnostic tests, the LM test is frequently computationally convenient as many of the test statistics are already available from the estimation of the null. The application of these tests principles and particularly the LM principle to a wide range of econometric problems is a natural development of the field, and it is a development that is proceeding at a very rapid pace.
Discrepancies between the Black-Scholes value of Japanese equity warrants and their observed prices are explained in part by the stochastic volatility of changes in prices of the underlying stocks. We fit GARCH and EGARCH models to the stochastic volatility and briefly compare their performance to the CEV model. A hopscotch algorithm is used to value the warrants in the presence of the stochastic stock price volatility. The stochastic volatility-hopscotch warrant values still differ substantially from corresponding prices; in contrast, away-from-the-money short-term Nikkei 225 options valued with the same stochastic volatility models are close to observed prices. A regression model is used to fit the differences between warrant values and prices as a function of proxies for market impediments.
This paper analyzes the robustness of the day-of-the-week (DOW) and weekend effects to alternative estimation and testing procedures. The results show that sample size can distort the interpretation of classical test statistics unless the significance level is adjusted downward. Specification tests reveal widespread departures from OLS assumptions. Hypothesis tests results are reported using robust econometric methods and a GARCH model. The strength of the DOW and weekend effect evidence appears to depend on the estimation and testing method. Both effects seem to have disappeared by 1975.
The expected market return is a number frequently required for the solution of many investment and corporate finance problems, but by comparison with other financial variables, there has been little research on estimating this expected return. Current practice for estimating the expected market return adds the historical average realized excess market returns to the current observed interest rate. While this model explicitly reflects the dependence of the market return on the interest rate, it fails to account for the effect of changes in the level of market risk. Three models of equilibrium expected market returns which reflect this dependence are analyzed in this paper. Estimation procedures which incorporate the prior restriction that equilibrium expected excess returns on the market must be positive are derived and applied to return data for the period 1926–1978. The principal conclusions from this exploratory investigation are: (1) in estimating models of the expected market return, the non-negativity restriction of the expected excess return should be explicity included as part of the specification: (2) estimators which use realized returns should be adjusted for heteroscedasticity.
In this paper we consider a class of dynamic models in which both the conditional mean and the conditional variance are endogenous stepwise functions. We first consider the probabilistic properties of these models: stationarity conditions, leptokurtic effect, linear representation, optimal prediction. In this first part most results are based on Markov chains theory. Then we derive statistical properties of this class of models; pseudo-maximum likelihood estimators, conditional homoscedasticity tests, tests of weak or strong white noise, CAPM test, factors determination, ARCH-M effects. We also discuss the introduction of exogenous variables and the case of multiple lags. Finally, an application to the Paris Stock Index is proposed.
Most models of market volatility use either past returns or ex post volatility to forecast volatility. In this paper, the dynamic behavior of market volatility is assessed by forecasting the volatility implied in the transaction prices of Standard & Poor's 100 index options. We test and reject the hypothesis that volatility changes are unpredictable. However, while our statistical model delivers precise forecasts, abnormal returns are not possible in a trading strategy (based on daily out-of-sample volatility projections) which takes transaction costs into account, suggesting that predictable time-varying volatility is consistent with market efficiency.
In this paper, we define dynamic and static factors and distinguish between the dynamic and static structure of asset excess returns. We examine the value-weighted market portfolio as a dynamic factor and propose an intuitively appealing procedure to search for more dynamic factors. We find evidence that the market is a dynamic factor but a three-dynamic-factor model is superior in modelling the decile portfolios. The two additional factors are correlated with a January dummy and Bond risk premium and with production growth and a recession dummy, respectively. We found that small firms are more sensitive to the January/Bond risk factor, while large firms are more sensitive to the Production/Recession factor. We found that after accounting for the systematic risk corresponding to the three dynamic factors, there is not much of a static component of asset risk premium and there is no evidence for a higher ‘unexplained’ return on small firm portfolios.
This paper examines the timing of mean and volatility spillovers between New York and London equity markets. Using an ARCH model it is found that the evidence of volatility spillovers between these markets is minimal and have a duration which lasts only an hour or so. The most significant effects surround the movement of share prices around the New York opening, but these results are not strong. Several new ARCH models are estimated including an asymmetric or ‘leverage’ model and a non-linear model which allows big shocks to have a different impact from small shocks.
This paper provides an analysis of the predictable components of monthly common stock and bond portfolio return. Most of the predictability is associated with sensitivity to economic variables in a rational asset pricing model with multiple betas. The stock market risk premium is the most important for capturing predictable variation of the stock portfolios, while premiums associated with interest rate risks capture predictability of the bond returns. Time variation in the premium for beta risk is more important than changes in the betas. Copyright 1991 by University of Chicago Press.
This paper will discuss the current research in building models of conditional variances using the Autoregressive Conditional Heteroskedastic (ARCH) and Generalized ARCH (GARCH) formulations. The discussion will be motivated by a simple asset pricing theory which is particularly appropriate for examining futures contracts with risk averse agents. A new class of models defined to be integrated in variance is then introduced. This new class of models includes the variance analogue of a unit root in the mean as a special case. The models are argued to be both theoretically important for the asset pricing models and empirically relevant. The conditional density is then generalized from a normal to a Student-t with unknown degrees of freedom. By estimating the degrees of freedom, implications about the conditional kurtosis of these models and time aggregated models can be drawn. A further generalization allows the conditional variance to be a non-linear function of the squared innovations. Throughout empirical e imates of the logarithm of the exchange rate between the U.S. dollar and the Swiss franc are presented to illustrate the models.
We show that there is an asymmetry in the predictability of the volatilities of large versus small firms. Using both univariate and multivariate ARMA-GARCH-M parameterizations, we find that volatility surprises to large market value firms are important to the future dynamics of their own returns as well as the returns of smaller firms. Conversely, however, shocks to smaller firms have no impact on the behavior of either the mean or the variance of the returns of larger capitalization companies. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.
This article analyzes the behavior of stock return volatility using daily data from 1885 through 1988. The October 1987 stock
market crash was unusual in many ways. October 19 was the largest percentage change in market value in over 29,000 days. Stock
volatility jumped dramatically during and after the crash. Nevertheless, it returned to lower, more normal levels more quickly
than past experience predicted. I use data on implied volatilities from call option prices and estimates of volatility from
futures contracts on stock indexes to confirm this result.
We introduce a new hybrid approach to joint estimation of Value at Risk (VaR) and Expected Shortfall (ES) for high quantiles of return distributions. We investigate the relative performance of VaR and ES models using daily returns for sixteen stock market indices (eight from developed and eight from emerging markets) prior to and during the 2008 financial crisis. In addition to widely used VaR and ES models, we also study the behavior of conditional and unconditional extreme value (EV) models to generate 99 percent confidence level estimates as well as developing a new loss function that relates tail losses to ES forecasts. Backtesting results show that only our proposed new hybrid and Extreme Value (EV)-based VaR models provide adequate protection in both developed and emerging markets, but that the hybrid approach does this at a significantly lower cost in capital reserves. In ES estimation the hybrid model yields the smallest error statistics surpassing even the EV models, especially in the developed markets.
Six different commodities are examined using daily data over two futures contract periods. Cash and futures prices for all six commodities are found to be well described as martingales with near-integrated GARCH innovations. Bivariate GARCH models of cash and futures prices are estimated for the same six commodities. The optimal hedge ratio (OHR) is then calculated as a ratio of the conditional covariance between cash and futures to the conditional variance of futures. The estimated OHRs reveal that the standard assumption of a time-invariant OHR is inappropriate. For each commodity the estimated OHR path appears non-stationary, which has important implications for hedging strategies. Copyright 1991 by John Wiley & Sons, Ltd.
SUMMARY In this paper issues of volatility persistence and the changing risk premium in the stock market are investigated using the GARCH estimation technique. We get a point estimate of the index of relative risk aversion of 4.5 and confirm the existence of changing equity premiums in the US during 1962-1985. The persistence of shocks to the stock return volatility is so high that the data cannot reject a non-stationary volatility process specification. The results of this paper are consistent with Malkiel and Pindyck's hypothesis that it is the unforseen rise ini the investment uncertainty during 1974 that causes the market to plunge.
The dangers of shouting ``fire'' in a crowded theater are well understood, but the dangers of rushing to the exit in the financial markets are more complex. Yet, the two events share several features, and I analyze why people crowd into theaters and trades, why they run, what determines the risk, whether to return to the theater or trade when the dust settles, and how much to pay for assets (or tickets) in light of this risk. These theoretical considerations shed light on the recent global liquidity crisis and, in particular, the quant event of 2007.
The authors find support for a negative relation between conditional expected monthly return and conditional variance of monthly return using a GARCH-M model modified by allowing (1) seasonal patterns in volatility, (2) positive and negative innovations to returns having different impacts on conditional volatility, and (3) nominal interest rates to predict conditional variance. Using the modified GARCH-M model, they also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility, whereas negative unanticipated returns result in an upward revision of conditional volatility. Copyright 1993 by American Finance Association.
No-arbitrage martingale analysis is used to study the effect of changes in the rate of information flow on asset prices. The analysis is first used to develop some simple tools for asset pricing in a continuous time setting. These tools are then applied to determine the effect of information on prices and price volatility, to extend Samuelson's theorem on prices fluctuating randomly, and to study the impact of the resolution of uncertainty on prices. The conditions under which uncertainty resolution is irrelevant for asset pricing are shown to be similar to those that support the Modigliani and Miller irrelevance theorems. Copyright 1989 by American Finance Association.
One option-pricing problem which has hitherto been unsolved is the pricing of European call on an asset which has a stochastic volatility. This paper examines this problem. The option price is determined in series form for the case in which the stochastic volatility is independent of the stock price. Numerical solutions are also produced for the case in which the volatility is correlated with the stock price. It is found that the Black-Scholes price frequently overprices options and that the degree of overpricing increases with the time to maturity. Copyright 1987 by American Finance Association.
This paper characterizes the rate of convergence of discrete-time multinomial option prices. We show that the rate of convergence depends on the smoothness of option payoff functions, and is much lower than commonly believed because option payoff functions are often of all-or-nothing type and are not continuously differentiable. To improve the accuracy, we propose two simple methods, an adjustment of the discrete-time solution prior to maturity and smoothing of the payoff function, which yield solutions that converge to their continuous-time limit at the maximum possible rate enjoyed by smooth payoff functions. We also propose an intuitive approach that systematically derives multinomial models by matching the moments of a normal distribution. A highly accurate trinomial model also is provided for interest rate derivatives. Numerical examples are carried out to show that the proposed methods yield fast and accurate results. Copyright Blackwell Publishers, Inc. 2000.
This paper examines the relation between stock returns and stock market volatility. We find evidence that the expected market risk premium (the expected return on a stock portfolio minus the Treasury bill yield) is positively related to the predictable volatility of stock returns. There is also evidence that unexpected stock market returns are negatively related to the unexpected change in the volatility of stock returns. This negative relation provides indirect evidence of a positive relation between expected risk premiums and volatility.
The dangers of shouting ``fire'' in a crowded theater are well understood, but the dangers of rushing to the exit in the financial markets are more complex. Yet, the two events share several features, and I analyze why people crowd into theaters and trades, why they run, what determines the risk, whether to return to the theater or trade when the dust settles, and how much to pay for assets (or tickets) in light of this risk. These theoretical considerations shed light on the recent global liquidity crisis and, in particular, the quant event of 2007.
The authors use an extension of the equilibrium framework of M. Rubinstein (1976) and M. Brennan (1979) to derive an option valuation formula when the stock return volatility is both stochastic and systematic. Their formula incorporates a stochastic volatility process as well as a stochastic interest rate process in the valuation of options. If the 'mean,'volatility, and 'covariance' processes for the stock return and the consumption growth are predictable, the authors' option valuation formula can be written in 'preference-free'form. Further, many popular option valuation formulae in the literature can be written as special cases of their general formula. Copyright 1993 by American Finance Association.
This paper introduces an ARCH model (exponential ARCH) that (1) allows correlation between returns and volatility innovations (an important feature of stock market volatility changes), (2) eliminates the need for inequality constraints on parameters, and (3) allows for a straightforward interpretation of the "persistence" of shocks to volatility. In the above respects, it is an improvement over the widely-used GARCH model. The model is applied to study volatility changes and the risk premium on the CRSP Value-Weighted Market Index from 1962 to 1987. Copyright 1991 by The Econometric Society.
Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditional heteroscedastic (ARCH) processes are introduced in this paper. These are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances. For such processes, the recent past gives information about the one-period forecast variance. A regression model is then introduced with disturbances following an ARCH process. Maximum likelihood estimators are described and a simple scoring iteration formulated. Ordinary least squares maintains its optimality properties in this set-up, but maximum likelihood is more efficient. The relative efficiency is calculated and can be infinite. To test whether the disturbances follow an ARCH process, the Lagrange multiplier procedure is employed. The test is based simply on the autocorrelation of the squared OLS residuals. This model is used to estimate the means and variances of inflation in the U.K. The ARCH effect is found to be significant and the estimated variances increase substantially during the chaotic seventies.
We use a multivariate generalized autoregressive heteroskedasticity model (M-GARCH) to examine three stock indexes and their associated futures prices: the New York Stock Exchange Composite, S&P 500, and Toronto 35. The North American context is significant because markets in Canada and the United States share similar structures and regulatory environments. Our model allows examination of dependence in volatility as it captures time variation in volatility and cross-market influences. Estimated time variation in volatility is significant and the volatilities are highly positively correlated. Yet, we find that the correlation in North American index and futures markets has declined over time.
This paper compares several statistical models for monthly stock return volatility. The focus is on U.S. data from 1834-19:5 because the post-1926 data have been analyzed in more detail by others. Also, the Great Depression had levels of stock volatility that are inconsistent with stationary models for conditional heteroskedasticity, We show the importance of nonlinearities in stock return behavior that are not captured by conventional ARCH or GARCH models. We also show the nonstationariry of stock volatility, even over the 1834-1925 period.
A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametric models are derived. Maximum likelihood estimation and testing are also considered. Finally an empirical example relating to the uncertainty of the inflation rate is presented.
The authors use predictions of aggregate stock return variances from daily data to estimate time-varying monthly variances for size-ranked portfolios. The authors propose and estimate a single factor model of heteroskedasticity for portfolio returns. This model implies time-varying betas. Implications of heteroskedasticity and time-varying betas for tests of the capital asset pricing model are then documented. Accounting for heteroskedasticity increases the evidence that risk-adjusted returns are related to firm size. The authors also estimate a constant correlation model. Portfolio volatilities predicted by this model are similar to those predicated by more complex multivariate generalized autoregressive conditional heteroskedasticity procedures. Copyright 1990 by American Finance Association.