Exponential GARCH Research Articles

A two-component realized exponential generalized autoregressive conditional heteroscedasticity model

This paper proposes a two-component realized exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model – an extension of the realized EGARCH model – for the joint modeling of asset returns and realized measures of volatility. The proposed model assumes that the volatility of asset returns consists of two components: a long-run component and a short-run component. The model’s unique ability to capture the long-memory property of volatility distinguishes it from the standard realized EGARCH model. The model is convenient to implement within the framework of maximum likelihood estimation. We apply the two-component realized EGARCH model and a restricted version of the model (the two-component realized EGARCH model with only short-run leverage) to four stock indexes: the Standard & Poor’s 500 index, the Hang Seng index, the Nikkei 225 index and the Deutscher Aktienindex. The empirical study suggests that the two-component realized EGARCH model and its restricted version outperform the realized GARCH model, the realized EGARCH model and the realized heterogeneous autoregressive GARCH model in terms of in-sample fit. Further, an out-of-sample predictive analysis demonstrates that the two-component realized EGARCH model and its restricted version yield more accurate volatility forecasts than the alternatives.

MEASURING CONTAGION BETWEEN ENERGY AND STOCK MARKET DURING FINANCIAL CRISIS: ASYMMETRIC DYNAMICS IN THE CORRELATIONS

This paper deals with the study of the Asymmetric Dynamic Conditional Correlation (ADCC) model developed by Cappiello et al. (2006). The A-DCC models carry out better than the non-asymmetric ones. The methodological design is an appropriate multivariate vector and autoregressive exponential GARCH (M-VAR-EGARCH) process which investigate the nature of the volatility and return spillover mechanism across markets. This article examines the dynamic linkages between the stock market and oil price in the US and the Euro-Zone from January 2, 2004 to July 5, 2013. The findings support the existence of a contagion effect during the Greek debt crisis but not the subprime crisis. The correlations between oil prices and stock return of the financial market reveal a certain degree of interdependence among oil market that is lower during the debt crisis.

COPULA FRANK UNTUK PERHITUNGAN VALUE AT RISK PORTOFOLIO BIVARIAT PADA MODEL EXPONENTIAL GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTICITY

Stocks are one type of investment that promises return for investors but often carries a high risk. Value at Risk (VaR) is a measuring tool that can calculate the amount of the worst loss that occurs in a stock portfolio with a certain level of confidence and within a certain time period. In general, financial data have a high volatility value, which causes the residuals are not normally distributed. ARCH/GARCH modoel is used to solve the heteroscedasticity problem. If the data also have an asymmetric effect, it is modelled with Exponential GARCH model. Copula-Frank is part of the Archimedian copula which is used to solve empirical cases. The data on this study were BBCA and KLBF stock price return data in the observation period 30 December 2011 – 6 December 2019. Furthermore, to test the validity of the VaR model, a backtesting test will be carried out using the Kupiec Test. The results showed that the best model used for BBCA stocks was ARIMA (1,0,1) EGARCH (1,1) and for KLBF stocks was ARIMA (1,0,1) EGARCH (1,2). The amount of risk with a 95% confidence level used a combination of the EGARCH and Copula-Frank models was 2.233% of today's investment. Based on the backtesting test used the Kupiec Test, the VaR model of the portfolio obtained was declared valid.

Estimating Stock Market Volatility Using Exponential Garch Model with Skewed Student- T Distribution

The aim of the study is to empirically investigate the performance of the EGARCH (1, 1) volatility model with the normal, skew-normal, and student t and skewed student t distributions on the NSE Nifty Fifty Index. Ten years of daily closing rates over the period of January 2010 to December 2020, for a total of 2730 observations, have been analyzed. According to the information criterion, this study has found that the EGARCH (1, 1) model under skewed student t distribution is a better fit than other distribution models.

Does the short squeeze lead to market abnormality and antileverage effect? Evidence from the Gamestop case

PurposeThis study examines the Gamestop (GME) short squeeze in early 2021. Using intraday data for the period 4/1/2021–5/2/2021, the author provides empirical evidence that the GME stock price exhibited abnormal behavior.Design/methodology/approachThe author uses the popular Runs test to show that the GME returns were not randomly distributed, which is an indication of a violation of the Efficient Market Hypothesis (EMH). The main objective of the paper is to provide new quantitative evidence that stock returns are abnormal when short squeeze conditions emerge. The author employs the asymmetry Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) models (the Exponential GARCH (EGARCH) and the Threshold GARCH (TGARCH)) and provides evidence that an exceptional time series feature emerged during the examined period: the antileverage effect.FindingsThe results show that the GME returns were not randomly distributed during the examined period and the asymmetry GARCH models indicate that, in contrast to what the time series normally show, volatility increased when the GME prices increased.Research limitations/implicationsThis paper presents a new/alternative approach for the study of EMH and abnormal returns in financial markets. Further studies on market performance during similar short squeeze conditions should be carried out in order to obtain empirical evidence for the antileverage effect abnormality.Practical implicationsThis paper could be useful for scholars who examine the EMH in financial markets because it suggests an additional method for testing abnormalities. It also presents a useful tool that allows practitioners to monitor for indications of abnormality in the stock market during a short squeeze, since the emergence of the antileverage abnormality could function as such an indication. Additionally, the outcome of this analysis could be useful for regulators because coordination among investors is easier than ever in the Internet era and such events may happen again in the future; even under normal (not short squeeze) conditions and lead to market instability.Originality/valueThis research differs from other studies that examine the GME case because it presents a new way to quantitatively present the abnormal performance of the stock markets for reasons that could be linked with the emergence of short squeeze conditions.

Stock Market Reaction towards Terrorism: An Evidence Based on Seasonal Variation in Pakistan

This study examined whether the impact of terrorism events on the stock market varies based on seasonal anomalies (i.e., spring, summer, autumn, and winter). For this purpose, this study selected and obtained the data of 344 terrorist events that occurred in Pakistan and daily closing index price data of KSE 100 for the period ranging from 2008 to 2017. To fulfil the study's objective, this study applies the event day analysis by using five days window (-2, -1, 0, +1, +2) by employing the Exponential Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model. The findings of this study shows that there is no significant impact of terrorist events on stock returns in Pakistan on pre-event day 2 and event day. However, terrorism events have a significant positive impact on stock returns on pre-event day 1 and post-event day 1. On the contrary, stock returns on post-event day 2 showed a significant positive but in negative direction. In addition, this study also found that stock market returns vary significantly based on seasonal anomalies. However, it is also revealed that the impact of terrorism (event day) on the stock market’s returns does not significantly vary during all seasons in Pakistan except autumn and similarly, the impact of terrorism (post-event day 1) on the stock market’s returns does not significantly vary during said weather seasons in Pakistan. Furthermore, the positive impact of terrorism (during post-event day 2) upon the stock market’s returns significantly differs during weather seasons of spring, summer, and autumn in Pakistan. As per the results, this study suggests that the investor should invest on event day and resell/ withdraw his investment on post-event day 1 in order to earn higher profit.

Tracking COVID-19 Decease Through Rolling Conditional Variance

The effects of COVID-19 have been devastating globally. However, countries have essential asymmetries regarding the disease spread dynamics and the respective mortality rates. In addition to containment strategies and boosting growth and economic development in the face of the COVID-19 pandemic, society calls for solutions that allow the development of vaccines, treatments for the disease, and especially, indicators or early warnings that anticipate the evolution of new infections and deaths. This research aims to track the total deaths caused by COVID-19 in the most affected countries by the pandemics after the approval, distribution, and implementation of vaccines from 2021. We proposed an Autoregressive Integrated Moving Average (ARIMA) specification as a first adjustment. Subsequently, we estimate the conditional variance of total deaths from an Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH). Finally, we compute a rolling density backtesting within a 7-day rolling window to demonstrate the robustness estimation for COVID-19 mortality. The work's main contribution lies in exhibiting a tracking indicator for volatility and COVID-19 direction, including a weekly window to observe its evolution.

Modelling and Forecasting the Conditional Heteroscedasticity With Different Distribution Densities – Frontier Market Evidence

This paper examines and compares alternative distribution density forecast methodology of three generalised autoregressive conditional heteroscedasticity (GARCH) models. We employed the symmetric GARCH, Glosten Jagannathan and Runkle version of GARCH (GJR-GARCH) and Exponential GARCH methodology to investigate the effect of stock return volatility using Gaussian, Student-t and Generalised Error distribution densities. The evidence reveals that news impact is asymmetric leading to the existence of leverage effect in stock returns. The presence of leverage effect suggests that investors in these markets are to be rewarded for taking up additional leverage risks. This implies that by allocating portfolios, fund managers and /or investors should go beyond the mean-variance analysis and look into information about volatility, information asymmetry, correlation, skewness, and kurtosis. Furthermore, the evidence exhibits reverse volatility asymmetry, contradicting the widely accepted theory of volatility asymmetry. Regarding forecasting evaluation, the results reveal that the symmetric GARCH model coupled with fatter-tail distributions presents a better out-of-sample forecast.

Volatility transmission within financial markets during the COVID-19 pandemic: are faith-based investors well off in Tunisia?

PurposeThis paper aims to investigate the risk-return and volatility spillover within the Tunisian stock market during the COVID-19 pandemic analyzing both the Islamic and conventional stocks’ performance.Design/methodology/approachBoth symmetric (GARCH and GARCH-M) and asymmetric (Threshold GARCH and Exponential GARCH) models are used to analyze the market returns and volatility response. Standard and Poor’s (S&P) index has been used to test both the Islamic and conventional stocks within the Tunisian stock market.FindingsThe findings suggest that both Tunisia Islamic and conventional stock markets are highly persistent; however, the conventional stock index showed a negative return spillover on the Islamic stocks during the pandemic. The conventional stock index has also shown a higher exposure to risk for a lower amount of return, and evidence of potential diversification benefit between both indexes was found during the pandemic, whereas the Islamic market showed a positive leverage effect, indicating a positive correlation between past return and future return; the conventional index implied a negative leverage effect.Originality/valueThe value of this paper emerges in studying three main aspects that are specific to the Tunisian stock market. This includes COVID-19 effect of return spillovers, volatility transmission across both conventional and Islamic stock market within the local financial market.

External Shocks and Volatility Overflow among the Exchange Rate of the Yen, Nikkei, TOPIX and Sectoral Stock Indices

In this paper, we examined the changes in volatility overflow among the exchange rate of the Japanese yen (JPY), the Nikkei Stock Average (Nikkei), the Tokyo Stock Price Index (TOPIX) and the TOPIX sectoral indices for the period of 10 February 2016 to 24 March 2017. We employed the exponential generalised autoregressive conditional heteroscedasticity (EGARCH) model, the cross-correlation function, and the daily logarithmic returns of JPY, Nikkei, TOPIX and the TOPIX components with a weight of 5% and more in estimations (banks, chemicals, electric appliances, information and communication, machinery and transportation equipment indices). The findings highlighted causality in variance (volatility spillover) among the variables. We revealed that volatility could also spread indirectly among the variables (from one variable to another through a third variable). We demonstrated how the impact of news about the results of the Brexit referendum (BR) and the United States presidential election (USE) in 2016 might spread among the variables indirectly within a week.

Improving the accuracy of tail risk forecasting models by combining several realized volatility estimators

The statistical properties of realized volatility estimators critically depend on the sampling frequency of the underlying intra-day returns and on the chosen estimation formula. This gives rise to a substantial model uncertainty when realized volatility is used as a regressor in tail risk forecasting models. In this paper, aiming to mitigate the impact of model uncertainty on the generation of tail risk forecasts, we propose parsimonious extensions of the Realized Exponential GARCH model that combine information from several volatility estimators. Both fixed and time-varying parameter models are considered. An application to the prediction of daily Value-at-Risk and Expected Shortfall for the S&P 500 provides evidence that modelling approaches based on the combination of different frequencies and estimation formulas can lead to significant accuracy gains.

Price Volatility for Selected Agricultural Commodities in Ethiopia: Evidence from GARCH Models

This study models the volatility of returns for selected agricultural commodity prices in Ethiopia using the generalized autoregressive conditional heteroskedasticity (GARCH) approach. GARCH family models, specifically threshold GARCH and exponential GARCH were employed to analyze the time varying volatility of selected agricultural commodities prices from 2010 to 2021. The data analysis results revealed that, out of the GARCH specifications, the EGARCH model with the normal distributional assumption of residuals was a better fit model for the price volatility of “teff” and “red pepper” in which their return series reacted differently to the “good” and “bad” news. The study indicated the existence of a leverage effect, which implied that the “bad” news could have a larger effect on volatility than the “good” news of the same magnitude, and the asymmetric term was statistically significant.

Determining the Appropriate Time Series Model for the Malaysia Stock Price during Continuous Pandemic Waves: Case of COVID-19

As the series of COVID-19 outbreaks was reported and the declaration of this disease as pandemic, the global financial market, including Malaysia has affected. The uncertainty of this pandemic has led to larger volatility and an appropriate time series model are required to guarantee that the market players made a wise investment decision. Therefore, this study aims to investigate the movement of FTSE Bursa Malaysia stock indices and determine the appropriate model for the sample period. We included the daily data from January 2020 to August 2021 to overview the stock market volatility and Autoregressive Integrated Moving Average (ARIMA) was applied to determine a reliable model. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models then was fitting in when the presence of heteroscedasticity in the data set was discovered. The result has shown that ARIMA (1,2,1) – GARCH (1,1) is the fitted model and the volatility was well-determined during the pandemic. In addition, the existence of leverage effect was confirmed using Exponential GARCH (EGARCH) and a positive risk premium was detected using Symmetric Mean GARCH (GARCH-M). Finally, it is recommended for researchers to use an extended sample period to see the behaviour of the stock market when Malaysia vaccination program has completed.

Reserve currency and the volatility of clean energy stocks: The role of uncertainty

Clean energy firms are among the most risky firms to invest in. Hence, it is essential to have a clear understanding of the risk profile of clean energy stocks. The main purpose of this study is to examine how changes in the reserve currency (US dollar) value affect the volatility of clean energy stocks in the absence/presence of uncertainty information. To this end, the volatility of clean energy stocks is first obtained by considering uncertainty information in the exponential generalized autoregressive conditional heteroskedastic (EGARCH) volatility estimates. Then, using the autoregressive distributed lag (ARDL) model, this study investigates the effect of reserve currency (US dollar) value fluctuations on the volatility of clean energy stocks. Controlling for monetary conditions, financial stress, and business cycle fluctuations, the study finds that, in the absence of uncertainty information, the volatility of clean energy stocks is not influenced by US dollar fluctuations. However, an appreciation of the US dollar against major foreign currencies significantly increases the volatility of clean energy stocks when uncertainties about economic policy, exchange rate market, and gold market are included in the picture. We find that economic uncertainty mediates the link between reserve currency and the volatility of clean energy stocks. The results shed more light on the risk profile of clean energy stocks and suggest the need for predictable and stable policies to increase the attractiveness of clean energy stocks.

Determining the Return Volatility of Major Stock Markets Before and During the COVID-19 Pandemic by Applying the EGARCH Model

With this study, we aim to determine the effect of the Covid-19 pandemic on the return volatility of the DJI, the DAX, the FTSE100 and the CAC40 stock indexes. We take return volatility between 1st January 2019 and 17th July 2020 and split it into two separate periods - before the Covid-19 pandemic outbreak and the first wave of the ‘In-Pandemic’ period. Only the so-called first wave of the pandemic was chosen to avoid the influence of knowledge of possible vaccines and antiviral solutions. Data were analysed by using the exponential GARCH (EGARCH) model. Findings show excessive volatility in the major stock markets with short volatility persistence and the presence of leverage in returns during the first wave of the Covid-19 pandemic outbreak. Moreover, during the pandemic period, positive shocks have been observed to have a greater effect than negative socks on the stock index return volatility.

Impact of Covid-19 pandemic on stock market returns volatility of Gulf Cooperation Council countries

This study examined the asymmetric impact of the COVID-19 pandemic on the Gulf Cooperation Council (GCC) stock market return volatility. The data included daily closing prices of the GCC stock market from the day of the acknowledgment of the first case of COVID-19 in each country to March 6, 2021. In addition, the study employed generalized autoregressive conditional heteroscedasticity (GARCH) family models. According to the Akaike information criterion, GARCH and exponential GARCH (EGARCH) were the most accurate models. The findings of the GARCH model indicate that the COVID-19 pandemic affected the GCC stock markets. The EGARCH model also confirmed the impact of the COVID-19 pandemic on the GCC stock markets, confirming that the COVID-19 negatively affected GCC stock market returns. The value of the persistence of this volatility continued over a long period. This study has potential implications for investors and policymakers in diversifying investment portfolios and adopting strategies to maintain investor confidence during such crises. Moreover, mechanisms must be developed for reducing risks in financial markets in times of crisis, and central banks should take financial measures to mitigate risks to capital markets. AcknowledgmentsThis achievement was made with the aid of my family’s support, thank you all.

A dynamic conditional score model for the log correlation matrix

This paper proposes a new model for the dynamics of correlation matrices, where the dynamics are driven by the likelihood score with respect to the matrix logarithm of the correlation matrix. In analogy to the exponential GARCH model for volatility, this transformation ensures that the correlation matrices remain positive definite, even in high dimensions. For the conditional distribution of returns, we assume a student-t copula to explain the dependence structure and univariate student-t for the marginals with potentially different degrees of freedom. The separation into volatility and correlation parts allows for a two-step estimation, which facilitates estimation in high dimensions. We derive estimation theory for one-step and two-step estimation. In an application to a set of six asset indices including financial and alternative assets we show that the model performs well in terms of diagnostics, specification tests, and out-of-sample forecasting.

Modelling & Forecasting Volatility of Daily Stock Returns Using GARCH Models: Evidence from Dhaka Stock Exchange

Modelling volatility has become increasingly important in recent times for its diverse implications. The main purpose of this paper is to examine the performance of volatility modelling using different models and their forecasting accuracy for the returns of Dhaka Stock Exchange (DSE) under different error distribution assumptions. Using the daily closing price of DSE from the period 27 January 2013 to 06 November 2017, this analysis has been done using Generalized Autoregressive Conditional Heteroscedastic (GARCH), Asymmetric Power Autoregressive Conditional Heteroscedastic (APARCH), Exponential Generalized Autoregressive Conditional Heteroscedastic (EGARCH), Threshold Generalized Autoregressive Conditional Heteroscedastic (TGARCH) and Integrated Generalized Autoregressive Conditional Heteroscedastic (IGARCH) models under both normal and student’s t error distribution. The study finds that ARMA (1,1)- TGARCH (1,1) is the most appropriate model for in-sample estimation accuracy under student’s t error distribution. The asymmetric effect captured by the parameter of ARMA (1,1) with TGARCH (1,1), APARCH (1,1) and EGARCH (1,1) models shows that negative shocks or bad news create more volatility than positive shocks or good news. The study also provides evidence that student’s t distribution for errors improves forecasting accuracy. With such an error distribution assumption, ARMA (1,1)-IGARCH (1,1) is considered the best for out-of-sample volatility forecasting.

Analysis of the impact of central bank communications on money market indicators

Press releases on monetary policy play an important role in the communication policy of the central bank. These press releases explain key rate decisions and provide signals about the future direction of the central bank’s monetary policy. Information signals can influence the expectations of financial market participants and increase the predictability and effectiveness of monetary policy. There are not enough research papers dedicated to the text analysis of the Bank of Russia press releases and the assessment of information signals. Hence, this article examines the impact of information signals about monetary policy on the money market rate, term and credit spreads. First, we estimate latent Dirichlet allocation to determine the topics of information signals. Second, we use sentiment analysis to construct signals about easing or tightening of the monetary policy. Third, the impact of signals about the future monetary policy on the money market indicators is assessed using the exponential GARCH model. Empirical research has shown that signals of future monetary policy easing are associated with lower money market rates and term spreads, and an increase in the credit spread. The result proved to be resistant to various ways of vectorizing the text of press releases. The article was prepared as a part of the state assignment research of Russian Presidential Academy of National Economy and Public Administration.

EFFECT OF VOLATILITY IN THE NAIRA - DOLLAR EXCHANGE RATE ON THE VOLUME OF IMPORTS TO, AND EXPORTS FROM NIGERIA

We analyzed the effect of volatility in the Naira-Dollar exchange rate on the volume of imports to and exports from Nigeria between 1990 and 2019. Data for all variables, except volatility, were sourced from the Central Bank of Nigeria (CBN), the National Bureau of Statistics (NBS), and the International Financial Statistics. The volatility of the naira exchange rate was calculated from the model. The study employed both the autoregressive distributed lagged (ARDL) and exponential generalized autoregressive conditional heteroscedasticity (EGARCH) models to test for the short and long-run relationships between changes in the Naira-Dollar exchange rate and the volume of imports and exports. Volatility in the Naira-Dollar exchange rate was found to be related to the volume of imports to and exports from Nigeria in the long run with no short-run effects because of the pass-through effect to domestic inflation. The study recommends that government should sustain efforts at promoting exports and reducing imports to improve the trade balance. The study brings into perspective another way of looking at the long-run relationship between the Naira-Dollar exchange rate and Nigeria's trade balance.Keywords: Foreign exchange rate, foreign exchange market, Imports, Exports, The balance of trade, Nigeria.JEL Classifications: F14, F31, 024.DOI: https://doi.org/10.32479/ijefi.11799