Exponential GARCH Model Research Articles

Semi-parametric financial risk forecasting incorporating multiple realized measures

A semi-parametric joint Value-at-Risk (VaR) and Expected Shortfall (ES) forecasting framework employing multiple realized measures is developed. The proposed framework extends the realized exponential GARCH model to be semi-parametrically estimated, via a joint loss function, whilst extending existing quantile time series models to incorporate multiple realized measures. A quasi-likelihood is built, employing the asymmetric Laplace distribution that is directly linked to a joint loss function, which enables Bayesian inference for the proposed model. An adaptive Markov Chain Monte Carlo method is used for the model estimation. The empirical section evaluates the performance of the proposed framework with six stock markets from January 2000 to June 2022, covering the period of COVID-19. Three realized measures, including 5-minute realized variance, bi-power variation, and realized kernel, are incorporated and evaluated in the proposed framework. One-step-ahead 1% and 2.5% VaR and ES forecasting results of the proposed model are compared to a range of parametric and semi-parametric models, lending support to the effectiveness of the proposed framework.

FORECAST ACCURACIES OF HYBRID OF BILINEAR AND EXPONENTIAL SMOOTH TRANSITION AUTOREGRESSIVE MODELS WITH GARCH MODELS

The study looks at the forecast accuracies of GARCH and Bilinear models on the one hand, and hybrids of Bilnear with GARCH (BL-GARCH) and ESTAR with GARCH (ESTAR-GARCH) models on the other hand. Necessary mathematical or theoretical frameworks were set up for the four models and were illustrated with inflation rate data from Nigeria (1994–2019). Stationarity tests conducted (Unit Root Test) show that at level (original data) the series is chaotic and volatile (non-stationary), but at the first difference the series is stationary. This, therefore, paved the way for the analysis. In and out of sample, the forecast accuracies of all the models used were checked and compared. Information criteria such as AIC, BIC, and FPE were used, where it was seen that ESTAR-GARCH performs best. Also, the performance measure indices used revealed that ESTAR-GARCH was very outstanding. The same goes for variance analysis (ESTAR-GARCH had the least variance). The results show that the two hybrid models give exceptional performances; also, the GARCH model's performance is fairly good but not comparable to the hybrids. Exponential GARCH models perform better than Bilnear-GARCH models and GARCH models. However, the ESTAR-GARCH and BL-GARCH models are comparable and could be interchangeably used by would-be forecasters, investors, academia, and other would-be users.

Sovereign Credit Default Swap Market Volatility in BRICS Countries Before and During the COVID-19 Pandemic

SCDS (Sovereign Credit Default Swaps) are becoming more widely used as a country risk indicator after 2008 and stand out for providing real-time information rather than periodic reporting. The COVID-19 pandemic has led to economic disruptions and a decline in international trade. Understanding how the Pandemic affects SCDS return volatility in emerging economies like BRICS forms the motivation for our research. With this study, we aim to determine the impact of the COVID-19 Pandemic on SCDS return volatility in Brazil, Russia, India, China and South Africa, known as the BRICS countries. We used the Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model to analyze the data, which consisted of the daily closing price data for SCDS. The date of the first COVID-19 case in each country has been taken as the beginning of the COVID-19 Pandemic in each country. The results of the estimated GARCH models show that the volatility processes of the SCDS return series differ between periods. EGARCH model results indicate that shocks created by news in these countries during the Pandemic have a small and persistent effect on Brazil and Russia's SCDS return volatility, while they have a large and enduring effect on China and South Africa's SCDS return volatility. The findings will guide policymakers and portfolio managers in determining risk management models.

Modeling the Effects of Volatility and Uncertainty in Psychological Errors on Collective Decision-Making of Investors in the Iranian Capital Market

Objective: The aim of the present study is to model the effects of volatility and uncertainty in psychological errors on the collective decision-making of investors in the Iranian capital market. Methodology: To test the hypotheses, a sample consisting of 204 companies from those listed on the Tehran Stock Exchange was selected using the systematic elimination method over a 5-year period from 2018 to 2022. The research data were collected on a monthly basis with a panel data approach and were analyzed using three multiple linear regression models. These models were calculated using the Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) and Threshold Generalized Autoregressive Conditional Heteroskedasticity (TGARCH) methods, with the help of Excel 2016 and Eviews13 software for statistical analysis. Findings: According to the results of the statistical tests of the research hypotheses, the volatility of the psychological error index and investors' trading behavior has a significant and negative impact on abnormal stock returns. Additionally, the volatility of the psychological error index has a significant and positive impact on the volume and frequency of abnormal stock trades. However, the volatility of investors' trading behavior has a significant and negative impact on the volume and frequency of abnormal stock trades. Conclusion: The results of the analysis of the EGARCH and TGARCH conditional heteroskedasticity models indicate asymmetry in the influence of collective investment decisions from past data and past volatility, which is consistent with the Prospect Theory that claims positive and negative returns have different effects on investor utility.

Transition E-Garch Model for Modeling and Forecasting Volatility of Equity Stock Returns in Nigeria Stock Exchange

The mean-equations that exhibit unconditional variance do not reflect real-world data characteristics and do not always fully embrace the thick tail properties of high-frequency financial time series. However, there are cases when mean-equations exhibit conditional and unconditional variances, which conventional Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models do not accommodate with assumptions of normal error innovation. The behaviour of equity in stock returns volatility was investigated using mean-equations that reflect both conditional and unconditional variances under the variants innovation distribution. The Nigeria Stock Exchange’s, (NSE’s), daily All Stock Index, (ASI) data from 3rd May 1999 to 18th March 2019 was utilized to characterize the volatility structure of equity in Nigeria Stock returns. The Transition Exponential GARCH Model (TEGM) with non-normal innovations was used to demonstrate the dynamic model performance and predictive power in modeling variances that transit between unconditional and conditional structures. Under various error innovations, the structural characteristics of the TEGM were examined, and the parameters were estimated. The TEGM result under Student’s t innovation distribution was significant for forecasting and predicting random series data. The error distribution has both the minimal and sufficient requirements for the best predictive capacity and forecasting capabilities. Over a longer period, the NSE’s daily ASI showed more unconditional variance than conditional variation. The Transition Exponential GARCH Model was found to be the best model for describing the volatility structure of financial assets in Nigerian stock returns, and is thus recommended for making informed investment decisions with better forecast performance.

Price Discovery and Volatility Spillover: An Empirical Analysis of Indian Futures-Spot Cardamom Markets

Price discovery and its related volatility spillover effect are significant indicators in commodity derivatives market to hedge the risk against sharp price fluctuations. This study empirically analyses the price discovery and volatility spillover using vector error correction model, Granger causality and bivariate exponential GARCH model (EGARCH) in Indian cardamom spot-futures markets. Daily time series data of spot market and near month futures contracts spanning the period from January 2009 to December 2020 have been used for the study. These price series data are based on the authenticated sources of Multi Commodity Exchange. The results of vector error correction model supported by Granger causality test indicates that spot market plays the role of leader as it is more efficient in reflecting the new information to prices. The results of bivariate EGARCH (1,1) model show that volatility spillover from cardamom spot market to futures market is dominant.

Analysing volatility patterns in emerging markets: symmetric or asymmetric models?

PurposeInvestors aim for returns when investing in stocks, making return volatility a crucial concern. This study compares symmetric and asymmetric GARCH models to forecast volatility in emerging nations like the G4 countries. Accurate volatility forecasting is vital for investors to make well-informed investment decisions, forming the core purpose of this study.Design/methodology/approachFrom January 1993 to May 2021, the study spans four periods, focusing on the global economic crisis of 2008, the Russian crisis of 2015 and the COVID-19 pandemic. Standard generalized autoregressive conditional heteroscedasticity (GARCH), exponential GARCH (E-GARCH) and Glosten-Jagannathan-Runkle GARCH models were employed to analyse the data. Robustness was assessed using the Akaike information criterion, Schwarz information criterion and maximum log-likelihood criteria.FindingsThe study's findings show that the E-GARCH model is the best model for forecasting volatility in emerging nations. This is because the E-GARCH model is able to capture the asymmetric effects of positive and negative shocks on volatility.Originality/valueThis unique study compares symmetric and asymmetric GARCH models for forecasting volatility in emerging nations, a novel approach not explored in prior research. The insights gained can aid investors in constructing more effective risk-adjusted international portfolios, offering a better understanding of stock market volatility to inform strategic investment decisions.

Oil Price Fluctuation And Exchange Rate In Nigeria: Is There A Volatility Transmission Effect

Over the period 1980-2022, we examined the transmission effect of oil prices on Nigeria's exchange rate. E-GARCH (Exponential GARCH) model is employed in this study. We used Augmented Dickey Fuller to determine a unit root, integrating exchange rates, crude oil prices, external reserves, GDP, inflation, and interest rates to one I(1) and zero I(0). We used Johansen Co-integration to determine long-term relationships. Interest rates, inflation, and crude oil prices all correlated positively with each other. A statistically insignificant result is shown by the variance equation, indicating there is no correlation between crude oil prices and exchange rates. The Nigerian exchange rate is not affected by volatility transmission or leverage due to fluctuations in crude oil prices. According to the study, governments should take monetary policy measures to stabilize exchange rates during unpredictable oil price fluctuations. It is necessary to adjust the naira exchange rate when oil prices fluctuate.

GARCH Models and Distributions Comparison for Nonlinear Time Series with Volatilities

The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is extensively used for handling volatilities. However, with numerous extensions to the standard GARCH model, selecting the most suitable model for forecasting price volatilities becomes challenging. This study aims to examine the performance of different GARCH models in forecasting crude oil price volatilities using West Texas Intermediate (WTI) data. The models considered are the standard GARCH, Integrated GARCH (IGARCH), Exponential GARCH (EGARCH), and Golsten, Jagannathan, and Runkle GARCH (GJR-GARCH), each with normal distribution, Student’s t-distribution, and Generalized Error Distribution (GED). To evaluate the performance of each model, the Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) are used as the model selection criteria, along with forecast accuracy measures such as absolute error, root mean squared error (RMSE), and mean absolute error (MAE). Post-estimation tests, including the Autoregressive Conditional Heteroskedasticity Lagrange Multiplier (ARCH-LM) test and the Ljung-Box test, are conducted to ensure the adequacy of all models. The results reveal that all GARCH models are suitable for modeling the data, as indicated by statistically significant estimated parameters and satisfactory post-estimation outcomes. However, the EGARCH (1, 1) model, particularly with Student’s t-distribution, outperforms other models in both data fitting and accurate forecasting of nonlinear time series.

Volatility Forecasting Using Quasi-Score-Driven Models with an Application to the Coronavirus Pandemic Period

Abstract We study the statistical and volatility forecasting performances of the recent quasi-score-driven EGARCH (exponential generalized autoregressive conditional heteroscedasticity) models. We compare the quasi-score-driven EGARCH models with GARCH, asymmetric power ARCH (A-PARCH), and all relevant score-driven EGARCH models of the literature. For score-driven and quasi-score-driven EGARCH, we use the following seven score-driven probability distributions: Student’s t-distribution; general error distribution (GED); generalized t-distribution (Gen-t); skewed generalized t-distribution (Skew-Gen-t); exponential generalized beta distribution of the second kind (EGB2); normal-inverse Gaussian distribution (NIG); Meixner distribution (MXN). We use all combinations of those distributions for (i) the probability distribution of the dependent variable, and (ii) the probability distribution which defines the quasi-score function updating term of the quasi-score-driven filters. We use daily data for the Standard & Poor’s 500 (S&P 500) index. We find that both in-sample and out-of-sample, quasi-score-driven EGARCH is superior to GARCH, A-PARCH, and score-driven EGARCH. We report in-sample results for the period of January 2000 to December 2020, providing evidence in favor of the quasi-score-driven EGARCH model for the last two decades. We report out-of-sample volatility forecasting results for a period within the coronavirus disease 2019 (COVID-19) pandemic, providing evidence in favor of the quasi-score-driven EGARCH model for a crisis period.

The information content of sentiment indices in forecasting Value at Risk and Expected Shortfall: a Complete Realized Exponential GARCH-X approach

The aim of this paper is to investigate the impact of public sentiment on tail risk forecasting. In this framework, we extend the Realized Exponential GARCH model to directly incorporate information from realized volatility measures and exogenous variables, thus resulting in a novel dynamically complete specification denoted as the Complete REGARCH-X model. Several sentiment indices related to social media and journal articles regarding the economy and stock market volatility are considered as potential drivers of volatility dynamics. An application to the prediction of daily Value-at-Risk and Expected Shortfall for the Standard & Poor’s 500 index provides evidence that combining the information content of realized volatility and sentiment measures can lead to significant accuracy gains in forecasting tail risk.

Modelling and Forecasting Volatility on Electric Power Exchange SEEPEX

Research Question: The launch and the beginning of trade on the South East Electric Power Exchange (SEEPEX) in Belgrade, early in 2016, opened the issue of forecasting volatility and price movements in the market. Motivation: The issue is of vital importance for all market actors for the purpose of maximising profits, reducing risks, planning production and making investment decisions. Forecasting volatility and price movements in electric power markets is important for traders with profit maximisation and yield-to-risk ratio optimisation in mind and, equally, for producers, large industrial consumers, investors and portfolio managers. Idea: Exploring models and techniques to forecast volatility in electricity markets and subsequently testing statistical methods based on time series data, the ARMA-GARCH being the preferred model, with a view to identifying optimal methods for this market. The volatility of the power market and price movements have been tested during a given period. The results can be used to gauge market parameters and opportunities to extrapolate future volatility and movements in electricity prices. Data: For the purposes of this analysis, a time series involving price movements and trade volumes were used, covering a period between the SEEPEX trade launch and the end of 2019. Tools: In the empirical part of the paper, "Stata 13" statistical and econometric software was used to explore stylised facts and model the volatility of SEEPEX electricity price returns. Findings: The authors offer an overview of different methods used in the research, having selected different specifications of the ARMA-GARCH model as the most reliable in predicting volatility in the given market. The exponential GARCH model with student-t error distribution is believed to have provided the best overall performance in modelling the SEEPEX return volatility, as well as the best volatility forecast. Contribution: This is one of the first empirical studies of the Serbian power market that deals with risk modelling. Forecasting time-varying electricity exchange volatility is important for all market participants interested in variance forecasts to be used to calculate risk and hedging measures.

Assessing the impact of the COVID-19 pandemic on the performance of the Vietnam stock exchange: An empirical analysis

The emergence of COVID-19 in Wuhan, China, in December 2019 led to a global crisis with profound implications for public health and the global economy. This study investigates the ramifications of the pandemic on the Vietnam Stock Exchange, recognizing its interconnectedness with global financial markets. Despite the considerable speculation surrounding the pandemic's influence on economic and financial systems worldwide, limited empirical research has been conducted on its specific impact on the Vietnam Stock Exchange. Employing historical data spanning from January 30, 2020, to April 27, 2022, sourced from a secondary dataset, this research empirically explores the performance of the Vietnam Stock Exchange during the COVID-19 pandemic period compared to a normal period. The findings reveal a significant decline in stock returns and heightened volatility during the pandemic, signaling adverse effects on the exchange's performance. Furthermore, the study applies Quadratic GARCH (QGARCH) and Exponential GARCH (EGARCH) models, incorporating a dummy variable, to scrutinize stock returns. The results corroborate the pandemic's negative impact on stock returns in Vietnam. This research underscores the importance of implementing strategic political and economic policies, including maintaining a stable political environment, promoting indigenous enterprises, diversifying the economy, and adopting a flexible exchange rate regime. These measures are recommended to enhance the resilience of the financial market and attract new investors to the Ho Chi Minh Stock Exchange.

Forecasting Value-at-Risk using functional volatility incorporating an exogenous effect

This paper proposes a novel extension of log and exponential GARCH models, where time-varying parameters are approximated by orthogonal polynomial systems. These expansions enable us to add and study the effects of market-wide and external international shocks on the volatility forecasts and provide a flexible mechanism to capture various dynamics of the parameters. We examine the performance of the new model in both theoretical and empirical analysis. We investigate the asymptotic properties of the quasi-maximum likelihood estimators under mild conditions. The small-sample behavior of the estimators is studied via Monte Carlo simulation. The performance of the proposed models, in terms of accuracy of both volatility estimation and Value-at-Risk forecasts, is assessed in an empirical study of a set of major stock market indices. The results support the proposed specifications with respect to the corresponding constant-parameters models and to other time-varying parameter models.

Comparison of GARCH and SVRGARCH models: Example of gold return

Gold has been a precious resource for people on earth from the past to the present. It is used as both a value gain and jewelry, and is the focus of interest for people in terms of receiving attention and protecting its value. Especially recently, it has been the most favorite for investors due to its excess value increase and decrease which is constantly monitored. The study aimed to compare the predictive performance of the gold price return using the Support Vector Regression-GARCH hybrid models combined with the traditional volatility models. It has been examined whether the Support Vector Regression GARCH models would increase foresight performance. The study used data on the daily frequency between 01/01/2010–01/04/2023. Generalized Autoregressive Conditional Variable Variance, Glosten-Jaganthan-Runkle GARCH, Exponential GARCH and hybrid model Support Vector Regression -GARCH are utilized as prediction methods. For all methods, the gold series is divided into two groups as training and test data. The Root Mean Square Error values are compared as a model performance criterion. The RMSE values and graphics outputs have been concluded that the Support Vector Regression-GARCH model based on predicted linear, radial-based and polynomial kernel predicts more effectively than the GARCH models.

Monetary policy responses to COVID-19 in emerging European economies: measuring the QE announcement effects on foreign exchange markets

This paper examines the effects of quantitative easing (QE) announcements by emerging market central banks in Europe during the COVID-19 pandemic, particularly on exchange rates with a higher frequency setting. Two different methodologies are used for analysing the policy announcement effects. The first methodology is the event study method that measures the sample exchange rates’ mean and cumulative mean abnormal return around the time of event. The second one is the time series approach that measures asymmetric behaviour of the exchange rate volatility to monetary policy shocks by employing exponential GARCH model. The results show that the foreign exchange markets respond to QE announcements in all selected countries. The response of exchange rates varies across countries and event windows. QE announcements cause appreciation of domestic currency in Hungary and Poland, and depreciation in Turkey. Additionally, the QE announcements increase exchange rate volatility in Hungary and Poland while they reduce volatility in Turkey. The asymmetric behaviour of domestic currencies prevails in all selected countries, but this asymmetry is sensitive to the exchange rate and the length of the window.

Score function scaling for QAR plus Beta-t-EGARCH: an empirical application to the S&P 500

ABSTRACT In the literature on score-driven models, alternative choices of the scaling parameters of the conditional score terms are used, but the optimal choice of those parameters is an open question. Although there are score-driven models for which the choice of the scaling parameters is irrelevant, there are important score-driven models for which score-driven scale filters appear in the information matrix, and the choice of the scaling parameters is relevant. We focus on the quasi-autoregressive (QAR) plus Beta--EGARCH (exponential generalized autoregressive conditional heteroscedasticity) model, by using data on the Vanguard Standard & Poor’s 500 (S&P 500) exchange-traded fund (VOO) and all available S&P 500 stocks for the period of 2013–2023. For QAR plus Beta--EGARCH, each updating term is the product of a scaling parameter and a conditional score, and we use specific alternative scaling parameters from the literature. For different scaling parameters in the scale filter (volatility), alternative location and scale filters coincide. For different scaling parameters in the location filter (expected return), alternative location and scale filters differ significantly. For the statistical and volatility forecasting performances of VOO and most of the S&P 500 stocks, the best-performing scaling parameter for the score-driven location is the conditional inverse information matrix.

Model Exponential GARCH (EGARCH) Untuk Memprediksi Harga Saham PT Merdeka Copper Gold Tbk

The price of gold is determined by trading in the gold market and its derivatives. This study aims to determine the EGARCH model in predicting gold stock prices at PT Merdeka Copper Gold Tbk and to obtain the prediction results of the EGARCH model at PT Merdeka Copper Gold Tbk. There are two asymmetric GARCH response modeling techniques, namely the Threshold GARCH model (TGARCH) from Glosten, et al (1993) and Exponential GARCH (EGARCH) from Nelson (1991). The research results show that the ARIMA model (0,1,1) has the smallest AIC value of 6096.38. The GARCH model is obtained by GARCH (0,1), so it can be modeled using the EGARCH model. The EGARCH model obtained is EGARCH (1.7).

The impacts of futures trading on volatility and volatility asymmetry of Bitcoin returns

The impact of Bitcoin futures introduction on the underlying Bitcoin volatility has been a controversial topic. Conflicting results had been obtained from different sample periods and methodologies. To address this debate, this study examines the impact of futures trading on volatility and volatility asymmetry of Bitcoin returns in the short and long run. Using exponential GARCH models, we introduce a dummy in the variance equation to capture the changes in the volatility after the introduction of Bitcoin futures. We find that after the introduction, spot return volatility decreases in the short run, but increases in the long run. Besides, in the short run, there exists an inverse leverage effect before and after the introduction; in the long run, the inverse leverage effect before the introduction changes to a usual level effect after the introduction. Finally, we examine whether greater futures trading activity, proxied by trading volume and open interest, is associated with greater Bitcoin volatility. To do so, we decompose each proxy into expected and unexpected components and document that, in the long run, Bitcoin volatility covaries positively with unexpected futures trading volume, but negatively with unexpected futures open interest.

Forecasting Stock Volatility Using Wavelet-based Exponential Generalized Autoregressive Conditional Heteroscedasticity Methods

In this study, we proposed a new model to improve the accuracy of forecasting the stock market volatility pattern. The hypothesized model was validated empirically using a data set collected from the Saudi Arabia stock Exchange (Tadawul). The data is the daily closed price index data from August 2011 to December 2019 with 2027 observations. The proposed forecasting model combines the best maximum overlapping discrete wavelet transform (MODWT) function (Bl14) and exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model. The results show the model's ability to analyze stock market data, highlight important events that contain the most volatile data, and improve forecast accuracy. The results were compared from a number of mathematical models, which are the non-linear spectral model, autoregressive integrated moving average (ARIMA) model and EGARCH model. The performance of the forecasting model will be evaluated based on some of error functions such as Mean absolute percentage error (MAPE), Mean absolute scaled error (MASE) and Root means squared error (RMSE).