Exponential GARCH Research Articles

Volatility Behaviour of Bitcoin as a Digital Asset

The objective of this study is to use the South African financial markets (Johannesburg Stock Exchange or JSE and USD/ZAR) as a case study to understand the volatility spillover dynamics of Bitcoin as a digital asset. Methodologically, the study applies the exponential generalized autoregressive conditional heteroskedastic (EGARCH) model, followed by a robustness check by applying the time-varying conditional correlation multivariate GARCH (VCC-MGARCH) model. The study utilizes the data set for the period 2011 to 2019, a period before the COVID‑19 pandemic. The research outcome revealed three interesting observations. First, Bitcoin and the South African stock market are independent of each other. Second, there is a bidirectional shock transmission between Bitcoin and USD/ZAR in the mean returns only, but not variance. Lastly, results confirm the existence of a bidirectional volatility spillover in both the mean and variance between the JSE stock market and the USD/ZAR market. The study outcome should enlighten investors who may want to consider Bitcoin as a diversifier in their investment and portfolio strategies.

Performance of Generalized Autoregressive Conditional Heteroscedasticity (GARCH) Models in Modeling Volatility of Brent Crude Oil Price

Fluctuations in the price of crude oil determines the economic state of many nations especially the oil producing ones, it becomes important to examine these fluctuations, hence the GARCH models were applied to model the volatility in the price of brent crude oil to determine the best model suitable for predicting future volatility. Descriptive statistics of the stock price and its returns were obtained, some inferential tests were employed to examine the stationarity and the goodness of fit of the daily price and the return under different distributions – the Gaussian, the Student t and the Generalized Error Distributions. Results showed that the price of crude oil dropped between 2014 and 2016 and drastically dropped in 2020. Among the competing models, Exponential GARCH(1,1) with Student t distribution was the best model with the least values of AIC, SBIC and HQIC respectively. The result showed negative significant value in the coefficient of its asymmetric parameter, suggesting that bad news or vital event such as COVID19 has larger effect on the volatility in the price of the Brent crude oil. This study therefore recommended the use of Exponential GARCH model in modelling or predicting volatility in the stock price of crude oils.

Asymmetric Shocks In Oil Price: An Exponential Generalized Autoregressive Conditional Heteroskedasticity Approach

This study empirically examined the asymmetric oil price shocks in Nigeria from 1981q1-2019q4 using the Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model. The EGARCH model was employed to investigate the asymmetric oil price shocks by obtaining the conditional variance from the estimated results. Empirical results revealed a weak indication for leverage effect and a strong indication for asymmetric effect. The positive egarch (L2) coefficient means that unanticipated increases in the price crude Oil are more profitable than unanticipated decreases in the price of crude Oil. Also, the results revealed strong asymmetry of oil price shocks in Nigeria. In specific terms, the positive asymmetric coefficient (1.8276) means an observed tendency of the crude oil price shock to be higher by approximately 1.83 per cent in declining oil prices in the crude oil market than in rising prices in the oil markets. Based on the above, the study recommended appropriate export diversification policies to reduce the dependency on crude oil exports as the major export (revenue) in the economy. This will offset crude oil price shocks such as the COVID-19 pandemic shock on Oil price, especially from an unanticipated decrease in crude oil prices in the international market. Key Words: Oil price, Oil Price Shocks, Asymmetry, EGARCH, Nigeria

Revisiting volatility in global natural resources commodities? Evidence from global data

Natural resource commodities are considered an important factor for economic growth and development. However, volatility in these commodities is a topic of interest, which currently has the attention of scholars. In this regard, the current study investigates volatility in global natural resource commodities while undertaking the Covid-19 pandemic. This study used coal rents (CR), forest rents (FR), mineral rents (MR), natural gas rents (NGR), oil rents (OR), and total natural resource rents (TNRR) to comprehensively measure volatility in natural resource commodities during the period from 1971 to 2020. For empirical investigation of volatility, this study employed autoregressive conditional heteroscedasticity (ARCH) specification, which indicates that CR, FR, MR, and NGR hold no volatility throughout the study period. However, OR and TNRR are found to be volatile throughout the period and during the Covid-19 pandemic. Besides, the generalized threshold ARCH (TGARCH) and exponential generalized ARCH (EGARCH) provide no evidence of positive-negative shocks asymmetry. Also, the results do not provide evidence that negative shock enhances volatility in natural resource commodities more than that of positive shock having the same magnitude. Based on the empirical findings, this study recommends some policy implications in the end.

Reconciling negative return skewness with positive time-varying risk premia

One of the implications of the intertemporal capital asset pricing model (ICAPM) is a positive and linear relationship between the conditional mean and conditional variance of returns to the market portfolio. Empirically, however, it is often observed that there is a negative skewness in equity returns. This article shows that a negative skewness is only compatible with a positive risk premium if the innovation distribution is asymmetric with a negative skewness. We extend recent work using the EGARCH-in-Mean specification to allow for asymmetric innovations, and give results for the unconditional skewness of returns. We apply the model to the prediction of Value-at-Risk of the largest stock market indices, and demonstrate its good performance. Keywords: Exponential GARCH, in-mean, risk premium, ICAPM, unconditional skewness, asymmetric distribution, portfolio selection, Value-at-Risk.

Modelling of Volatility in Nigeria Crude Oil Price Using symmetric and asymmetric GARCH models

Accurate modelling of volatility is important in finance, particularly as it relates to the modelling and forecasting of crude oil prices. This paper examines which of the model can best handle the price volatility of the Nigeria Crude Oil market. The models consider in this work are the Generalized Autoregressive Conditional Heteroskedasticity (GARCH), Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) and Power Autoregressive Conditional Heteroskedasticity (PARCH). The analysis displays the evaluation of the enactment of Nigerian crude oil price for GARCH (1, 1), EGARCH (1, 1) and PARCH (1, 1) models. The data used was collected from the Central Bank of Nigeria website for twelve (12) years (2010 – 2021) which make up of 2422 observations. Time Series was carried out using Eviews 9 and the result shows that the GARCH model outperforms EGARCH and PARCH models based on the value of Akaike Information Criteria.

The Effects of COVID-19 outbreak on the Nigerian Stock Exchange performance: Evidence from GARCH Models

The recent COVID-19 was first identified in Wuhan, China in December 2019 and now it has caused huge death and spread to almost all over the world. There are news that most of the world economy and financial markets would be affected due to protocols such as lockdown and social distancing. In Nigeria, the first case of COVID-19 was identified on 27th February 2020 and this present study examines the effect of COVID-19 outbreak on the performance of the Nigeria stock exchange using secondary data for the period of 2nd March 2015 to 16th April, 2020. Also the study considered the COVID-19 period of 2nd January 2020 to 16th April 2020, the results from GARCH models revealed a loss in stock returns and high volatility in stock returns under the COVID-19 period in Nigeria as against the non COVID-19 period. Also, the Quadratic GARCH (QGARCH) and Exponential GARCH (EGARCH) models with dummy variable were applied to the stock returns which shown that the COVID-19 has had negative effect on the stock returns in the Nigeria stock markets. The study therefore recommended that economic policy such as incentive to indigenous companies to create new employments, diversification of the economy to attract new investors, and flexible exchange rate regime that will aid business between Nigeria investors and the international market (trade) be implemented. Lastly, the government of Nigeria should ensure policy that ensures stable political environment and reduction in insecurity in the country.

Forecasting Commodity Market Returns Volatility: A Hybrid Ensemble Learning GARCH‐LSTM based Approach

SummaryThis study investigates the advantage of combining the forecasting abilities of multiple generalized autoregressive conditional heteroscedasticity (GARCH)‐type models, such as the standard GARCH (GARCH), exponential GARCH (eGARCH), and threshold GARCH (tGARCH) models with advanced deep learning methods to predict the volatility of five important metals (nickel, copper, tin, lead, and gold) in the Indian commodity market. This paper proposes integrating the forecasts of one to three GARCH‐type models into an ensemble learning‐based hybrid long short‐term memory (LSTM) model to forecast commodity price volatility. We further evaluate the forecasting performance of these models for standalone LSTM and GARCH‐type models using the root mean squared error, mean absolute error, and mean fundamental percentage error. The results highlight that combining the information from the forecasts of multiple GARCH types into a hybrid LSTM model leads to superior volatility forecasting capability. The SET‐LSTM, which represents the model that combines forecasts of the GARCH, eGARCH, and tGARCH into the LSTM hybrid, has shown the best overall results for all metals, barring a few exceptions. Moreover, the equivalence of forecasting accuracy is tested using the Diebold–Mariano and Wilcoxon signed‐rank tests.

Modeling the volatilities of globally listed private equity markets

PurposeThis paper aims to analyze the characteristics of stochastic volatility processes in globally listed private equity (LPE) markets, which are represented by nine global, regional and style indices, and reveals transmissions in the conditional variances between the different markets, based on weekly data covering the period January 2011 to December 2020.Design/methodology/approachThe study uses the generalized autoregressive conditional heteroscedasticity [GARCH(p, q)] model and its exponential GARCH (EGARCH) and GARCH-in-mean extensions.FindingsThe estimates of the volatility models GARCH, EGARCH and GARCH-in-mean GARCH-M for testing the stylized properties persistence, asymmetry, mean reversion and risk premium lead to very different results, depending on the respective LPE index.Practical implicationsThe knowledge of conditional volatilities of LPE returns as well as the detection of volatility transmissions between the different LPE markets under investigation serve to support asset allocation decisions with respect to risk management or portfolio allocation. Hence, the findings are important for all kinds of investors and asset managers who consider investments in LPE.Originality/valueThe authors present a novel study that examines the conditional variance for globally LPE markets by using LPX indices, offering valuable insight into this growing asset class.

Does commitment to environment and society pays? Evidence from COVID-19 impact on stock volatility

Purpose This study aims to analyse whether investment in green and sustainable stocks provide some cushion during current precarious time. To compare the impact of COVID-19 on the volatility of sustainable and market-capitalisation-based stocks, daily returns from Greenex, Carbonex, Large-Cap, Mid-Cap and Small-Cap index have been analysed over a period of six years from 2015 to 2021. Design/methodology/approach At the outset, logarithmic return of all selected indices has been tested for possible unit root and heteroscedastic. On confirmation of stationarity and heteroscedasticity of data, auto-regressive conditional heteroscedastic models have been applied. Thereafter, volatility is modelled through best suitable model as suggested by Akaike and Schwarz information criterions. Findings The findings indicate the positive impact of COVID-19 on the volatility of the indices. Asymmetric power ARCH model indicates highest significant impact of COVID-19 over the volatility of Large-Cap index, whereas exponential GARCH model detected highest significant impact of COVID-19 over the volatility of Mid-Cap Index. Originality/value To the best of the authors’ knowledge, the present study is original in the sense that it aimed at comparing the possible impact of COVID-19 over sustainable and market-capitalisation-based indices.

CONTAGION ACROSS FINANCIAL MARKETS DURING COVID-19: A LOOK AT VOLATILITY SPILLOVERS BETWEEN THE STOCK AND FOREIGN EXCHANGE MARKETS IN SOUTH AFRICA

The onset of the novel coronavirus pandemic (COVID-19) and previous financial and currency crises have heightened interest in understanding the nature of the interaction of stock market and exchange rate volatility. This paper aims to investigate the interdependence and volatility transmissions between the stock and foreign exchange markets for South Africa over the period of 1979:01–2021:08, including the effect the COVID-19 pandemic has had on the interdependence and volatility transmissions. Through the use of bivariate Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH) modeling, the empirical outcomes from this study provide strong evidence in support of the “stock-orientated” approach, where significant price and volatility spillovers propagate from the stock market into the foreign exchange market, whilst evidence of the “flow-orientated” approach is seen in the second moment and significant shock and asymmetric spillovers from the exchange to stock market are found. The results support the asymmetric and long-range persistence volatility spillover effect and show strong evidence of contagion between stock and foreign exchange markets. These spillovers became more pronounced during the COVID-19 pandemic, confirming heightened contagion in these markets during the periods of crisis. The results heed important implications for not only policymakers who are concerned by the contagion across financial markets and better regulations of these markets to promote economic growth, but also investors and fund managers who seek to hedge investment risks in South Africa.

Equity Price Risk of Commercial Banks in India

This study is directed at gauging the equity price risk of the Indian commercial banks for the period 2003–2020. Parametric value-at-risk (VaR) is employed to estimate the downside risk. Further, the univariate exponential generalized auto regressive conditional heteroskedasticity (EGARCH) model is also used to find out the existence of stylised aspects of volatility. The outcomes point towards the existence of volatility clustering, persistence and asymmetry, but differ from bank to bank. Furthermore, the parametric VaR model that assumes normal distribution and student’s t-distribution is not found to be an accurate model for all the banks. Tail risk is also found to be significant, and thus, justifies the Basel Committee’s decision to shift towards an expected shortfall. However, these conventional VaR models should be supplemented by internal models, taking into consideration, bank-specific characteristics. JEL: G01, G15, I15, G17, G28

The impact of COVID-19 on gold seasonality

ABSTRACT This study investigates the impact of COVID-19 on the seasonality of gold returns by means of an asymmetric EGARCH model (Exponential GARCH). We find that the so-called ‘autumn effect’, or the traditional seasonal increase in gold returns in fall, vanishes and even shows a reverse pattern during the COVID-19 pandemic. We ascribe this phenomenon to the decaying demand for gold, which substantially decreased in the third quarter of 2020. In contrast, we find no evidence of seasonal effects in gold volatility, which is in line with earlier researches on this topic. Our results also confirm the positive asymmetric effect of gold volatility.

Measuring natural resources rents volatility: Evidence from EGARCH and TGARCH for global data

Natural resources and their impact on various economic and non-economic indicators have been a topic of interest for the last few decades. However, natural resources volatility has been relatively less explored by researchers. Following the recent trend, this study measures natural resource volatility from a global perspective. This study used the data for total natural resources rents (TNR), coal rents (CR) oil rents (ORR) and natural gas rents (NGR) over the extended period from 1970 to 2021. Appropriate measures of volatility in time variables, the threshold generalized autoregressive conditional heteroscedasticity (TGARCH) and the exponential generalized autoregressive conditional heteroscedasticity (EGARCH) models are used to measure volatility in the study variables. Empirical findings of the study asserted that the TNR, CR, and ORR are volatile in the selected time period. Instead of stability, these rents follow an unstable path during the study period. In contrast, no volatility has been observed in NGR. Besides, the TGARCH and EGARCH approach revealed that the influence of negative shock is greater and stronger on the three volatile variables. Events such as the energy price hike, Gulf war, Asian financial crisis, the global financial crisis, and others are the events that report higher volatility. Based on the empirical findings, this study suggests price ceiling or price freezing policies, natural resources hedging, isolation of natural resources rents from external shocks to tackle volatility in natural resources rents.

COVID-19 pandemic and risk dynamics of financial markets in G7 countries

PurposeThe purpose of this study is twofold: to examine the effects of the COVID-19 pandemic on the risk dynamics of stock and bond markets in G7 countries; and to examine if the stock-bond risk dynamics can be linked to government measures to contain the pandemic.Design/methodology/approachTo examine the pandemic impact on the risk dynamics of the bond and stock markets, this study chooses G7 countries for their efficient financial market properties. This study uses standard generalized autoregressive conditional heteroskedasticity (GARCH) (1,1) and exponential GARCH (1,1) models to determine the most volatile and sensitive market, most persistent market during the crisis and the leverage effect between stock and bond markets. This study then uses a panel study to investigate whether this volatility in stock and bond markets is affected by the COVID-19 cases and various government responses (fiscal stimulus packages, monetary policy, emergency investment in health care and vaccine investment).FindingsThe findings of the study confirm that the bad news of the pandemic is causing higher volatility than good news for all seven stock markets. Canadian stock and bond markets are the most volatile, and Italian bond and stock markets are the most sensitive G7 countries. Japan has shown the highest persistence, and the stock market exhibits higher leverage than the bond market. Fiscal stimulus packages are helping to reduce bond market volatility, but none of these measures are effective in the stock market.Research limitations/implicationsThe pandemic is still spreading, and the rate at which it spreads wildly will always pose a limitation to any attempt to examine its full effect.Practical implicationsInvestigation of market volatility will help policymakers and market players formulate the best strategies to overcome and exit the crisis and plan post-pandemic solutions. It provides valuable insights for investors to rebalance their portfolios during highly volatile markets while preserving their risk appetite and investment objectives.Originality/valueThe paper provides evidence on the impact of the pandemic-induced crisis and the respective government responses on the volatility of competing capital markets (stock and bond) in countries that are considered most efficient in reflecting news.

Value at Risk with Performing Exponential Generalized Autoregressive Conditional Heteroscedasticity–Generalized Pareto Distribution

Stocks are an investment that many investors are interested in but often have a high risk. Value at Risk (VaR) is one tool that is often used in risk measurement. In general, financial data fluctuate rapidly so that the variants of the residuals are not constant or heteroscedasticity. The condition of heteroscedasticity is modeled using the ARCH/GARCH model. If there is an asymmetric effect on the data, it is modeled using an asymmetric GARCH model, namely Exponential GARCH (EGARCH). In addition to the impacts of heteroscedasticity and asymmetric events, extreme events in fat distribution tails are modeled using the Extreme Value Theory method, namely the Peaks Over Threshold method with the Generalized Pareto Distribution (GPD) approach. The data in this study is the return data of PT. Indocement Tunggal Prakarsa Tbk (INTP) for the period of March 1, 2013 - October 31, 2018. It was found that the data was heteroscedasticity, asymmetric, and there were also fat distribution tails, so it was modeled using a combination of EGARCH-GPD models. ARIMA ([2], 0, [2,13]) EGARCH (1,1) has the smallest AIC compared to other models, and then we choose it as the best model. The amount of risk with a 95% confidence level obtained with the GPD approach is 0.333% of current investment.

Study of Exchange Rate Volatility and Its Effect on Indonesian Economic Indicators With Potential Exchange Rate Crisis

Exchange rate volatility occurred when exchange rate movement was wildly fluctuating which could depict uncertainty. Since Indonesia used an open economy, exchange rate fluctuation became important to be maintained due to crisis potential. This research was conducted to analyze the effect or impact of exchange rate volatility on the Indonesian economy in general and few related case using time series analysis. ARIMA (Autoregressive Integrated Moving Average) and EGARCH (Exponential Generalized Autoregressive Conditional Heteroscedasticity) were used for measuring the volatility in the period between 1997-2021. Then, regressions were applied to analyze the impact of exchange rate volatility on few macroeconomic indicators. The result shows that exchange rate volatility yielded a significant negative effect on GDP Growth rate, export, and import. Logistic regression was used to analyze the factors that were affecting the crisis potential. The result showed only a negative GDP growth rate and high volatility that gave more risk which could lead to crisis. Therefore, it is important to keep exchange rate volatility stable.

MONETARY POLICY VOLATILITY AND PERFORMANCE OF BANKING INDUSTRY IN NIGERIA

Health volatility due to the Covid-19 pandemic presented a new-fangled trial to the banking industry with a spillover effect of monetary policy volatility, which extremely affected the performance of the banking industry in Nigeria. It has become a matter of concern to assess monetary policy volatility and performance of the banking industry in Nigeria. The paper used annual time series data that spanned the period of 2008 to 2020. The paper employed Autoregressive Distributed Lag (ARDL) and Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) as its techniques of estimation. Based on the ARDL result, it was exposed that monetary policy volatility had a negative impact on the activities of the banking industry in Nigeria within the study time. In addition, according to the EGARCH test result, the paper generalized that monetary policy volatility had constantly been accompanied by a new volatility. Therefore, as a result of the universal financial predicament experienced in 2008, this caused a higher monetary policy volatility in 2020 in the face of Covid-19. The paper observed that a rise in monetary policy volatility led to a decline in the performance of the banking industry in Nigeria within the study period, and the current monetary policy volatility led to its uncertain volatility in the period ahead. The paper recommended based on the findings that banks through the Central Bank of Nigeria should employ tactical monetary policy strategies to reduce monetary policy volatility during the Covid-19 pandemic toward enhancing the performance of Nigeria’s banking industry.

Investigating contagion effect of the recent Turkey currency crisis

This study empirically analyses the contagion effect of Turkey Lira crisis 2018 on the currencies of selected Asian (Indonesia, Malaysia, South Korea and India) and other six countries (Chile, Argentina, Mexico, Brazil, Russia and South Africa) using correlation and volatility analysis. The results of correlation analysis show that Turkey's lira bears a positive correlation with all the other select currencies in all the three periods; the whole period, the pre-crisis period and the post-crisis period. Almost all the correlation coefficients are significant at 1% or 5% level of significance across the crisis and have increased after the recent turkey lira crisis. From the results of volatility spillover analysis using exponential generalised autoregressive conditional heteroscedasticity (EGARCH) model, we infer that the Turkey currency crisis has affected the volatility of currencies of India, Brazil, Argentina & South Africa, and the effect being the least on the Indian rupee volatility while the maximum impact on the South African rand volatility.

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.