COVID-19 pandemic & financial market volatility: Evidence from GARCH models

Khan, Maaz; Kayani, Umar Nawaz; Khan, Mrestyal; Mughal, Khurrum Shahzad; Haseeb, Mohammad Article COVID-19 pandemic & financial market volatility: Evidence from GARCH models Journal of Risk and Financial Management Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Khan, Maaz; Kayani, Umar Nawaz; Khan, Mrestyal; Mughal, Khurrum Shahzad; Haseeb, Mohammad (2023) : COVID-19 pandemic & financial market volatility: Evidence from GARCH models, Journal of Risk and Financial Management, ISSN 1911-8074, MDPI, Basel, Vol. 16, Iss. 1, pp. 1-20, https://doi.org/10.3390/jrfm16010050 This Version is available at: https://hdl.handle.net/10419/275146 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Citation: Khan, Maaz, Umar Nawaz Kayani, Mrestyal Khan, Khurrum Shahzad Mughal, and Mohammad Haseeb. 2023. COVID-19 Pandemic & Financial Market Volatility; Evidence from GARCH Models. Journal of Risk and Financial Management 16: 50. https://doi.org/10.3390/ jrfm16010050 Academic Editors: Robert Brooks and Shigeyuki Hamori Received: 5 October 2022 Revised: 6 January 2023 Accepted: 10 January 2023 Published: 13 January 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Journal of Risk and Financial Management Article COVID-19 Pandemic & Financial Market Volatility; Evidence from GARCH Models Maaz Khan 1,* , Umar Nawaz Kayani 2, Mrestyal Khan 3, Khurrum Shahzad Mughal 4 and Mohammad Haseeb 5 1Department of Management Sciences, COMSATS University Islamabad, Islamabad 45550, Pakistan 2College of Business, Al Ain University, Abu Dhabi P.O. Box 122612, United Arab Emirates 3Department of Management Sciences, Balochistan University of Information Technology, Engineering & Management Sciences (BUITEMS), Quetta 87300, Pakistan 4Islamabad Policy Research Institute—IPRI, Islamabad 45710, Pakistan 5China Institute of Development Strategy and Planning, and Center for Industrial Economics, Wuhan University, Wuhan 430072, China *Correspondence: [email protected] Abstract: Across the globe, COVID-19 has disrupted the financial markets, making them more volatile. Thus, this paper examines the market volatility and asymmetric behavior of Bitcoin, EUR, S&P 500 index, Gold, Crude Oil, and Sugar during the COVID-19 pandemic. We applied the GARCH (1, 1), GJR-GARCH (1, 1), and EGARCH (1, 1) econometric models on the daily time series returns data ranging from 27 November 2018 to 15 June 2021. The empirical findings show a high level of volatility persistence in all the financial markets during the COVID-19 pandemic. Moreover, the Crude Oil and S&P 500 index shows significant positive asymmetric behavior during the pandemic. Apart from this, the results also reveal that EGARCH is the most appropriate model to capture the volatilities of the financial markets before the COVID-19 pandemic, whereas during the COVID-19 period and for the whole period, each GARCH family evenly models the volatile behavior of the six financial markets. This study provides financial investors and policymakers with useful insight into adopting effective strategies for constructing portfolios during crises in the future. Keywords: COVID-19; financial markets; GARCH; GJR-GARCH; EGARCH; volatility 1. Introduction The COVID-19 pandemic has a significant influence on the global economy (Maital and Barzani 2020;McKibbin and Fernando 2020;Ozili and Arun 2020). Numerous countries have implemented strict policies on international travel, such as the adoption of quarantine, and several cultural festivals and sports events have been canceled, which limited economic activities across the globe. The evidence shows that the long-term impact of COVID-19 on economies will be high in terms of business failure and unemployment (Amankwah-Amoah et al. 2021;Holder et al. 2021;Montenovo et al. 2020) since the volatility and connectedness of financial markets have increased due to the COVID-19 pandemic (Aslam et al. 2020b; Chaudhary et al. 2020;Corbet et al. 2021;Khan and Khan 2021;Sadiq et al. 2021). The speculative bets in the financial markets by international investors generates an influx of financial transactions in the financial markets, creating an extreme level of volatile behavior in the prices of financial assets. A speculative bubble can be observed in the financial market in the last few years. The multiple crashes and high level of fluctuation in financial returns during the pandemic has a negative impact on international investment. These unexpected crashes and fluctuations have become a major problem for financial investors across the world. Furthermore, Zhang and Hamori (2021) concluded that COVID-19 has an adverse effect on the performance of the financial markets, with investor behavior also affected due to the fear and risk associated with COVID-19 (Budiarso et al. 2020;Ortmann J. Risk Financial Manag. 2023,16, 50. https://doi.org/10.3390/jrfm16010050 https://www.mdpi.com/journal/jrfm J. Risk Financial Manag. 2023,16, 50 2 of 20 et al. 2020). We explore the financial volatility of all six major financial markets by using one financial asset from each of the markets (cryptocurrency, exchange rate, stock index, metal market, oil, and agriculture) during the COVID-19 pandemic. The sample of financial assets used in the study are prominent in terms of market capitalization and have top trading representation in their respective financial markets. In financial markets, there exists asymmetry in the return and volatility relationship. Under the black swan events hitting the financial markets, such as the COVID-19 pandemic, it is vital to analyze the dynamics of the volatility across the financial markets for the sake of investors and policymakers. Moreover, financial markets reflect a complex and dynamic asymmetric dependence (Baruník et al. 2016), with tail dependence across the equity sectors (Aslam et al. 2022). Furthermore, during the bearish trend in the financial markets, the correlation across the returns is stronger than the bullish trend. As a result of a stronger reaction to negative shocks, price volatility becomes asymmetric, reducing the benefits of diversification (Amonlirdviman and Carvalho 2010). Considering the COVID-19 pandemic, studies have investigated the impact of this contagious disease on the financial markets. Empirical evidence suggests that when compared to other crises, COVID-19 has had devastating effects on the financial markets (Baker et al. 2020;Umar et al. 2021;Zhang et al. 2020). In particular, this pandemic caused severe losses to the stock markets (Khan et al. 2021;Pavlyshenko 2020;Topcu and Gulal 2020;Umar et al. 2021). Furthermore, Al-Awadhi et al. (2020) found that all companies’ stocks in China reacted negatively to both the infected cases and deaths per day due to COVID-19. Similarly, Alfaro et al. (2020) showed that COVID-19 had a significant negative impact on the returns of US stock. Using GARCH family models, Osagie Adenomon et al. (2020) reported that COVID-19 negatively affected the Nigerian stock market returns. Additionally, Zhang et al. (2020), found that COVID-19 had significant negative effects on the equity markets of Singapore, Japan, and Korea, along with the 10 other stock markets, having the highest number of infected cases in March 2020. Besides, Liu et al. (2020) and He et al. (2020) investigated the effects of COVID-19 on stock markets globally and reported that returns of these stock markets gave negative returns during the COVID-19 pandemic. Thus, the drastic effects of COVID-19 on financial markets have caused economic policymakers across the world to enact prohibitions to minimize market losses and reduce uncertainty (Kodres 2020). The measurement of volatility has significant importance in economic and financial models. The estimation of financial risk is extremely critical in the financial markets. For example, financial stocks in the returns are highly dependent on the behavior of stock market volatility. Therefore, if we are able to estimate the market volatility, then we can also identify the asymmetric behavior in the financial retunes. In addition, the volatility in financial markets is highly connected to investment risk. Most of the portfolio allocations are based on the concept of volatility, such as the Markowitz mean-variance framework. Prior evidence also suggests that economic factors have a strong contribution to financial market volatility. For example, it is observed that the increase in the interest rate by the central bank has a strong impact on the financial market volatility behavior (Adrian et al. 2022). It is also reported that emerging markets across the globe are facing a high level of risks, such as high volatility in the commodity markets and a high level of inflation. Therefore, in this research paper, we examine the different aspects of volatility in the financial markets. The finding of the study reveals that a high level of volatility behavior can be observed at the beginning COVID-19 pandemic. Financial time series data have a few characteristics that separate them from normal time series data. Researchers have previously recommended that the volatility of the time series returns is highly related to market uncertainty (Bali and Zhou 2016;Connolly et al. 2005). Hence, volatility is among the key parameters in most investment decisions. Volatility is defined as the best risk indicator for the unfailing forecasting of returns in the financial markets (Green and Figlewski 1999). Also, volatility refers to the magnitude of the uncertainty related to the changes in an asset’s price. Higher volatility shows that J. Risk Financial Manag. 2023,16, 50 3 of 20 an asset’s price can potentially be spread out over an extensive range of values. In other words, the asset price can vary dramatically over the short term in either direction. IN contrast, lower volatility reflects that the asset’s price does not vary dramatically and tends to be more stable. Higher volatility indicates a greater probability of a bearish trend in the market, whereas lower volatility is linked with increased chances of a bullish trend in the market (Ang and Liu 2007). Thus, the analysis of financial asset returns is different from the returns of other classes of assets, i.e., volatility clusters, the “fat-tail” phenomena, and the leverage effect. Thus, during periods of a financial crisis, the volatility of the returns cannot be modeled by methods based on the assumption of normal distributions. As a result, dynamic volatility models are required (Rastogi 2014). When modeling time-varying volatility, Engle (1982) proposed the autoregressive conditional heteroscedasticity (ARCH) model. Later, in order to incorporate the limitations of the ARCH model, Bollerslev (1986) came up with a generalized autoregressive conditional heteroskedasticity (GARCH) model. The GARCH models have regularly been used in the financial literature, with the reason being their ability to give the most accurate results; therefore, the GARCH family of models has importantly become the standard methodology for modeling volatility in financial time series data (Brooks and Rew 2002). Thus, keeping in view the GARCH families, this study applied three different GARCH family models, namely GARCH (1, 1), GJR-GARCH (1, 1), and E-GARCH (1, 1), to identify the best-fitted model that captures the volatilities of the six representative assets of the financial markets and the effect of the COVID-19 outbreak on them. However, until now, there are very limited studies that investigate market volatility based on different GARCH family models, particularly during the COVID-19 pandemic. These alternative models used in this research paper have their own contribution to the existing literature. The GJR-GARCH model is based on the indicator function, which allows the model to react more toward negative shocks. Furthermore, the most significant advantage of the EGARCH model is its logarithmic specification, which enables the positive constraints among the parameters to be relaxed. Moreover, the EGARCH model also has a significant advantage since it is considered to be the most appropriate model for capturing volatility persistence shocks in a financial series. Moreover, this research paper used AIC to evaluate the most superior model for capturing the volatility in all six financial markets. The findings of this paper are compared over three different periods, i.e., the pre-COVID period, the COVID period, and the whole period. The results of our study indicate that the performance of the GARCH models is dependent upon the time period. Generally, the overall analysis showed that the asymmetric GARCH models are the best-fitted model for capturing market volatility in the financial time series. The results show that the EGARCH model is the best performing GARCH model for Bitcoin and EUR, while the GJR-GARCH model shows better performance in the volatility measurement of the S&P 500 index and Crude Oil. This study is a unique contribution to the existing literature in distinct ways. Firstly, this paper investigated the performance of the volatility in the financial returns of all six major financial markets (Bitcoin, EUR, S&P 500, Gold, Crude Oil, and Sugar) during the period of the COVID-19 pandemic by applying the three most effective GARCH family models, known as GARCH (1, 1), GJR-GARCH (1, 1), and EGARCH (1, 1). Secondly, our findings show evidence of volatility clustering, leptokurtic phenomena, and leverage effects in financial returns of all financial markets during the COVID-19 pandemic. International investors have been using different instruments and strategies to invest in the financial markets since the COVID-19 pandemic. Therefore, the findings of the study provide detailed information for international investors to address their strategic requirements in terms of investing in the financial markets. 2. Materials and Methods 2.1. Data We used six financial assets, i.e., one from each financial market based on their market capitalization (cryptocurrency, exchange rate, stock index, metal, oil, and agriculture). The J. Risk Financial Manag. 2023,16, 50 4 of 20 financial commodities for metal, crude oil, and agriculture (Gold, Crude Oil, and Sugar) were collected based on real-time commodity future prices. The dataset of daily closing prices for this study was downloaded from investing.com over the period of 27 November 2018 to 15 June 2021, with a daily frequency for total observations of 650. The reason for choosing this data sample period was that on 11 March 2020, the World Health Organization (WHO) declared COVID-19 as a ‘global pandemic’. Therefore, we divided our data set into three periods: The whole period, before COVID-19 period, and during COVID-19 period. Before the COVID-19 period starts from 27 November 2018 to 10 March 2021. In contrast, the during COVID-19 period starts from 11 March 2020 to 15 June 23 2021, with equal observations (325) in each period. Furthermore, the study used daily data due to the fact that they are superior for short-term econometric modeling. Additionally, daily data are quicker at reacting to level shifts and changes in trends, as the data are modeled daily vs. week/month to observe the new data. The daily returns are calculated via Equation (1). Rt=ln(Pt/Pt−1)(1) where financial returns of the markets are denoted by Rt at time t . Pt and Pt−1 represent the current price and previous day price, respectively. Primarily, there are three measures of volatility, namely the standard deviation, skewness, and kurtosis. Among them, the standard deviation is the most used; however, it is based on the unrealistic assumption that returns follow the pattern of a normal distribution. Meanwhile, skewness focuses on the extremes in the data rather than incorporating the mean returns (Chang et al. 2013). Another volatility measure is known as ‘Kurtosis’, which also deals with the extremes in the dataset (Mei et al. 2017). However, an econometric test called Jarque-Bera is used to detect the normality in the data, i.e., if its value is different from zero, then this refers to the absence of the normal distribution in the dataset (Thadewald and Büning 2007). Summary statistics of financial returns are represented in Table 1, which includes the measures of central tendency. Moreover, we adopted the Jarque-Bera test to examine the goodness of fit for the distribution of the returns. It can be seen that the standard deviation of financial returns increased during the COVID-19 pandemic. Moreover, Crude Oil exhibits the highest market risk with an SD value of 0.058, followed by Bitcoin with a value of 0.049, during the COVID-19 period. However, Bitcoin is regarded as the riskiest among the set of financial assets, with an SD value of 0.042, followed by Crude Oil (0.028). The kurtosis coefficient of all the financial assets returns is greater than 3, except for Sugar for the whole period and during the COVID-19 period, which indicates fat-tail phenomena in the financial markets. Furthermore, the statistics extracted from the Jarque-Bera test prove that the returns of all six financial assets follow the asymmetric distribution in all three selected periods. Table 2illustrates the Augmented Dickey–Fuller (ADF) test results; it can be seen that the ADF values for each of the assets under observation are significant at a 1% critical level. Thus, the stationary characteristics in the returns series of the selected assets confirmed and rejected the null hypothesis statement of the presence of unit root. J. Risk Financial Manag. 2023,16, 50 5 of 20 Table 1. Summary Statistics for the selected financial assets. Particulars Bitcoin EUR S&P 500 Gold Crude Oil Sugar Whole Period Mean 0.003875 0.000103 0.000712 0.000561 0.000503 0.000512181 Standard Deviation 0.046004 0.003986 0.015302 0.01076 0.046245 0.017879922 Kurtosis 5.782102 4.008026 16.1689 5.736385 47.81848 1.605894798 Skewness −0.379280 −0.385170 −1.03143 −0.15575 −2.74082 0.10688875 Range 0.518336 0.042611 0.217335 0.10748 0.891307 0.155743422 Minimum −0.315290 −0.028140 −0.12765 −0.05121 −0.57167 −0.078285363 Maximum 0.203046 0.014467 0.089683 0.056266 0.319634 0.077458059 Jarque-Bera Test 904.27 442.44 7078.9 877.35 61768 69.216 Count 650 650 650 650 650 650 Before COVID-19 Mean 0.002273 0.000016 0.000231 0.000793 −0.00125 0.00002700 Standard Deviation 0.042580 0.003403 0.011625 0.008599 0.028384 0.01546058 Kurtosis 3.685524 1.655074 9.873348 9.734605 31.4296 2.55831721 Skewness 0.297774 0.294543 −0.966510 0.145929 −2.80747 0.48522149 Range 0.362072 0.026953 0.127414 0.103186 0.41915 0.13021202 Minimum −0.159030 −0.01261 −0.079010 −0.04877 −0.28221 −0.05275396 Maximum 0.203046 0.014345 0.048403 0.054414 0.136944 0.07745805 Jarque-Bera Test 181.3 39.815 1325.2 1240.6 13378 97.32 Count 325 325 325 325 325 325 During COVID-19 Mean 0.005478 0.00019 0.001192 0.00033 0.002259 0.00099736 Standard Deviation 0.049205 0.004498 0.01826 0.012564 0.058924 0.02002169 Kurtosis 6.920719 4.253854 14.05538 3.665246 34.35576 0.95215866 Skewness −0.84048 −0.69099 −1.01749 −0.21382 −2.41754 −0.09999114 Range 0.506817 0.042611 0.217335 0.10748 0.891307 0.14083676 Minimum −0.31529 −0.02814 −0.12765 −0.05121 −0.57167 −0.07828536 Maximum 0.191527 0.014467 0.089683 0.056266 0.319634 0.06255140 Jarque-Bera Test 663.4 261.13 2642.5 177.05 15794 11.978 Count 325 325 325 325 325 325 Table 2. Augmented Dickey–Fuller test results for the selected financial assets. Particulars BTC EUR S&P 500 Gold Crude Oil Sugar ADF Value −17.8 *** −16.68 *** −17.765 *** −18.078 *** −19.99 *** −17.373 *** Probability Value 0.01 0.01 0.01 0.01 0.01 0.01 Note: *** shows the 1% significance level. Figures 1and 2show the price trends and return fluctuations of the financial markets. An extensive decline has been observed in the price of the S&P 500 index, Crude Oil, and Sugar in March 2020. Additionally, the price of Bitcoin experienced a massive shock in May 2021. The returns graphs also show a high level of fluctuations at the beginning of the COVID-19 pandemic. Bitcoin and Crude Oil show a high level of volatility during COVID19, ranging from − 0.31 to 0.19 and − 0.57 to 0.31, respectively. Moreover, the presence of volatility clustering can be seen in the returns graphs of all the financial markets. J. Risk Financial Manag. 2023,16, 50 6 of 20 J. Risk Financial Manag. 2023, 16, x FOR PEER REVIEW 6 of 21 Figure 1. Price trends in the financial markets over the period of 27 November 2018 to 15 June 2021. . Figure 2. Returns fluctuations in the financial markets over the period of 27 November 2018 to 15 June 2021. 2.2. GARCH Model The financial time series shows a period of low-level volatility, which is followed by a period of high-level volatility, which is called volatility clustering. ARCH and GARCH Figure 1. Price trends in the financial markets over the period of 27 November 2018 to 15 June 2021. J. Risk Financial Manag. 2023, 16, x FOR PEER REVIEW 6 of 21 Figure 1. Price trends in the financial markets over the period of 27 November 2018 to 15 June 2021. . Figure 2. Returns fluctuations in the financial markets over the period of 27 November 2018 to 15 June 2021. 2.2. GARCH Model The financial time series shows a period of low-level volatility, which is followed by a period of high-level volatility, which is called volatility clustering. ARCH and GARCH Figure 2. Returns fluctuations in the financial markets over the period of 27 November 2018 to 15 June 2021. 2.2. GARCH Model The financial time series shows a period of low-level volatility, which is followed by a period of high-level volatility, which is called volatility clustering. ARCH and GARCH are the most common models adopted to model the volatility of both economic and financial J. Risk Financial Manag. 2023,16, 50 7 of 20 time series. The GARCH model was proposed by Bollerslev (1986) and is an extension of the ARCH to model for conditional variance. The GARCH (p, q) model is represented as σ2 t=ω+ p ∑ i=1 αiµ2 t+ q ∑ j=1 βjσ2 t−j(2) where the parameters of the model are denoted by ω,αi, and βj. The GARCH family has the ability to account for dynamic volatility phenomena and volatility clustering in the modeling of financial returns volatility. Therefore, one of the models chosen is known as the GARCH (1, 1) model. Karmakar (2005) recommends GARCH (1, 1) to model the conditional volatility of market returns. Thus, the mathematical illustration of GARCH (1, 1) is given in Equation (3): σ2 t=ω+αµ2 t−1+βσ2 t−1(3) 2.3. GJR-GARCH Model The GJR-GARCH model is applied to financial returns to examine the asymmetric behavior of financial market returns. The model assumes that investor reaction toward negative returns has more concern when compared to positive financial returns, which results in the leverage effect. The GJR-GARCH (1, 1) model equation is computed as follows: σ2 t=ω+α1u2 t−1+βiσ2 t−1+γiIt−1u2 t−1(4) The symbol It−1in the equation above is the dummy variable: It−1=1when µt−1<0shows postive shocks 0when µt−1≥0shows negative shocks where the symbol σ2 t refers to the conditional variance, ω is the constant term, u2 t−1 and σ2 t−1 represent the return square at time t− 1, and conditional variance at time t− 1. γ refers to the leverage effect coefficient. 2.4. EGARCH Model The exponential GARCH (EGARCH) model is proposed by Nelson (1991) to accommodate the asymmetry in the basic GARCH model. The EGARCH model has the ability to account for more lags in conditional variance. The mathematical equation of the EGARCH (1, 1) model is computed as follows: log ht=(ω−1)+α|ηt−1|+γηt−1+βlog ht−1(5) where log ht=Eε2 tIt−1 , α , β , and γ are the parameters for the estimation of the model. There is no restriction with respect to the model parameters because the EGARCH model is based on log variance. Furthermore, investors are more reactive toward bad news than good news. Hence, it will have a strong impact on the returns volatility, and the expected value for the γwould be negative. 3. Results The empirical results with respect to the different GARCH models for the three selected periods (before and during the COVID-19 pandemic and the whole period) are illustrated in Tables 3–5, respectively. As per Table 3, the Akaike information criteria (AIC) values for each of the six financial assets suggest that E-GARCH (1, 1), in comparison with the other GARCH family models, is the best-fitted model in terms of modeling the returns volatilities of BTC, EUR, S&P 500, Gold, Crude Oil, and Sugar before the COVID-19 pandemic. The volatility among all of the six financial market retunes is extremely high during the COVID19 pandemic, as shown in Appendix A. J. Risk Financial Manag. 2023,16, 50 8 of 20 Table 3. Empirical results based on the GARCH models before the COVID-19 Pandemic (27 November 2018 to 10 March 2020). Asset Class Model µ ω α (ARCH) β(GARCH) α+β γ (Gamma) Log Likelihood AIC BTC GARCH (1, 1) 0.001575 0.000062 0.124018 * 0.874982 *** 0.999 - 619.8894 −3.7778 GJR-GARCH (1, 1) 0.001534 0.000054 0.143439 * 0.887696 *** 1.031135 −0.061479 620.1043 −3.7729 EGARCH (1, 1) 0.001244 −0.174239 * 0.036888 0.972107 *** 1.008995 0.258452 *** 624.1617 −3.7979 EUR/USD GARCH (1, 1) −0.000093 0.000001 0.076241 0.845516 *** 0.921757 - 1398.076 −8.5666 GJR-GARCH (1, 1) 0.00003 0.000001 0.118079 ** 0.894921 *** 1.013 −0.114815 1398.97 −8.566 EGARCH (1, 1) 0.000001 −1.058863 *** 0.098288 ** 0.906961 *** 1.005249 0.116547 *** 1399.502 −8.5692 S&P 500 GARCH (1, 1) 0.001054 0.000004 0.247109 *** 0.72983 *** 0.976939 - 1104.323 −6.7589 GJR-GARCH (1, 1) 0.000627 0.000004 *** 0 0.76639 *** 0.76639 0.37726 *** 1115.677 −6.8226 EGARCH (1, 1) 0.000445 −0.575678 *** −0.310019 *** 0.940752 *** 0.630733 0.095304 *** 1120.224 −6.8506 Gold GARCH (1, 1) 0.000738 0 0.002481 0.99647 *** 0.998951 - 1143.298 −6.9988 GJR-GARCH (1, 1) 0.000776 0 0.009621 0.999803 *** 1.009424 −0.021082 *** 1143.438 −6.9935 EGARCH (1, 1) 0.000563 −3.918943 *** −0.057158 0.592084 *** 0.534926 0.412796 *** 1146.25 −7.0108 Crude Oil GARCH (1, 1) −0.000072 0.000043 0.122254* 0.827323 *** 0.949577 - 790.1403 −4.8255 GJR-GARCH (1, 1) −0.000989 0.000015 *** 0 0.919419 *** 0.919419 0.130378 *** 795.7955 −4.8541 EGARCH (1, 1) −0.001059 −0.178794 *** −0.14327*** 0.975897 *** 0.832627 0.030163 ** 797.5716 −4.8651 Sugar GARCH (1, 1) −0.00005 0 0 0.999 *** 0.999 - 906.4832 −5.5414 GJR-GARCH (1, 1) −0.000144 0.000052 0 0.678175 *** 0.678175 0.234051 * 911.2845 −5.5648 EGARCH (1, 1) −0.00019 −1.69632 * −0.12458 * 0.79802 *** 0.67344 0.22667 * 911.3619 −5.5653 Note: *** refers to 1% significance level, ** refers to 5% significance level, and * refers to 10% significance level. Table 4. Empirical results based on the GARCH models during the COVID-19 Pandemic (11 March 2020 to 15 June 2021). Asset Class Model µ ω α (ARCH) β(GARCH) α+β γ (Gamma) Log Likelihood AIC BTC GARCH (1, 1) 0.005133 0.000046 0.086228 *** 0.912772 *** 0.999 - 575.4589 −3.5044 GJR-GARCH (1, 1) 0.005136 0.000036 0.096668 ** 0.919377 *** 1.016045 −0.033637 575.6774 −3.4996 EGARCH (1, 1) 0.00523 −0.067 0.035923 0.98845 *** 1.024373 0.191335 *** 577.3427 −3.5098 EUR/USD GARCH (1, 1) 0.000215 0 0.009999 0.986357 *** 0.996356 - 1309.744 −8.023 GJR-GARCH (1, 1) 0.000178 0 0.002145 0.987274 *** 0.989419 0.012225 1310.42 −8.021 EGARCH (1, 1) 0.000248 −0.727561 *** −0.023663 0.933762 *** 0.910099 0.136151 *** 1311.029 −8.0248 S&P 500 GARCH (1, 1) 0.001318 0.000007 0.21278 *** 0.754481 *** 0.967261 - 993.6005 −6.0775 GJR-GARCH (1, 1) 0.001023 0.000008 0.102173 * 0.765049 *** 0.867222 0.19395 ** 995.3024 −6.0819 EGARCH (1, 1) 0.000802 −0.423212 ** −0.104427 ** 0.952725 *** 0.848298 0.367853 *** 993.2619 −6.0693 Gold GARCH (1, 1) 0.000468 0 0.021306 0.973694 *** 0.995 - 998.6812 −6.1088 GJR-GARCH (1, 1) 0.000459 0 0.012131 0.977937 *** 0.990068 0.011201 998.8752 −6.1038 EGARCH (1, 1) 0.000395 −0.300879 *** −0.017036 0.966609 *** 0.949573 0.138397 998.9916 −6.1046 Crude Oil GARCH (1, 1) 0.002534 0.000037 * 0.21892 *** 0.762427 *** 0.981347 - 705.1272 −4.3023 GJR-GARCH (1, 1) 0.001641 0.000033 *** 0.000142 0.815486 *** 0.815628 0.296711 *** 711.4222 −4.3349 EGARCH (1, 1) 0.001699 −0.220348 *** −0.177449 *** 0.970494 *** 0.793045 0.250228 *** 710.1545 −4.3271 Sugar GARCH (1, 1) 0.001186 0.000108 0.117035 0.603234 * 0.720269 - 818.7832 −5.0017 GJR-GARCH (1, 1) 0.001087 0.000008 *** 0.000002 0.969072 *** 0.969074 0.018919 815.9888 −4.9784 EGARCH (1, 1) 0.001229 −1.745254 0.040641 0.778879 * 0.81952 0.207247 * 818.2776 −4.9925 Note: *** refers to 1% significance level, ** refers to 5% significance level, and * refers the 10% significance level. Furthermore, the parameters of the E-GARCH (1, 1) model show that each of the financial market’s representatives exhibit a long-term memory effect and an asymmetric effect at different significance levels. With respect to the EGARCH model, the finding confirms that the financial markets show significant asymmetric behavior (except for the gold market) during the COVID-19 pandemic. However, the leverage effect was observed in the gold commodity before the COVID-19 pandemic, with a leverage coefficient of 0.41. Moreover, BTC shows the highest volatility persistence (β=0.98) , followed by crude oil (β=0.97) during the pandemic. The gold commodity also shows higher volatility persistence (β=0.96) during COVID-19 when compared to before the pandemic J. Risk Financial Manag. 2023,16, 50 15 of 20 J. Risk Financial Manag. 2023, 16, x FOR PEER REVIEW 16 of 21 Figure A4. Volatility in Gold time series. Figure A4. Volatility in Gold time series. J. Risk Financial Manag. 2023,16, 50 16 of 20 J. 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