The effect of the Covid pandemic on stock market volatility: Separating initial impact from time-to-recovery

1.   Introduction

The COVID-19 pandemic has impacted economies in many different ways. One of these is the impact on stock markets. Looking across countries, a common pattern is a sudden increase in stock market volatility at the time when the pandemic took hold, followed by a gradual return to normal levels of volatility. This paper is concerned with identification and measurement of this pattern for a selection of major stock markets.

The pattern differs between different stock markets in important ways. First, the timing of the onset of the crisis appears to differ between stock markets; some experienced the volatility shock later than others. Second, the initial volatility shock and the time taken to return to normal levels also appear to differ between stock markets. This strongly suggests that some sets of investors are more sensitive than others to adverse news, and that some stock markets are better prepared than others to absorb the impact of crises such as the COVID-19 pandemic.

The purpose of this study is first to identify the date at which the pandemic took hold for each of the selected stock markets, and second to estimate the magnitude of the volatility shock, along with the "half-life" of the shock, for each stock market. This enables rankings to be drawn up according to the sensitivity of investors and the preparedness of stock markets for crises. Estimation will be performed using daily data on stock market index returns, in the framework of the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model (Bollerslev, 1986). We develop a new variant of the GARCH model that separately estimates the magnitude of the initial impact of the crisis and the speed of recovery following the initial impact. We will refer to this variant as the GARCHX-NL model.^* The profile likelihood method is used for estimation.

^*The NL suffix represents the nonlinearity of the volatility equation in the GARCHX model. See Section 2.2.2.

Many studies of the modeling of volatility in financial markets have been conducted in the framework of the GARCH model. An obvious way of allowing for the impact of a crisis such as COVID on the volatility is to include a zero-one dummy variable, covering the period of the crisis, in the conditional volatility equation of the GARCH model. When independent variables are introduced to the conditional volatility equation, the model becomes the GARCHX model. The GARCHX framework has been used in a variety of applications including the impact of market volatility on stock price volatility (Hwang and Satchell, 2005), the impact of day-of-week on electricity-price volatility (Sucarrat et al., 2016), and the impact of macroeconomic factors on food-price volatility (Apergis and Rezitis, 2011).

Studies of the impact of the COVID-19 pandemic on stock markets have been surveyed by Anggraini et al. (2022). Many researchers have already used the GARCHX approach to measure the impact of the pandemic on stock market volatility. These include Onali (2020), Yousef (2020), Kusumahadi and Permana (2021), Bora and Basistha (2021), Duttilo et al. (2021), Golder et al. (2022), Adenomon et al. (2022), Curto and Serrasqueiro (2022), and Apergis and Apergis (2022). As expected, many of these studies find that the COVID-19 pandemic had a positive impact on the volatility of stock prices or stock price indexes. International comparisons of the impact of the COVID-19 pandemic on stock markets have been made by Ledwani et al. (2021).

With the exception of Onali (2020) and Apergis and Apergis (2022), who both use number of COVID cases and number of COVID deaths as explanatory variables in the conditional volatility equation, all of the studies cited in the last paragraph simply use a dummy variable to capture the crisis, and hence they make an implicit assumption that the impact of the crisis is constant over the period of the crisis. The empirical evidence presented in Section 2 below appears to contradict this assumption, and it is for this reason that we develop a model that assumes an initial impact followed by a gradual decay. Note that our model nests the dummy variable model, so the importance of our generalization can be easily tested.

A further advantage of the GARCHX-NL model that we propose is that it provides a deterministic prediction of the time path of volatility following a crisis. This is likely to be of practical use to finance professionals since the predicted volatilities may be used as inputs in portfolio management and option pricing (Poon and Granger, 2003).

The paper is organized as follows. Section 2 presents the data used in the analysis, with the objective of conveying the key stylized facts, and then describes the GARCHX-NL model that is used in estimation. Section 3 presents results from estimation of the GARCHX-NL model on the data described in Section 2. Section 4 draws conclusions, in particular by linking the econometric results to theoretical predictions appearing in previous literature.

2.   Materials and method

2.1.   Data

We consider stock market indexes for 20 major economies (see Table 1 below). We have taken care to include emerging as well as developing economies. In Figure 1a, we present time series plots of the daily returns for each of the stock market indexes, from 11 June 2015 to 10 June 2021.^† The reason for choosing the start date in 2015 is to ensure that the data set contains a reasonably long stretch of pre-pandemic data, which is useful for identifying the "baseline" volatility process.

Table 1.  Key results from estimation of GARCHX-NL model (2), using profile likelihood method, applied to all indexes. Indexes ordered by date of onset. Date of onset estimated using procedure outlined in Section 2.2.1. Estimates of $\theta_1$ and $\theta_2$ shown with asymptotic standard errors (a.s.e.). a.s.e for $\theta_2$ obtained using (5). LR test stat (with p-value) shown for testing $H_0: \theta_2 = 0$ against $H_1: \theta_2 > 0$. LR test stat computed using (3). Final column contains estimate of half-life, obtained using (6). Maximum half-life set (arbitrarily) to 1 year.

REGION	INDEX	onset date	$\theta_1$ (a.s.e.)	$\theta_2$ (a.s.e.)	LR (p-value)	half-life
Australia	SP/ASX	24-Feb-20	4.77	4.60	36.59	0.15
			(0.485)	(0.76)	(0.00)
Germany	DAX 30	24-Feb-20	5.75	14.80	38.02	0.05
			(0.376)	(2.40)	(0.00)
Italy	FTSE MIB	24-Feb-20	4.88	8.00	38.78	0.09
			(0.366)	(1.28)	(0.00)
Brazil	BRAZIL(IBX)	26-Feb-20	5.01	12.00	58.40	0.06
			(0.479)	(1.57)	(0.00)
Indonesia	IDX	26-Feb-20	3.63	4.00	15.64	0.17
			(0.383)	(1.01)	(0.00)
Bahrain	MSCI BAHRAIN	2-Mar-20	3.74	4.40	148.69	0.16
			(0.152)	(0.36)	(0.00)
Hong Kong	HANG SENG	9-Mar-20	5.04	30.00	14.42	0.02
			(0.514)	(7.90)	(0.00)
UK	FTSE100	10-Mar-20	2.80	2.00	8.07	0.35
			(0.377)	(0.7)	(0.00)
Japan	NIKKEI 225	11-Mar-20	4.53	28.00	5.86	0.02
			(0.956)	(11.57)	(0.02)
Korea	KOSPI	11-Mar-20	1.88	1.80	5.50	0.39
			(0.336)	(0.77)	(0.02)
Taiwan	TAIEX	11-Mar-20	4.52	30.00	8.95	0.02
			(0.976)	(10.03)	(0.00)
UAE	DFM	11-Mar-20	0.44	0.80	0.26	0.87
			(0.220)	(1.56)	(0.61)
Canada	SP/TSX	17-Mar-20	1.93	1.40	1.91	0.50
			(0.464)	(1.01)	(0.17)
Malaysia	FBMKLCI	17-Mar-20	1.23	0.80	0.23	0.87
			(0.835)	(1.66)	(0.63)
USA	DOW JONES	17-Mar-20	2.79	2.40	6.06	0.29
			(0.507)	(0.98)	(0.01)
Singapore	STI	19-Mar-20	5.21	29.80	3.29	0.02
			(1.427)	(16.43)	(0.07)
Vietnam	MSCI VIETNAM	19-Mar-20	0.49	0.00	0.00	1.00
			(0.157)	-	(1.00)
Thailand	BANGKOK S.E.T	20-Mar-20	1.22	0.00	0.00	1.00
			(0.286)	-	(1.00)
India	SP BSE	24-Mar-20	0.75	0.00	0.00	1.00
			(0.196)	-	(1.00)
China	SHANGHAI (A)	No evidence of structural break

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Figure 1. 

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^†Time series plots of the indexes themselves are presented in Figure A1 of the Appendix.

The key stylized fact in which we are most interested is the sudden boost in volatility seen for the majority of the indexes in early 2020. Importantly, this sudden boost appears to occur on different dates for different indexes, and the first part of the econometric exercise will be to identify the most likely date for each index. We are interpreting this date as the time at which the COVID-19 pandemic started to have an impact on the financial market of the economy in question. Another important feature of most of the plots is that following the sudden boost, the volatility remains higher than it was before the pandemic, but appears to fall steadily toward the pre-pandemic volatility level. This feature is made even clearer in Figure 1b, in which we plot volatility over time, with volatility measured as a 20-day rolling standard deviation of returns. Our econometric model will also incorporate this feature.

Another feature of Figure 1 that informs the econometric modeling is that some of the graphs do not appear to exhibit an episode of higher volatility in 2020. One notable example is the Shanghai (A) Index, as already noted by Ledwani et al. (2021). This is interesting because it suggests that the impact of the pandemic on these financial markets was negligible.

2.2.   Econometric methodology

2.2.1.   Sup-Wald test for identifying onset of COVID period

The first task is to establish the date at which the COVID-19 pandemic started to have an impact on each stock market. For this purpose we apply a structural break test to the following version of the ARCH(1) model:

where $r_t$ is the daily return on a stock market index, defined as $r_t = ln(P_t) - ln(P_{t-1})$, with $P_t$ being the stock market index on day $t$. Equation (1) is estimated by OLS, and this is a very basic method of estimating the ARCH(1) model (see Gujarati and Porter (2009)).

The objective here is simply to identify the most likely break-point in the ARCH(1) process. Since the ARCH equation (1) has been estimated by OLS, we may follow Bai (1994) by applying a standard structural break test at every possible break-point, and then choosing the break-point giving the most significant test result. Since we use a Wald-test for structural stability testing, we refer to this procedure as the Sup-Wald test.

Figure 2 shows the Sup-Wald test applied to each return series. We see that, for nearly all of the indexes, a single break-point is clearly identified in early 2020. We will refer to this point as $t_{COVID}$, since this point will be taken to represent the time of onset of the crisis. For one index, Shanghai (A), the test statistic is never above the (size-adjusted) critical value, indicating that there is no evidence that the crisis had any impact on volatility in this stock market.

Figure 2.  The Sup-Wald test. Structural break test statistic measured on vertical axis. Horizontal line drawn at (size-adjusted) 5$\%$ critical value. Break-point identified by highest point (above size-adjusted critical value) attained by test statistic.

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2.2.2.   GARCHX-NL model

A popular way of measuring the impact of independent variables on volatility is to estimate the GARCH(1, 1) model (Bollerslev, 1986) with multiplicative heteroscedasticity.^‡ Such a model is referred to as the GARCHX model. A feature of this model is that the determinants of volatility enter the model linearly. Most of the studies cited in the fifth paragraph of Section 1 use this approach, with the independent variable in the conditional volatility equation simply being a dummy variable indicating the period of the COVID crisis.

^‡See Judge (1985) for a full explanation of multiplicative heteroscedasticity.

A complication faced here is that the specification required in the conditional volatility equation is nonlinear, and hence the model will be referred to as the GARCHX-NL model. The GARCHX-NL model is defined as follows:

where $\tau_t \equiv (t-t_{COVID})/260$ is the lapse of time, measured in years, since the structural break ($t_{COVID}$) identified using the procedure outlined in Section 2.2.1, and $\mathbb{I} (.)$ is the indicator function.

The parameters $\alpha$ and $\beta$ in model (2) are respectively the ARCH and GARCH parameters, representing the volatility structure prevailing at normal times. The parameters of central interest are $\theta_1$ and $\theta_2$: $\theta_1$ represents the initial impact of the crisis on volatility; $\theta_2$ represents the speed at which the market returns to pre-pandemic levels of volatility.

The time-path of the exponent of leading term of the conditional volatility equation (2) is illustrated in Figure 3. This graph makes it clear that (conditional on the prevailing GARCH process) the parameter $\theta_0$ represents "baseline" (i.e. pre-COVID) volatility, and that at time $t_{COVID}$, volatility jumps suddenly by an amount represented by $\theta_1$. Thereafter, volatility returns gradually toward the baseline level represented by $\theta_0$.

Figure 3.  The impact of the COVID crisis on the time-path of stock market volatility, according to the GARCHX-NL model defined in (2). $\theta_{0}$ represents the baseline (pre-COVID) volatility; $\theta_{1}$ represents the initial impact of the crisis on volatility; $\tau^h$ is the "half-life" of the shock, defined in (6) below.

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Certain special cases are of interest. First, if $\theta_1 > 0$ and $\theta_2 = 0$ in (2), this implies that the impact of the pandemic is permanent and constant, and the model is equivalent to one that simply includes, in the conditional volatility equation, a "COVID dummy" $\mathbb{I}(\tau_t > 0)$, taking the value 1 after the onset of the crisis and never reverting to 0. Second, if $\theta_1 > 0$ and $\theta_2 = \infty$ in (2), this implies that the impact of COVID is only felt on day $t_{COVID}$ and has no effect thereafter. This model is similar to an "event study" model in which the impact of COVID on volatility is captured by the presence of a dummy variable taking the value 1 on day $t_{COVID}$ only. Third, if $\theta_1 = 0$ in (2), this implies that the pandemic has no effect whatsoever on volatility. Note that in this case, the parameter $\theta_2$ is not identified and is therefore not estimated.

2.2.3.   Estimation of the GARCHX-NL model using the profile likelihood method

Estimation of the GARCHX-NL model specified in (2) is not completely straightforward. This is because, while GARCH estimation routines in some econometric software packages do include features that allow the volatility to depend on independent variables, the equation in which these variables are introduced is assumed to be linear in parameters.^§ The exponent of the leading term in the conditional volatility equation in (2) is clearly nonlinear, and hence (2) cannot be estimated directly using these routines.

^§For example, the arch command in STATA has a het(.) option, in which one or more independent variables may be introduced.

We address this problem using the profile likelihood method. This method consists of a grid search on the parameter $\theta_2$. A grid of values of $\theta_2$ is chosen including $\theta_2 = 0$. For each value of $\theta_2$ in the grid, the variable $\exp(-\theta_2 \tau_t) \mathbb{I} (\tau_t \ge 0)$ is generated, and enters the conditional volatility equation of the GARCHX model. The MLE of $\theta_2$ is the value in the grid at which the maximized log-likelihood, from estimation of the GARCHX model, is highest. Let us denote the MLE as $\hat{\theta_2}$.

Of course, we would also like to make inferences about the parameter $\theta_2$. Let the maximized log-likelihood obtained assuming a given value of $\theta_2$ be $l(\theta_2)$. Consider the likelihood ratio (LR) test for testing the null hypothesis $\theta_2 = 0$. This test statistic is given by:

The LR test statistic (3) has a $\chi^2 (1)$ distribution (asymptotically) under the null hypothesis $\theta_2 = 0$. Acceptance of this null implies that the impact of the pandemic is constant and persists indefinitely, while rejection implies that the impact of the pandemic decays over time.

An alternative test of the null hypothesis $\theta_2 = 0$ is the Wald test, carried out using the statistic:

It is well-known that the two test statistics (3) and (4) are asymptotically equivalent (Buse, 1982). This asymptotic equivalence may be exploited in order to obtain an expression for the asymptotic standard error of the MLE of $\theta_2$ in terms of the LR test statistic given in (3):

Another quantity that may be deduced from the model estimates is the "half-life" of the shock, $\tau^h$. By this, we mean the time taken (in years) for the initial shock to halve in magnitude, as illustrated in Figure 3 above. This quantity is obtained using:

2.3.   Illustration of estimation of GARCHX-NL model

Here, we illustrate the estimation procedure described in Section 2.2.3 using data on the returns of a selection of the indexes presented in Figure 1a above.

Figure 4 shows the profile likelihood, obtained using the procedure outlined in Section 2.2.3, for four of the indexes. For both the FTSE100 and the Dow-Jones, we see that the profile likelihood has an interior maximum, giving estimates of $\theta_2$ of 2.00 and 2.40 respectively. For India's BSE30 index, we see that the profile log-likelihood has a maximum at zero, meaning that the estimate of $\theta_2$ is zero, implying that volatility does not recover at all after the initial onset. For Taiwan's TAIEX index, we see that the profile log-likelihood has a maximum at a large value (possibly $\infty$), meaning that the estimate of $\theta_2$ is $\infty$, implying that volatility returns to normal levels immediately after the onset of the crisis.

Figure 4.  Profile log-likelihood against $\theta_2$ for selected Indexes.

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Estimates of the parameters of central interest are presented, for all indexes, in the next section.

3.   Results

Complete sets of results from all GARCHX-NL estimations are presented in Tables A1 and A2 in the Supplementary section. Only the key results for each index are presented here in Table 1. The indexes are ordered by the date of onset, which is estimated separately for each index using the method outlined in Section 2.2.1. It is notable that these dates are spread over the period of exactly one month, from 24 February 2020 to 24 March 2020. Also shown in Table 1 are estimates of the key parameters $\theta_1$ and $\theta_2$, along with asymptotic standard errors. The asymptotic standard error for $\theta_2$ has been obtained using (5).

The next column of Table 1 contains the LR test statistic, obtained using (3), for testing $H_0: \theta_2 = 0$ against $H_1: \theta_2 > 0$ for each index. An accompanying p-value is also shown. Note that a rejection of $H_0$ by this LR test amounts to evidence that the GARCHX-NL model (2) is statistically superior to a GARCHX model containing only a COVID dummy. This is the case for 12 of the 19 indexes. In nearly all of these 12 cases, the evidence is strong.

The final column of Table 1 contains the estimate of the half-life of the shock for each index, obtained using (6). Markets for which $\theta_2$ is estimated to be zero are (arbitrarily) assigned a half-life of one year.

We may now consider differences in impacts between stock markets. Figure 5 shows a scatterplot of initial impact ($\theta_1$) against date of onset ($t_{COVID}$). It appears that later dates of onset are associated with smaller initial impacts. Figure 6 shows a scatterplot of half-life against initial impact ($\theta_1$). Here we see a very clear negative relationship: markets with higher initial impacts tend to have shorter half-lives.

Figure 5.  Initial impact ($\theta_1$) against date of onset. Regression $R^2 = 0.47$.

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Figure 6.  Half-life (years) against initial impact ($\theta_1$). Half-life set (arbitrarily) to 1 year for indexes for which $\theta_2$ is estimated to be zero. Regression $R^2 = 0.88$.

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It is natural to ask which types of market appear in different regions of these plots. In Figure 6 we see that markets with low initial impact and long half-life tend to be emerging markets such as Vietnam, India, and Thailand. In contrast, markets with high initial impact and short half-life tend to be well-established stock markets in developed countries, such as Germany, Singapore, and Japan.

4.   Discussion

This study builds on the recent literature that tests the impact of the COVID-19 pandemic on financial market volatility. Most of the previous literature uses a dummy variable to capture the COVID period, in the context of the GARCHX model. Our model (GARCHX-NL) adds a layer to the GARCHX model, whereby the conditional volatility is assumed to jump suddenly at the onset of the crisis, and then to decay gradually toward its previous levels. To the best of our knowledge, this is the first study that decomposes the impact into two separate measures in this way. The specification of the model requires the use of the method of profile likelihood for estimation.

The first step in the estimation procedure has been to identify the date of onset of the crisis, and this was done using a structural stability testing procedure. Note that if the crisis is modeled using a single 0/1 dummy variable, an end-date for the crisis must also be assumed, but the end-date is much less clearly identifiable than the date of onset. A clear advantage of the modeling approach adopted in this paper is that there is no need to identify an end-date, since it is instead assumed that the impact of the crisis diminishes exponentially toward zero.

Another advantage of the approach adopted in this study is that the GARCHX-NL model (2) nests the more conventional GARCHX model in which the crisis is represented by a 0/1 dummy variable. A straightforward LR test has been used to test the statistical superiority of GARCHX-NL over GARCHX, and this superiority has been established for the majority of the indexes considered.

As mentioned at the outset, a yet further advantage of the proposed approach is that it leads to a deterministic prediction of the time path of volatility in the period following a crisis. This is made clear by Figure 3 above, which illustrates a typical deterministic time path of volatility. The problem of predicting volatility into the future is central to areas of finance such as portfolio management and option pricing (Poon and Granger, 2003). Having a deterministic prediction of the future path of volatility is likely to be highly useful in such applications.

We have found striking differences between the responses to the crisis in different stock markets. First, we have found that stock markets which responded to the crisis earliest, tended to have higher initial impacts. Second, we have found that markets whose initial impacts were higher tended to recover more quickly, and therefore displayed shorter "half-lives". Furthermore, stock markets with low initial impacts and long half-lives tend to be emerging markets, while those with high initial impacts and short half-lives tend to be developed economies with well-established stock-markets. These findings may be seen as building on the extant literature which explains cross-country differences in stock market volatility using variables such as the education level of investors (Xing, 2004).

Our new findings can also be linked to theories of investment. The early days of the COVID-19 pandemic was undoubtedly a period of abnomally high uncertainty. According to the theoretical model of Veronesi (1999), investors become more sensitive to news during such periods, hence increasing financial market volatility. This theory suggests that the reason why well-developed stock-markets exhibited higher initial impacts is because investors in these markets are more sensitive to news. The strong relationship between news stories relating to COVID and stock-market volatility in the USA has been quantified using text-based methods by Baker et al. (2020). However, the reason why the well-developed stock markets also appeared to recover faster is likely to be because these markets are better able to absorb the longer-term effects of a crisis. This is confirmed by the recent empirical evidence of Uddin et al. (2021), who found key country-level mitigation factors to be capitalism score, governance score, productivity score, quality of health system, and development of financial institutions index.

Use of AI tools declaration

The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.

Acknowledgments

We are very grateful to the Editor and to three anonymous reviewers for providing useful feedback on an earlier version. We are also grateful to the English Editor for improving the presentation. The work carried out in this article was not dependent on any funding sources.

Conflict of interest

All authors declare no conflicts of interest in this article.

Supplementary

Figure A1.  The stock market indexes over time. Daily data; 11 June 2015 to 10 June 2021.

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Table A1.  GARCHX-NL.

	UK	USA	Japan	Brazil	India	Italy	Singapore	Australia	Canada	Hong Kong
	FTSE100	DowJones	NIKKEI225	BRAZIL(IBX)	SP BSE	FTSE MIB	STI	SP/ASX	SP/TSX	HangSeng
main
$\gamma_1$	0.0168	-0.0286	-0.0484	-0.0532	0.0339	-0.0780**	0.0554	-0.0197	0.0485	-0.00217
	(0.0293)	(0.0298)	(0.0283)	(0.0294)	(0.0301)	(0.0274)	(0.0297)	(0.0262)	(0.0305)	(0.0269)
$\gamma_0$	0.000256	0.000904***	0.000640*	0.000971**	0.000769***	0.000541*	0.000181	0.000396*	0.000482***	0.000316
	(0.0002)	(0.0002)	(0.0003)	(0.0003)	(0.0002)	(0.0003)	(0.0002)	(0.0002)	(0.0001)	(0.0003)
HET
$\theta_1$	2.803***	2.791***	4.529***	5.008***	0.751***	4.879***	5.206***	4.767***	1.930***	5.041***
	(0.3771)	(0.5073)	(0.9561)	(0.4790)	(0.1958)	(0.3661)	(1.4269)	(0.4854)	(0.4637)	(0.5143)
$\theta_2$	2.00***	2.40**	28.00*	12.00***	0.00	8.00***	29.80	4.60***	1.40	30.00***
	(0.7039)	(0.9751)	(11.5687)	(1.5703)	-	(1.2846)	(16.4343)	(0.7605)	(1.0130)	(7.9008)
$\theta_0$	-12.00***	-12.35***	-11.72***	-11.24***	-12.92***	-11.88***	-12.42***	-13.12***	-13.12***	-13.29***
	(0.1708)	(0.1259)	(0.1483)	(0.1989)	(0.2440)	(0.1816)	(0.1920)	(0.2281)	(0.2091)	(0.2474)
ARCH
$\alpha$	0.158***	0.228***	0.127***	0.0606***	0.100***	0.116***	0.124***	0.0966***	0.213***	0.0372***
	(0.0173)	(0.0209)	(0.0124)	(0.0121)	(0.0103)	(0.0114)	(0.0147)	(0.0108)	(0.0198)	(0.0056)
$\beta$	0.760***	0.727***	0.819***	0.862***	0.873***	0.841***	0.817***	0.871***	0.758***	0.948***
	(0.0271)	(0.0227)	(0.0171)	(0.0226)	(0.0153)	(0.0162)	(0.0225)	(0.0137)	(0.0242)	(0.0068)
N	1564	1564	1564	1564	1564	1564	1564	1564	1564	1564

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Table A2.  GARCHX-NL.

	Germany	Korea	Vietnam	Thailand	Malaysia	Indonesia	Taiwan	UAE	Bahrain
	DAX30	KOSPI	MSCI VIETNAM	BANGKOK SET	FBMKLCI	IDX	TAIEX	DFM	MSCI BAHRAIN
main
$\gamma_1$	-0.0187	-0.0000595	0.0526	0.0463	0.0301	0.0183	0.0189	0.114***	0.0143
	(0.0257)	(0.0305)	(0.0282)	(0.0281)	(0.0262)	(0.0273)	(0.0269)	(0.0291)	(0.0328)
$\gamma_0$	0.000530*	0.000375	0.000404	0.000197	-0.0000516	0.000321	0.000653**	-0.00000906	0.000168
	(0.0002)	(0.0002)	(0.0003)	(0.0002)	(0.0001)	(0.0002)	(0.0002)	(0.0002)	(0.0003)
HET
$\theta_1$	5.748***	1.878***	0.486**	1.216***	1.227	3.633***	4.518***	0.445*	3.740***
	(0.3757)	(0.3360)	(0.1568)	(0.2857)	(0.8352)	(0.3832)	(0.9760)	(0.2203)	(0.1518)
$\theta_2$	14.80***	1.80*	0.00	0.00	0.80	4.00***	30.00***	0.80	4.40***
	(2.4002)	(0.7675)	-	-	(1.6609)	(1.0114)	(10.0268)	(1.5629)	(0.3608)
$\theta_0$	-13.07***	-12.15***	-12.21***	-14.30***	-14.77***	-12.35***	-11.95***	-11.94***	-10.53***
	(0.1898)	(0.1967)	(0.1462)	(0.2176)	(0.3523)	(0.1885)	(0.1439)	(0.1540)	(0.2311)
ARCH
$\alpha$	0.0561***	0.106***	0.110***	0.0969***	0.0758***	0.0973***	0.0810***	0.135***	0.0614***
	(0.0072)	(0.0142)	(0.0130)	(0.0083)	(0.0076)	(0.0128)	(0.0076)	(0.0120)	(0.0094)
$\beta$	0.923***	0.821***	0.850***	0.900***	0.917***	0.843***	0.835***	0.799***	0.669***
	(0.0091)	(0.0230)	(0.0141)	(0.0078)	(0.0089)	(0.0195)	(0.0184)	(0.0188)	(0.0701)
N	1564	1564	1564	1564	1564	1564	1564	1564	1564

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