key: cord-1040238-a5p6z3dw
authors: Hussain, Saiful Izzuan; Nur-Firyal, R.; Ruza, Nadiah
title: Linkage transitions between oil and the stock markets of countries with the highest COVID-19 cases
date: 2021-12-02
journal: nan
DOI: 10.1016/j.jcomm.2021.100236
sha: 05d73fde5839490b4288f0c924a8a7c058b074e8
doc_id: 1040238
cord_uid: a5p6z3dw

This paper employed dynamic copulas and Extreme Value Theory (EVT) to analyze the linkages between oil and the stock market of countries with the highest number of COVID-19 cases. Many papers have reported small but significant negative dependence between oil and the markets before the pandemic. This work enhances the understanding of these links by exploring the tail behavior. There are many extreme returns during these periods. Integration between copula with EVT does help to understand these extreme returns better. The linkages for an overall dependence structure began to decrease dramatically and volatile after the pandemic outbreak. Lower dependence for most pairs seems to be stronger most of the time during COVID-19. The research results have possible effects on portfolio and risk management and provide insights that could be used to assess the long- and short-term effects of the pandemic.

The new pandemic crisis called coronavirus, or COVID-19, was first detected at the end of December 2019 in Wuhan, China, and has spread rapidly across the world. As of December 2020 it has infected more than 75 million people in over 200 different countries, as reported by the World Health Organization (WHO) (WHO, 2020) . The COVID-19 pandemic which is a rare event has had a major effect not only on the global economy and capital markets but also prompted a range of unparalleled government actions. Their effects on international financial markets during this period remains largely unexplored as people does not expect the pandemic to be a long term effect. The economy was not only affected because of government interventions, but also people behaviour due to less consumption and work during the pandemic period (Goldstein et al 2021) . This will affect the entire economic system and the magnitude of the effects still need to study. This article attempts to, at least to some extent, fill this gap by focusing on one of the main elements of global financial market instability: the interdependence between financial assets and diversification. The linkages are the dominant consideration of financial markets during turbulence. There have also been several efforts to examine and understand the relationship between the coronavirus crisis and market volatility, especially stock markets, which are normally associated with countries' economies (Baek et al. 2020; Baker et al. 2020; Chaudhary et al. 2020) .

Theoretically, the pandemic crisis could lead to market instability around the world. The pandemic could affect international markets and cause asset prices to fall across markets because of the loss of confidence. The reactions of the stock market to this pandemic are faster than other factors in the financial and economic system. The chaos could create capital flight and speculative runs and bring uncertainty to the financial market. There is the possibility of a huge loss in markets funds as investors panic. The COVID-19 pandemic is considered to have extremely negative effects on the international economy and could be the source of systemic risk (Sharif et al. 2020) . The contagion effect in finance is hard to explain based on the fundamentals of the economy. This transmission shock across financial markets is normally described in paper by understanding the linkages between financial assets (Wen et al. 2012) . The evidence of a significant increase in several financial market linkages could be an alert to the existence of this phenomenon. Thus, to discover the linkage patterns for oil prices and stock markets during the pandemic, it is necessary to understand the behaviors of these dependent structures.

Most of the time, studies show that the linkages between oil and stock markets are stable except during financial crises (Martin-Barragan et al. 2015; Bampinas et al. 2017) . The interaction between stock markets and the oil market were highly correlated since 2004 and increased after the global financial crisis. This is because of future prices that allow the investor to purchase the commodities at a fixed price in the future leads to higher volatility in the commodities market (Bampinas & Panagiotidis, 2015) . Geman and Kharoubi (2008) reported a negative dependence between oil and stock markets. Other research has shown a causal relationship between stock markets and oil where oil prices can cause stock market volatility in tail distributions (Ding et al. 2016; Adaramola 2017) . This proves that the stock markets are highly dependent on oil prices and that changes in oil prices can influence the stock markets.

Extreme movements of one market can substantially affect other markets. This could be seen during the financial crisis (Du & He, 2015) . Early in 2020, most countries enforced national lockdowns and reduced oil demand. Because of this, both oil and stock markets experienced cross shocks that impacted industries, such as oil, real estate, and hospitality, causing them to fall dramatically, with corresponding extreme stock market volatility (Mazur et al. 2020) . Bai et al. (2020) reported that this pandemic has greatly impacted international stock market volatility.

There is still a gap regarding the empirical literature that focuses on understanding the linkages between oil and stock markets during COVID-19. The nearest studies could be found is Salisu et al. (2020) . This study applied a panel Vector Autoregressive (pVAR) model to examine the behavior of stock markets and oil. This preliminary research showed the oil market had a greater impact than the stock markets following the COVID-19 announcement. While Cui et al. (2020) employed wavelet coherence and time-frequency to show total risk spillovers among stock markets, the empirical results also addressed those transmitted to the stock market for the long run.

Other studies done during COVID-19 show that oil prices and stock markets are related by small correlations and can act as negative signals to each other (Parabhees, 2020) . This can be seen from the fact that lockdown periods paused global economic activities, which impacted oil prices. Another paper shows that COVID-19 infections have an impact on oil prices (Narayan, 2020) which means that higher numbers of positive cases can reduce oil prices. Another study shows that COVID-19 cases and deaths increase oil price volatility by 8%-22% (Devpura, 2020 , Jeris, 2020 . A recent study showed that the impact of COVID-19 on oil and stock markets exceeds the 2008 global financial crisis (Zhang, 2021) . These results are based on the restrictions on many economic activities such as travel, public gatherings, businesses, and schools.

Owing to high volatility during crises and fat-tailed distributions in financial data, the insightful information linkages in the stock market have become more appealing. The risk of financial losses can increase dependence or correlations. Thus, it is imperative to analyze the linkages between oil and stock markets during the crisis to determine risk management strategies during the uncertain period. With oil prices becoming increasingly important in the economy, policymakers, investors, and stakeholders have paid greater emphasis to find correlations between energy and stock markets. A specific, asymmetric dependency structure in these periods can have a major effect on international diversification of oil economies. The linkages between the stock markets and oil differ between the oil-importing and oil-exporting countries. The shock from a pandemic could adversely affect the linkages between oil and international stock markets, although the pandemic may contribute to short-term economic impacts. To be specific, higher oil prices have a negative impact on stock markets of oil-importing countries as they increase the macroeconomic variables and factors (Jammazi et al. 2017) . Cui et al. (2020) also report that spillover between countries varies. The stock markets in Russia, EU, and the United States (US) bring significantly greater risk of spillover to the oil market.

This study aims to understand the relationship between oil and stock markets and especially on the tails during this COVID-19 period. This study will also compare oil and stock market prices before and after COVID-19 was declared a pandemic. The main focus of this study is on the upper and lower tail dependence, especially lower because the price tends to be low during this period. The integration between the GARCH model and EVT is useful to improve the whole distribution model where the central data is employed via GARCH and EVT is used for the tail to understand the linkages of oil and the stock market with consideration of the extreme behavior. EVT is a tool in statistics used to capture and model extreme data. This approach looks at the fat tail and stochastic volatility that is essential for financial applications. EVT has J o u r n a l P r e -p r o o f been demonstrated to be useful for modeling the stylized fact of financial data with the existence of extreme returns during the crisis. Tail modeling is able to give insightful information regarding extreme behavior. A lot of earlier literature that applied EVT in finance can also be found in past studies, e.g. Longin (1996) , Straetmans (1998 ), McNeil (1999 , Danielsson & de Vries (2000), and McNeil & Frey (2000) .

Even though other methods and models have been used to understand the linkages between oil and the international stock market, there still exist limitations on time-varying characteristics. Most of the methods tend to work in normality framework and ignore the finalized styles of financial data (Embrechts et al. 2001; Chen & Fan 2006) . One of the approaches for examining the dependence structure between oil and international stock markets is the Pearson correlation coefficient. This value does not allow for non-linearity and, despite its simplicity, captures the distribution based on the normality assumption.

Multivariate analysis is able to provide better information than Pearson, but the fact that nonlinear behavior regarding contagion effects and asymmetric linkages occur means that it is not adequate to be employed in this case (Longin & Solnik 2001; Poon et al. 2004 ). Another approach is to apply the Dynamic Conditional Correlation (DCC) model that has been widely applied for examining dynamic linkages (Engle 2002; Engle & Colacito (2012) . However, the limitation of the existence of asymmetry in a rear correlation will result in partial estimates in the DCC model properties (Silvennoinen & Terasvirta 2009; Tsafack 2009 ). DCC has no moments and the parameters for the QMLE have a asymptotic normal distribution or works based on stated rather than derived importance (Caporin & McAleer 2013 ).

This makes a copula function a better alternative for understanding these linkages. A copula approach helps to overcome several limitations for the multivariate model. Since this method allows a range of marginal distributions outside the normality assumption and can integrate more detailed information into the joint distribution, which is useful to understand the linkages between oil and stock markets. Previous studies found that stock markets crash together but remain unrelated during a stable duration (e.g. Poon et al., 2004; Longin & Solnik, 2001) . With the flexibility of copula, this behavior is able to be captured by using Symmetrized Joe-Clayton (SJC) copulas to understand the dependence of the tail and the overall dependence that could be captured via a Gaussian copula. Further current information on copula implementations in finance can be found in Liu et al. (2019) , Garcia-Jorcano & Muela (2020), Gong et al. (2020), and Xiao (2020) .

It is important to gain information that can be used to measure the reaction of the linkages of these assets to the pandemic for short-and long-term periods. The integration of EVT and copulas can provide an effective method of modeling dependency between stock markets to improve risk analysis and portfolio management performance Nguyen 2012, Hussain and Li 2018) . Previous studies have shown that COVID-19 influences oil prices (Baek et al. 2020; Aloui et al. 2020) . Our research explores this literature gap and makes numerous contributions. First, we examine the effect on linkages between oil and the stock market during the recent health and economic crisis. This allows us to understand the degree to which oil could serve as a diversification agent between stock markets against oil prices during the COVID-19 outbreak. Secondly, our study period (January 3, 2019, to October 30, 2020) allowed us to investigate how stock market-oil relationships have changed, and to evaluate the shifts in oil and risk contagion from short-and long-term perspectives. Third, our research applied a third methodological concept in addition to the existing empirical contributions by considering nonlinearity and extreme behavior. Combinations of EVT and copula are applied in the usual sense. We use the dynamic movement of the dependence structure to understand the linkages between J o u r n a l P r e -p r o o f oil prices and the stock market. Interestingly, the behaviors between these assets rely on how the effect of pandemics differ over time. To sum up, our research on how oil prices coincide with oil price volatility will help us understand both the shifts and the ties within the framework. The rest of this paper is organized accordingly.

The following section describes the methodology applied in this paper. Section 3 describes the descriptive statistics and data. Section 4 addresses the results of the analysis. The conclusion of the study is in Section 5.

This section addresses methodologies that have been used. It consists of two parts separated for better understanding: marginal distribution and dependence structure. Section 2.1 elaborates on the Extreme Value Theory. Part of the marginal distribution can be found in Section 2.2. The process of implementation of the appropriate copula is showed at 2.3. Estimation methods and model selection based on the marginal distribution and copula function is present in the final section.

EVT works based on extreme data. From there, a new distribution associated with the tail is introduced. In this research, the Generalized Pareto Distribution (GPD) is employed to fit with these extreme data. The data is considered to be extreme if the values are over the certain threshold that has been identified.

The new distribution could be written based on the theorem below. Let ( 1 , 2 , … ) be a sequence of independent and identically distributed random variables with the distribution function . The distribution of GP can be approximately fit for a large class of underlying distribution and large , the conditional excess distribution function ,

where the scale parameter is α, the shape parameter is ξ for GPD and

for ≥ 0 when ξ ≥ 0 and 0 ≤ y ≤ ( − ) when ξ < 0.

More details about the approximation of GPD can refer to Balkema &De Haan (1974) . We derive the tail distribution below based on the marginal distribution.

The GJR-GARCH model with the mean return model is employed as an AR(1) process (Engle & Ng 1993) . Other GARCH models can also be used to compensate for the heteroskedasticity J o u r n a l P r e -p r o o f of the returns. The returns, , and conditional variance, ℎ 2 of the model can be formulated as in equation below:

( 3 )

A Student-t distribution is used to model the standardized residual as in the equation below,

The tail behavior of returns is fitted based on the GPD model. The method known as conditional EVT results from the combination of empirical distribution of the GJR-GARCH model for the central data and the GPD model for the tails. We employed the threshold value at the 10 th and 90 th percentiles of the whole sample for the tail (Hussain & Li, 2018) .

The conditional EVT is:

Where the scale parameter is α, the shape parameter is ξ, and the lower (upper) threshold is ( ), the number of observations is n, the empirical distribution function is ∅, and the number of observations below (exceeding) the threshold ( ) is ( ).

The Copula approach was first implemented in finance in the early 2000s (Cherubini et al. 2004 ). The method was used to explain the asymmetrical structures of dependency that exist between financial markets. Copula models are gaining in popularity as they are useful for modeling variables without the restrictions of normality. Due to flexibility assumptions and the ability to transfer information from a common probability distribution, copula models were used in many applications (Masseran & Hussain, 2020) . A bivariate copula model can be understood as the following equation:

( 1 , 2 ) = ( 1 ( 1 ), 2 ( 2 ))

where the copula function is and the marginal distribution is 1 ( 2 ) for the random variables 1 ( 2 ).

This study used Gaussian and Symmetrised Joe-Clayton (SJC) copulas to understand the overall and the tail linkages of oil and the stock markets.

The Gaussian copula is used to understand the overall dependence. It works based on underlying multivariate normal distribution. The random variables and are bivariate normal and thus the dependence structure of Gaussian copula can be defined as below:

where Φ and Φ are describing the standard normal CDF's and the linear correlation of is a coefficient between and .

Student-t copula formula can be written as:

where the linear correlation of is referred to as corresponding to the bivariate of distribution.

To capture the time-varying dependence, the linear dependence parameter that evolves in the DCC (1,1) model as suggested by Eagle (2002) is used as:

where Ǭ is a sample covariance of , Ǭ is a square matrix with zeros as off-diagonal elements, and diagonal elements are the square root of those of . The parameter of constraints to capture this behavior can be written as :

J o u r n a l P r e -p r o o f

Joe-Clayton copula is defined as:

( 15 ) and ( 0,1 ), (0, 1 )

represent the upper and lower tail dependence, respectively.

The new modification copula was introduced in 1997 and are called SJC copula. This type of copula is applied to understand the linkages for the lower and upper tail instantaneously. The SJC copula is defined as the equation below:

where the Joe-Clayton copula is (13).

The parameters for SJC copula evolves based on the Patton (2006a Patton ( ,2006b works:

where the logistic transformation is ̃. The equation of ̃( ) = (1 + − ) −1 ensures the parameter of / follows (0,1). / pursues an ARMA (1,10) -type process in which / −1 / signifies as the autoregression, the forcing variable is / , and the persistence effect and variation in dependence is

Maximum Likelihood Estimation (MLE) is a method that uses the maximizing of the likelihood function to estimate the parameters. The full estimation of this integration can be written as:

where the MLE of α and ξ are denoted α and ̂, respectively.

IFM methods are selected because of the flexibility compared to the MLE. IFM can assess and fit the marginal distribution separately and overcome the limitation in MLE that need the parameters for both marginal distributions and copula functions to be estimated at the same time.

IFM method consists of the following two steps:

Step 1: Parameters of marginal distribution is estimated using MLE

where the log-likelihood function of the marginal distribution is .

Step 2: The copula parameters are estimated based on ̂ ̂= arg ( ) = arg ∑ log ( ( 1 ( 1 , 1 ), … , ( , ); )) =1

where the likelihood function of the copula is . The estimators are consistent under standard regularity conditions.

For the selection of the better model than fi with data, the values of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) is calculated. This model selection is a standard, widely used process in the selection of copulas.

AIC can be referring as:

J o u r n a l P r e -p r o o f where the number of parameters applied in the model is k. A lower AIC value means that a model is better suited to empirical evidence. AIC explores the possibility of overfitting models as the number of parameters increases.

BIC can be referred to as:

where the number of data is n and the number of parameters used in the model is k. Similar to AIC, a lower BIC value shows the best fit model. BIC is similar to AIC except the number of parameters is subject to different penalties.

The oil price for this study is data from WTI (West Texas Intermediate grade) spot oil prices. The stock market selection was based on the countries that had been hard hit by COVID-19, based on WHO (2020). These were: In this analysis, we use daily returns that offer more information than the weekly and monthly data. The regular closing prices are obtained from Investing.com from January 3, 2019 to October 31, 2020. Any observations without similar trading dates between series are eliminated. The returns for the stock markets and oil series can be calculated as = − −1 where is the closing level of the index at time t in our study. For standardized comparisons of the performance of all indexes, the values of the relative daily index were calculated based on the standard index when the actual index level is calculated. Figure 1 showed the relative daily index series of the stock markets and oil for the entire sample period.

The data involves daily data for each stock market. The date of March 11, 2020 was chosen to separate between pre-and post-COVID-19. The date is when COVID-19 was declared as a pandemic by WHO. The price movements could be explained based on the before and after the announcement of the pandemic. A drastic, significant downward trend could be found after March 11, 2020. We could see that most of the financial markets dropped significantly after that date. The largest drop is seen from the oil market. As for the stock market series, the largest drop was at the ARG stock market index. From Figure 1 , we could see that the movement of the series was huge and volatile after March 11, 2020 compared to previously. The correlation coefficients between the return series are reported in Table 2 . The oil-related pair based on linear correlation values range from 0.0916 to 0.3718. Table 2 also shows that the average correlation range is about 0.2000. However, the highest correlation with oil is Russia (0.3781), while the lowest correlation with oil is India (0.0916). As we compare the correlation between before and after the pandemic announcement, we could see most of the correlation show a decrease value. For example, the correlation of Oil-COL is reduced from 0.4074 to 0.2252. While the correlation of Oil-IND is reduced from 0.2091 to 0.0614. The results of this linear correlation show that the opportunity for diversification seems to increase.

To be specific, a lower correlation of Oil-IND means that the oil sector can be an excellent alternative for investors in India's stock market from a risk management perspective. This can be a sign of diversification for investors as both markets are not related. However, this may be a misleading interpretation as the linear correlation is based on the normality framework. The non-linear phenomena can be better explained using copula modelling. Insightful information regarding lower and upper extreme data is well-captured by copula.

The results based on the empirical data using EVT and copula models are presented in this section.

In this analysis, the marginal distributions are based on the semi-parametric methods. This approach is GARCH-derived innovation. First, as defined in Section 2.2, estimated residuals are obtained. We use EVT method for tail modeling. Table 3 below presents the parameters of upper and lower tails obtained for the GPD. Table 3 presents the lower and upper tails parameter estimation of GPD. The rate changes for the tail to decrease is based on the shape parameter (ξ). The behavior of the tail is finite if the shape parameter is negative. The tail declines like a polynomial if the shape parameter is positive. The heaviness of the tail depends on the value of absolute value.

Based on the upper tails in Table 3 , the highest value with ξ = 0.3079 belongs to Russia. India follows at second place with ξ = 0.1833 and Argentina with ξ = 0.0528. The results shows that stock markets that belongs to Russia, India, and Argentina have long tail behavior compared to other markets for the upper tail. Short tail behavior is found for remaining stock markets series with France stock market has the lowest upper tail value of ξ= −0.4168. Referring to the lower tails, Table 3 reported long tail behavior for the most series of stock markets. Only Columbia and Mexico has a negative value of ξ with −0.2902 and −0.3539 which indicates a short tail behavior. The highest value of ξ is India with 0.3990 and followed by the US with ξ = 0.2428 which indicates long behavior for the lower tail.

Heaviness could be associated with frequency. In terms of heaviness, the French stock market for the upper tail shows the greatest heaviness compared to all. This is made obvious by the absolute highest value of ξ = −0.4168 for the French stock market compared to others. This could mean that France has the highest frequency of extreme values. Spain also could be described to have heaviness with the next highest of absolute value of ξ = −0.3915. Columbia and US reports the lowest absolute value of ξ with −0.0081 and −0.0085, respectively. Regarding the lower tails, the highest absolute value of ξ = 0.3990 is India. Mexico is the second higher with the value of ξ = −0.3539. Argentina has the lowest absolute value of ξ = 0.0797.

To sum up all the result based on the values obtained, it is concluded that most of the stock market series have short tails for the upper extreme observations and long tails for the lower extreme observations. Figure 2 illustrates the complete CDF of the study which considered as semi-parametric marginal distributions. As shown above, the GARCH model tends to perform poorly for the tail and can be solved by combining it with EVT for the tails. EVT is used to improve the accuracy of the tails while the GARCH model is used to explain inner data. The GARCH model has been well adapted for the distribution interior body. Overall, Tables 3 and Figures 2 demonstrate that the data is better fit with the model. 

This research explores the structure of dependence between oil and major stock markets. A combination of EVT tools helps to successfully capture the tail phenomena. In this respect, both the Gaussian and Student-t copula and the SJC copula have been used for their complex models. Gaussian and Student-t copula are applied to analyze the overall structure of dependence while SJC copula examines compatibility of the upper and lower tails. Equation (10) and (11) are used for the Gaussian and Student-t's parameters and Equation (18) for the direction of SJC's parameters.

Tables 4, 5, and 6 estimate the parameters for the Gaussian, Student-t, and SJC copulas. Lower values of AIC or BIC identify the suitability of the models and indicate a better fit. To assess the path of the parameter for every pair in the process to see the specific changes during the period, Figure 5 consist of the path for the dependence is used as well. 

The overall dynamic linkages for the 10 pairs of stock markets with the oil are analyzed in this section. Figure 3 shows the overall dependence of time paths for both Gaussian and Student-t copulas.

As seen in Figure 3 , the linkages between oil and stock market series shift strongly over time due to the presence of the pandemic. An interesting detail is that the dependence volatility is higher following the COVID-19 announcement. This insightful information is important to risk portfolio managements so that they are more careful in allocating investments in different assets. The changes of the path to be stronger than before is similar to past literature that indicated a stronger dependence during the crisis.

For the Oil-ARG pair, the dependence parameter for the time-varying Gaussian and Studentt copula ranges between 0.2 and 0.3. The values started to increase as the date drew closer to March 11, 2020 (before COVID-19 was declared a pandemic). There is a significant drop after March 11, before it started becoming more constant and fluctuating between 0.2 and 0.3. These behaviors indicate that the overall dependence increased and dropped significantly when COVID-19 was declared a pandemic before it stabilized several months later. The same behavior could also be seen at Oil-BRA pair. The parameter of for this pair fluctuates between 0.25 and 0.35. It peaks during the pandemic and hits the lowest dependence a few months after COVID-19 is declared a pandemic. The contagion effect which normally would be associated with significant changes in dependence can be seen in this pair.

For the Oil-COL pair, the path movements for the dependence parameter in the time-varying Gaussian and Student-t copula model move slightly around 0.35. This path of is very stable and there are no changes in behavior, both before and after the COVID-19 announcement. The pandemic seems to have had no effect on the relationship between oil and COL. This indicates that the relations between oil and COL are the same before or after the pandemic. The same goes for the Oil-RUS and Oil-SPA pairs, where the range of dependence fluctuates around 0.33 and 0.27, respectively.

The Oil-MEX pair has a range of 0.25-0.30. For the Oil-UK and Oil-US pairs, both have the same ranges from 0.20 to 0.40. The same conclusion can be drawn as Oil-ARG, where there is an increase near the COVID-19 announcement and a decrease a few months later. Moreover, we can see a recent decrease for Oil-US dependence. The Oil-UK and Oil-US have the widest ranges of the dependence parameter for both models. There are also differences in the dependence parameter for Oil-IND and Oil-FRA.

Overall, we could see most of the pairs show a significant increase of dependence before COVID-19 but a significant drop after the data announcement. This behavior could be seen for ARG, BRA, FRA, IND, MEX, UK, and US, while there are no changes for COL, RUS, and SPA in terms of linkages with oil. The results indicate the linkages between Oil and COL, RUS and SPA are less volatile and more stable. Both Gaussian and the Student-t copula model show very similar results.

The details of the linkages for the upper and lower structure between the 10 pairs of stock markets with the oil is discussed in this section. The time path for the lower and upper tail dependence is shown in Figure 4 using both SJC copulas. In this study, it is indeed possible to differentiate time variations in dependency measures between return series by coefficients, and as in Equation (18). The results for the time-varying SJC copula model in Table 6 showed that the values of persistence coefficient β are larger than the variation coefficient α for most of the time. These results show that the path is able to provide insightful information into the behaviors of the upper and lower tails. However, this is where the values for the variation coefficient α are relatively higher than the persistence coefficient β for a few pairs. We can conclude that a few of the time paths of the pair are close to white noise and unable to provide better information.

Our main finding in this section entails the existence of linkages, especially on the tails between the stock markets and the oil. For the Oil-ARG, the path for τ U in the time-varying SJC copula model moves from 0.0 to 0.5, while for τ L the range is between 0.0 and 0.3 most of the time. The value for the upper tail decreased to zero at the end of the period. This indicates that the upward movement for oil and ARG will not move together after COVID-19 was declared a pandemic. The dependence for the lower tail is volatile, the same as before the announcement. This implies that COVID-19 affected oil-ARG on the upper tail after the announcement. For the Oil-BRA, the path for τ L in the time-varying SJC copula model ranges between 0.0 and 0.5 while for the τ U the range is between 0.0 and 0.3 most of the time. There is a significant increase of lower tail dependence after the announcement of the pandemic. In terms of the path, compared to the lower tail, the upper tail dependence for this pair is more stable.

For the Oil-ARG and Oil-BRA pairs, most of the time the values of dependence for the upper parameter were higher before the pandemic. However, the trend changes with the lower tail dependence are higher than with the upper tail dependence. It is also interesting to see that lower tail dependence increases and becomes stronger after the pandemic announcement. This means that dependence for the oil with these countries is affected at the lower tails. The downward movement for the oil will also affect the downward trend for these countries and vice versa. For the Oil-COL, the path for τ L in the time-varying SJC copula model ranges between 0.2 and 0.4, while the τ U ranges between 0.0 and 0.3 most of the time, with a few spikes ranging between 0.1 and 0.4 after the pandemic announcement. For the Oil-FRA, the path for τ L in the timevarying SJC copula model is stable, ranging around 0.2, while the τ U ranges between 0.0 and 0.5. We could see a significant downward trend for the upper dependence with a small spike after the COVID-19 declaration as a pandemic. As for the Oil-COL and Oil-FRA pairs, the values of the path of dependence for the lower parameter is higher than the upper dependence most of the time, regardless if it is before or after the pandemic.

For the Oil-IND, the values for τ U are close to zero. However, the values for τ L range from 0.0 to 0.5. The pattern of this path seems to increase with a few significant peaks. The same pattern could be seen in Oil-MEX pair. There is also a significant increase in terms of lower dependence post-announcement, especially for Oil-MEX where the price did not drop below 0.2 until October 2020. Overall, oil seems to have a stronger dependence with the Indian and Mexican stock markets in terms of lower tail dependence compared to upper tail dependence. There are significant changes for lower tail dependence for these pairs.

For Oil-RUS, the path for τ L in the time-varying SJC copula model ranges from 0.1 to 0.4 most of the time, while for the τ U the range is between 0.0 and 0.2. There are not many changes after the pandemic announcement for the upper and lower dependence. However, the dependence for the lower tail is much higher than the upper tail dependence before and after the announcement. For the Oil-SPA, the path for τ L in the time-varying SJC copula model ranges between 0.0 and 0.3, while for the τ U the range is 0.0-0.4 most of the time. There was a significant increase after the pandemic for the lower tails. For the Oil-RUS and Oil-SPA pairs, the lower tail path dependence was higher than the upper tail dependence over time with the Oil-RUS lower tail to be very volatile.

For the Oil-UK, the path for τ L in the dynamic SJC copula model moves from 0.1 to 0.4 most of the time, while for the τ U , the ranges between 0.0 and 0.4. Both paths for upper and lower dependence is very volatile and we could see a few spikes for both tails. In contrast, the upper tail dependence for the oil-US pair is more stable and ranges between 0.05 and 0.15, while the path for τ L in the time-varying SJC copula is highly fluctuant and moves between 0.05 and 0.40. The lower dependence seems to be much higher after the pandemic announcement. For the Oil-UK and Oil-US pairs, we could indicate that the oil dependence between stock markets has a greater impact on the lower tail linkages more than the upper tail. The movement in terms of upward movement does not change much compared to the movement during the crash.

We would also like to understand the potential diversification among the selected stock markets in this study. The dependence of oil and indexes may help define the diversification potential. Based on Figure 4 , most of the paths in most countries showed that the path of lower tail dependence is higher than upper tail dependence. Thus, the dependence of oil on the selected indexes has been stronger during the crisis. This could mean that there is no possibility of diversification during the pandemic for the selected stock markets and risk diversification is not effective during a pandemic for these pairs.

As we refer to previous Table 2 , Oil-IND seems to be a good diversification pair with a low linear correlation. However, it is not true as we investigate the behaviour of these returns. The lower tail dependence is higher than the upper tail most of the time. These indicate the lower dependence is stronger than the upper dependence that could be associated with more extreme negative returns related. There is almost no opportunity for diversification for Oil-IND considers these extreme behaviours.

However, there are a few cases where the path dependence for the upper tail is higher than lower, specifically Oil-RUS, Oil-SPA, Oil-UK, and Oil-US for a certain period. There is an opportunity for diversification in these pairs during the pandemic based on their upper tail dependence. All this information could not be seen from Table 2 that based on linear correlation. The results from copula can bring significant information for other financial risk management processes.

The linkages between financial markets have been actively studied over the last few years with most approaches in the past subject to the assumption of normality. However, most financial information is non-linear, non-stationary, and heavy-tailed. Therefore, appropriate models are required to implement these features. This study aims to evaluate the structure of dependency between oil and other major stock markets during the COVID-19 period, using EVT and Copula models. The results show that the epidemic affects all countries, especially those hit hard by COVID-19. These approaches offer more knowledge regarding perceptions of the abilities of risk diversification and risk management policy. Dependence varies over time and the linear correlation may be insufficient to represent the effects of COVID-19 on the oil and the stock market.

Our findings show that the degree of dependency on oil prices and most stock markets is shifting. The dependency on these pairs was much greater before the pandemic, with major shifts in the downward movement of dependency following the COVID-19 announcement. After the pandemic declaration, the reliance between oil and stock market tended to be lower. This shows that any movement between petroleum and selected stock markets was no longer connected after the pandemic. This evidence shows the contagion effect as described by the previous literature, as transmission shocks involved changes across the range of financial assets. This information is important to study as these patterns were, to the best of our knowledge, unrecorded in any literature.

As for the upper and lower tails, the dependence for the upper tail does not show any significant changes while dependence for the lower tails tends to be and significantly increased and stronger. This outcome implies that the probability of a downward extreme movement is high between oil and the stock markets. Most of the time, the lower dependence is higher than the upper dependence for all pairs, regardless if it's before or after the announcement of the pandemic. This means that the stock market will have an extreme downward movement when the oil price moves downward, regardless if it's before or after the crisis. This is another important finding that can be useful in the future. Overall, this study enhances the understanding of oil prices and their link to developed stock markets by exploring the overall and tail behaviors. We conclude that the oil price still maintains strong dependence with most of the major stock markets. In terms of diversification, it is observed that the linkages for these pairs is greater before the announcement and significantly decreased afterwards. The diversification of portfolios through these pairs during a downturn would have several advantages and can help policymakers and risk management professionals to make better decisions in terms of portfolio allocation. For instance, this knowledge will allow investors to build confidence and look for opportunities for risk diversification in other asset classes. We may also find the ability to diversify risks on selected pairs such as oil with the Russian, UK, and US indexes during the pandemic. For a certain period of time, the prospect of diversification between these two financial markets has strengthened. This work makes a significant contribution to the current study in terms of the dynamic dependence for the oil and stock market under extreme perspective. As a limitation, details regarding the reason behind the dependence results have not been explored. A full discussion of the dependence on these pairs is beyond the scope of this study. The study from Kilian & Park (2009) might be useful to understand the reasons behind these linkages.

Our results have practical implications. Although COVID-19 is a rare event in which it is a world health crisis, we see that it also impacted the financial market similar to the 2008 global financial crisis. This study is important to various market players or investors to predict price changes, portfolio diversification, cross-hedging, and cross-speculation to make a profit during this crisis. Several dynamic diversifications could be applied. The results can be used by policymakers to improve economic stability, especially during this period where most countries suffer from COVID-19. Understanding behavior is very important because the correlation between oil prices and overall economic activity could affect the economic cycle. In the future, we can better understand the effects of crisis on the oil industry and find ways to mitigate them.

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