key: cord-0864826-ndykubau
authors: Tabak, Benjamin Miranda; Silva, Igor Bettanin Dalla Riva e; Silva, Thiago Christiano
title: Analysis of Connectivity between the World’s Banking Markets: The COVID-19 Global Pandemic Shock
date: 2022-03-15
journal: Q Rev Econ Finance
DOI: 10.1016/j.qref.2022.03.002
sha: a298b2170859824fc7795c4ae65697691cf10d8f
doc_id: 864826
cord_uid: ndykubau

We contribute to the literature on financial networks by presenting empirical evidence that the global shock of the COVID-19 pandemic caused changes in the forms and intensity of banking sector connections between different countries. These changes include providing the highest level of connectivity observed in the timeline initiated in 2005. We used a comprehensive set of information containing data from 35 countries (developed and emerging economies) and showed the change in the classification of transmitting and receiving spillover during the COVID-19 crisis. Our results provide relevant insights into systemic integration between countries’ banking markets, especially during difficult times. Our results are significant to Central Banks, banking sector investors, and governments seeking assistance from banks in the solutions for the resumption of the economy in the face of the COVID-19 shock.

The interconnection between markets has been studied through different techniques and approaches. The relevance of these studies stems from the attempt to understand the relationships between different countries, markets, and types of assets, in a context of globalization of information, displacement of people, trade, industry, crises, and public health situations. These features make international connections a preponderant factor in understanding internal behaviors. In this sense, and due to the current interdependence of world markets, the financial system has become one of the main risk propagators, serving as the trigger for recent crises, such as the subprime crisis and the Eurozone's public debt crisis. However, the current COVID-19 pandemic has placed markets worldwide in a crisis, which began due to an external factor to the financial sector. The COVID-19 spread rapidly throughout the world, differently from recent crises that originated in the banking market itself.

Studying the banking market is essential because it is a source of crises and because it is a sector that promotes and finances the functioning of other activities, such as providing citizens with the anticipation of consumption. Thus, it presents itself as a critical component of the macroeconomic scenario that requires extensive mapping, with its behavior very well understood. Silva et al. (2017) show how the financial sector may act as a financial accelerator -with a feedback mechanism -that enhances financial crisis. Even small shocks to the financial sector may be amplified and generate negative spillovers to the real economy, worsening the crisis. 1 Observing the connectivity mechanisms provides a better basis for constructing crisis coping and risk mitigation strategies, being a concern of regulatory bodies, like the Central Banks and economic agents, to strengthen their management strategies. For policymakers, mapping the movements adds an understanding of the systemic risks to which their country is exposed. It allows them to evaluate which markets should be on their radar and subsidize the construction of risk matrices that associate frequency and severity to the domestic market in the face of shocks from other countries.

We observe the impacts of the current health crisis through the Spillover Index, as presented by Diebold & Yilmaz (2015a) , among the banking markets of 35 countries around the world, with a sample of developed and developing economies, from different geographical regions and different economic blocs. We use indices representing the share values of companies in the banking sector in each of the countries studied between July 2005 and December 2021, analyzing the volatilities in each country. We compare the results for the complete sample with 2020 during the COVID-19 crisis. We employ Vector Autoregressive (VAR) Models and the Spillover Index (Diebold & Yilmaz (2015a) ). This methodology has been widely used in analyzes of this nature in the most recent studies on the subject (Kang et al. (2019b) , Kang & Lee (2019) , Kang et al. (2019a) , Apostolakis (2015) , Demirer et al. (2018) , Yarovaya et al. (2016b) , Baruník et al. (2016) , Yarovaya et al. (2016a) , Wang et al. (2016) , Wu et al. (2019) , Liow (2015) , Antonakakis & Kizys (2015) , Demirer et al. (2018) ). 2 Our primary research question is whether the pandemic (worldwide exogenous shock) has changed the connectedness across banking markets. The answer is positive. We construct a rank-ing of spillover for the main transmitters of shocks and main receivers. We then evaluate whether increases in spillover and connectedness are mainly due to geographic proximity.

Our results demonstrate the connectivity of volatilities between the banking markets of all the countries studied, varying in intensity over time. We observe that the general level of spillover increases in times of crisis. The increase in the spillover that occurred in 2020 for the banking markets' volatilities is the largest in the historical series, surpassing the 2008 peak. However, the year 2021 showed different behavior even during the crisis, with a reduction in the level of connectivity as countries sought reopening measures still under the impact of waves of infection that affected them in different ways.

The 2005-2019 sample analysis shows that blocks with a higher degree of connectivity formed according to the countries' geographic locations, with a more substantial spillover effect among the nearest neighbors. The characteristic formation of blocks linked to geographical proximity lost relevance in the face of the pandemic shock. These results provide essential insights to guide portfolio allocation and risk management decisions.

We have three significant contributions to the literature. The first is to unravel the impacts of the pandemic caused by the new Coronavirus -COVID-19 (SARS-COV-2) on the banking systems of emerging and developed countries. Second, we show that spillover between banking systems increased sharply during the pandemic shock period. Third, we show that the ranking of countries that transmit or receive the most initial shocks changes during the pandemic. These results are essential to discuss and improve the financial regulation of these countries. The increase in spillover found in the paper during the COVID-19 paves the way for potential widespread losses across different economic agents and countries. Thus, when designing stress-test scenarios, one should also consider adverse scenarios further in the tails of loss distributions during periods in which the spillover is very strong.

We structure this paper into five sections and this introduction. The second contains a brief literature review, and then we detail our methodology. We then present some information about our database, whereas the fifth section discusses our empirical results. Section six concludes the paper.

Cross effects between stock markets have a large amount of work done to understand the movements and explain the relationships between their components. Among the techniques most used in these studies is the methodology proposed by Diebold & Yilmaz (2009) based on the decomposition of variance errors using autoregressive vectors to measure the volatility transmitted between markets. The methodology went through an evolution (Diebold & Yilmaz (2012) ), making the workflow with vectors indifferent to the ordering of the variables and making it able to measure the total and directional spillover effects. The analysis technique of connectivity and spillover effects is due to Diebold & Yilmaz (2015a) .

The measurement technique of the Spillover Index (Diebold & Yilmaz (2015a) ) can be used to observe: market risk, portfolio concentration risk, credit risk, counterparty risk, systemic risk, business cycle risk. In addition to these risks, it is also possible to monitor crises from a financial and macroeconomic perspective.

We summarize the current literature on connectivity between different markets and countries in Table 1 . The literature provides ample evidence on spillovers from financial markets. Kang et al. (2019b) find positive spillover effects between the ASEAN-5 and world stock markets and increases in return and volatility spillover during times of crisis. Kang & Lee (2019) show that the highest levels of spillover occur during financial crises and that the connectedness is sensitive to economic and financial events. Kang et al. (2019a) study dynamic spillovers and connectedness between several financial assets such as stocks, commodities, bonds, and VIX and provide evidence that emerging equity markets are net receiver of shocks. Wu et al. (2019) study Chinese sectors and find that the industrial sector is the systemically most important one. In contrast, sectoral linkages show time-varying features, whereas Zhang et al. (2019) focuses on volatility spillover and finds evidence of time-varying connectedness for G20 stocks. Demirer et al. (2018) find that global bank equity connectedness has a robust geographic component, which increases during a crisis. Roni et al. (2018) find that volatility and return spillovers behave very differently over time, especially during a crisis. Baruník et al. (2016) study U.S. stock market sectors and find that spillovers are transmitted at magnitudes that change over time in different sectors. Ben Rejeb & Arfaoui (2016) find that there is substantial volatility spillover between emerging and developed markets and across emerging markets, there is a role for geography (volatility transmission amplification), and that interdependence varies over time according to market conditions. Several studies focus on the effects of exchange rates on stock markets. Jebran (2018) studies volatility dynamics for the exchange rate and stock market and find unidirectional volatility spillover in quiet times and bidirectional volatility spillover in the post-crisis period. de Oliveira & Maranhão (2018) test for the existence of spillovers from exchange rate shocks to the stock market index, finding that there are spillovers from exchange rate to the stock market. Reboredo et al. (2016) study spillover between exchange rate and stock markets and find an asymmetric effect between upside and downside risk spillover. Sui & Sun (2016) study the exchange rate and stock market for the U.S. and BRICS and show that financial crisis aggravated spillover effects between exchange rates and stock markets. Wang et al. (2016) study the Volatility spillovers among China's stock, bond, commodity futures, and foreign exchange markets. They find the stock market is the most prominent transmitter of shocks, whereas the financial crisis aggravated spillovers between the exchange rate and stock markets. Georgiadis (2016) shows how U.S. monetary policy generates output spillovers to other countries depending on their characteristics. Mensi et al. (2016) study volatility spillovers between the U.S. and BRICS and find that Brazil, India, China, and South Africa markets are strongly affected by the Global Financial Crisis, which supports the hypothesis of recoupling (with increased linkages). In contrast, the decoupling hypothesis occurs for the Russian stock markets only. Yarovaya et al. (2016a) find that markets are more susceptible to domestic and region-specific volatility shocks than to inter-regional contagion. They also provide evidence that because the size of return and volatility spillovers across futures is more significant than between spot indices, the futures markets are more efficient conduits for the transmission of information. Yarovaya et al. (2016b) study volatility spillovers patterns across six stock markets in Asia and find that there is an asymmetric nature of volatility transmission channels. Antonakakis & Kizys (2015) study the dynamic link between returns and volatility of commodities and currency mar-4 J o u r n a l P r e -p r o o f kets -show the importance of performing a dynamics analysis (changing role of transmitters and receivers of return and volatility spillovers). Liow (2015) shows that high volatility transmission across real estate, currency, equity, and all assets and that general equity is the main contributor to total volatility spillovers, whereas Apostolakis (2015) presents evidence that securities markets are the central net transmitter of financial stress to all other markets.

Most of the literature on spillovers and connectedness employs a Vector Autoregression Spillover Index due to Diebold & Yilmaz (2009 ), Diebold & Yilmaz (2012 and Diebold & Yilmaz (2015b) to estimate these spillovers. Several authors employ other econometric models such as Antonakakis et al. (2020) which defends the use of a Time-Varying Parameter Var (TVP-VAR)to estimate connectedness and spillovers and perform an empirical exercise using exchange rates. Bouri et al. (2021) presents evidence of spillovers of realized higher moments and jumps among U.S. stock, crude oil, and gold. The authors also employ a time-varying parameter vector autoregressive (TVP-VAR) spillover framework. They find that all spillovers seem to intensify during crisis periods.

Li & Giles (2015) find significant unidirectional shock and volatility spillovers from the U.S. market to both the Japanese and the Asian emerging markets. Volatility spillovers between the U.S. and Asian markets are more potent and bidirectional during the Asian financial crisis. Syriopoulos et al. (2015) encounter significant return and volatility spillover dynamics between BRICS-US markets and business sectors. Joshi (2011) examines the return and volatility spillover among Asian stock markets in India, Hong Kong, Japan, China, Jakarta, and Korea. According to the author, there is evidence of spillover in most stock markets in terms of return, shock, and volatility in both directions. Volatility correlations are small, showing a lack of interconnectedness across Asian stock markets. Fedorova & Saleem (2010) find unidirectional volatility spillovers from currency to stock markets. The results show clear evidence of integration of Eastern European markets within the region and with Russia. Gao et al. (2021) analyzed return and volatility spillovers between the green bond and financial markets and found significant spillovers between the green bond market and other bond markets, and that some events alter the level of risk spillover between markets.

Vo & Hung (2021) investigate the spillover effects and time-frequency connectedness between SP 500, crude oil prices, and gold. Overall, their results shed light on that compared to the pre-COVID-19 period, the return transmissions are more apparent during the COVID-19 crisis. Hanif et al. (2021) examine the impacts of COVID-19 on the spillovers between the U.S. and Chinese stock sectors and find that COVID-19 intensifies the risk spillovers for all markets between March 2020 and April 2020. Borri & di Giorgio (2021) employ a shorter sample characterized by the COVID-19 shock and find that sovereign default risks considerably influenced systemic risk contribution of all banks. Arreola et al. (2020) study banking sector and find that the most significant emerging market spillover transmitters and receivers are the banks from Brazil. They also present evidence that since the COVID-19 epidemic, developing market banks' overall connection is more important than established American institutions. Laborda & Olmo (2021) apply the spillover index to seven economic sectors of U.S. economic activity and find that Banking Insurance, Energy, Technology, and Biotechnology are the main channels through which shocks propagate to the rest of the economy. Therefore, the banking sector 5 J o u r n a l P r e -p r o o f is a vital shock transmitter that can amplify crises whenever they occur. Overall, we can summarize these findings as follows: 1) there seem to be relevant spillovers (return and risk) among financial markets; 2) these spillovers change over time due to significant events -the COVID-19; 3) the level of spillover may depend on the geography of markets involved in the analysis; 4) financial crisis are followed by substantial increases in spillover.

We contribute to the literature by studying the spillover effects in the banking sector for a large sample of countries (most papers focus on a small subset of countries). We also contribute by studying the effects that the COVID-19 has had on the banking sector. Even though we find that spillovers substantially increase during COVID-19, governments adopted many measures to mitigate and reduce contagion, such as social distancing, preventing people from working. Many firms had to close -at least temporarily -and the effects were more pronounced on specific sectors -such as the tourism sector. The banking sector is crucial in this sense as it is one of the primary providers of credit for many economies, and the COVID-19 crisis could be amplified due to a cascade of failures. Understanding how the banking sector reacted during the COVID-19 crisis is essential to enhance our knowledge of the connectedness of banking sectors worldwide and discuss and improve financial regulation. 

We calculate the relationship between the countries' banking markets volatility by applying the vector autoregressive (VAR) methodology, variance decomposition, and the general Spillover Index by Diebold & Yilmaz (2015a) , allowing us to examine the direction and net directional result.

We follow Diebold & Yilmaz (2009) , Diebold & Yilmaz (2012) and Diebold & Yilmaz (2015b) and construct a spillover matrix of volatilities for bank sectors for countries in our sample using a generalized Vector Autoregression. Let Y t be a covariance stationary VAR(P) process as follows:

where Y t stands for a vector of N − 1 endogenous variables, the coefficients Φ i are N × N autoregressive coefficient matrices and the vector of independent and identically distributed error terms is given by ε ∼ (0, Σ), with zero mean and covariance matrix Σ. We can rewrite the VAR in its moving average representation as:

The coefficients B i (N × N matrices) obey a recursion form as follows:

with B i = 0 for i < 0 and B 0 being the identity matrix (N × N). Using the generalized VAR structure, the decomposition of the variance of the generalized forecast error ahead H is as follows:

in which Λ i j is the spillover from j to i, Σ is the covariance matrix of the error terms, σ j j is the standard deviation of the error term for the j − th equation and the term e i is a selection vector in which the i − th element is one and all other elements are zero. The connection index is generated by an array N × N:

where each entry provides the contribution of the variable j to the error of forecasting the variance of the variable i. Since the variables' own and cross contributions do not add up to one under the generalized decomposition, each entry in the variance decomposition matrix is normalized by the following summation:Λ

7 J o u r n a l P r e -p r o o f with ∑ N j=1Λ i j (H) = 1 and ∑ N i, j=1Λ i j (H) = N per construction. The total index of spillover or total connectivity (CT) across all countries is presented as follows:

This index measures total shock transmission across all countries. Elements outside the main diagonal denote shocks to/from each other, while elements on the main diagonal denote shocks coming from oneself.

Shocks received by a specific country i from all countries j are expressed as:

Changing direction and observing from one country i to all other countries j:

Thus, the net directional connection, or net directional spillover is:

in which CL i (H) helps identify the nature of the market or asset, whether it is a net recipient or influence transmitter. It is possible to analyze the net directional connection for (CDL(H)) or spillover where shocks are considered only between two markets. The CDL between pairs of countries is the difference between shocks transferred from i to j for those transferred from j to i:

We transform the connection of the banking sectors of these countries into a network. Following the interpretation of Diebold & Yilmaz (2015a) , the variance decomposition matrix provides a weighted and directed network. Each elements in this matrix is a directional pair-wise connection (CL i (H)). The sums in the rows of this matrix are the total of the CD i← j (H) directional connection received by one country i from the others and the sum in the columns the total of the directional connection CD i→ j (H) sent by the country i to others.

We can present impact decomposition in a table format to facilitate the visualization and understanding of the connection relationships and spillover, according to Diebold & Yilmaz (2015a) .

We exemplify the format in the Table 2. 8 J o u r n a l P r e -p r o o f x 1 x 2 · · · x n From others:

The table fields represented by x 1 , x 2 , x n indicate the markets to which the rows and columns refer. The cells referenced by d 1←1 , d 1←2 , d N←N indicate the spillover impact values verified in country i from shocks in country j. In this way, it is possible to check the values of the impacts sent and received for each market combination two by two. It is also possible to verify how much of the impact results from self-influence by the main diagonal values.

Thus, we have in the table cells:

We follow Nicholson et al. (2020) and Nicholson et al. (2017) to implement the VAR-Lasso approach. Assume that there is a Vector Autoregression with endogenous variables y t (p lags) and exogenous variables x t (s lags). We have a VARX k,m (p, s) given as follows:

In a low dimensional setting the coefficients (ν, Φ, β ) can be estimated using multivariate least squares as:

in which the expression A F = ∑ i, j A 2 i j denotes the Frobenius norm of a matrix A, which reduces to the L 2 norm when A is a vector. The term ν is a k × 1 vector of intercepts, and we have k endogenous variables and m exogenous variables.

The estimate of k(1 + kp + ms) regression parameters is necessary for the VARXk, m(p, s) without regularization. The aim behind the VAR-LASSO is to reduce the parameter space of the VARX by enforcing sparsity in Φ and β on numerous convex penalties.

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

The VAR-LASSO can be estimated as follows:

in which λ ≥ 0 is a penalty parameter, which is selected in a sequential, rolling manner, P y (Φ) denotes a penalty function on endogenous coefficients, and P z (β ) denotes a penalty function on exogenous coefficients. We employ the Basic VARX-L, which results in penalties of the form

The L 1 penalty will induce sparsity in the coefficient matrices Φ and β by zeroing individual entries.

The computational tractability of the Basic VARX-L is a key benefit of this device. It is possible to use a technique known as "coordinate descent" to solve the Basic VARX-L by dividing it into smaller problems for each of the scalar variables [Φ, β ]i j and solving them one at a time until convergence is reached. Because each subproblem in the Basic VARX-L context has a closed-form solution, this strategy is computationally efficient.

The parameter λ is not known and is normally determined through cross-validation. The problem is not well-suited to typical K-fold cross-validation because of time-dependence. Following Nicholson et al. (2020) and Nicholson et al. (2017) , we use the solution of minimizing the H-step ahead mean-square forecast error (MSFE), in which H = 1, 2, 3, . . . specifies the desired prediction horizon. Nicholson et al. (2020) and Nicholson et al. (2017) propose to select theλ as the minimizer of

where the period T 1 + 1 through T 2 is the training period and is used to select the λ parameter, and T 2 + 1 through T is used for the evaluation of the forecast accuracy.

The information used was obtained from Russel FTSE (Financial Times and Stock Exchange) and included data from an equity index for the banking sector in 35 countries between July 2005 and December 2021. The information used corresponds to the daily index for each country. All indices are denominated in U.S. dollars.

We present the countries in our sample and their respective acronyms in table 3.

J o u r n a l P r e -p r o o f We construct our sample due to the availability of the banking sector index for that particular country. The focus on the bank sector is due to its relevance in channeling funds to the economy and its role that may help amplify crises when they occur. The exogenous shock that COVID-19 generated worldwide can be severe depending on the degree of severity of the health crises in the country (number of cases and deaths).

Due to the COVID-19 pandemic, the global crisis generated human and economic losses in various sectors around the world. The severity of the problems in the health area led to border, company, and trade closures, with deleterious effects on employment and production. Difficulties have hampered global production chains in meeting the demand for goods and services in many countries. The solutions given by several countries to fight the pandemic -social distancing and lockdown have unequivocally contributed to amplifying the damage to the economy. Before the advent of vaccines, there were no clear measures that could help fight the pandemic other than distance and, in many cases, lockdown.

The COVID-19 pandemic has damaged many markets and the production of goods and services. It adversely affected the labor market with a significant increase in the number of unemployed in many countries and productivity. Financial losses added to human losses. COVID-19 can be understood as a global shock that affected all countries -to a greater or lesser degree. From the perspective of the banking system, we can understand it as an exogenous shock that severely affects the prospects for generating results for the banking system in the future. There was a significant increase in uncertainty and financial volatility.

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

The value of the indices was analyzed using the average price between two subsequent days to mitigate the reading of the spillover effects from the time zone differences given the countries' geographic breadth. Therefore, we employ an average of two business closing prices as our final price (Rigobon & Rigobon (2016) ) to compute the volatility.

Dates on which no business took place, such as holidays, are included in the historical basis with the repetition of the previous day's value. We remove from our sample the days on which there was a repetition of values larger than 30% for the countries globally (or within the European, Asian and American blocks) in line with Sandoval & Franca (2012) .

In line with Diebold & Yilmaz (2015a), we measure the Spillover Index. To calculate the vector autoregressive (VAR) models, we apply the LASSO technique to reduce the number of predictor variables for each country. We use ten periods as our forecasting "H" horizon, representing 20 working days, approximately a month.

The Spillover Index was calculated for the entire period and through a rolling window. The general result of the period brings gains to the study as it presents more stability and indicates countries' behavior in the long run. Observation through a rolling window allows seeing the fluctuations over time and the country's most recent conditions. The windows used has a size equal to 130 periods, equivalent to approximately 364 consecutive days. In this method, spillover is measured for each reference date considering the previous 129 periods. This window is shifted daily, measuring the effect over the entire historical series. The COVID-19 period analysis used two windows, the first starts in January 2020 and ends in December 2020 and the second starts in January 2021 and ends in December 2021. The 2005 to 2019 analysis used a full sample Spillover Index.

We estimate connectivity relationships and spillover contagion effects using Heat Maps and Minimum Spanning Tree for each time frame. We compare the COVID-19 period with the total period.

The analysis of volatilities shows, for the analyzed sector, the systemic communication of market risk. With this information, it is possible to identify the countries with the most significant effect on systemic risk in the banking sector. It is also possible to identify the locations with the most stable market and least susceptible to receiving external influences and those with the highest risk reception from third parties.

The Minimum Spanning Tree (MST) is a graphical representation that presents the connections between the variables, illustrating the weight of the connecting links and the level of information sent by each country. It seeks to approximate the variables with the highest association with the minimum number of connections while maintaining a single network component. Kruskal (1956) 's approach is used to estimate the Minimum Spanning Tree (MST) from our N x N spillover matrix. We analyze the amount and growth of dependency among indices based on 12 J o u r n a l P r e -p r o o f this approach by constructing a MST. Despite the literature providing many different network construction techniques, the MST technique provides a reasonable explanation for how bank systems for each country spillover on each other.

As Mantegna (1999) suggests, the following is a basic summary of the MST building process: Consider each index as a node in a network and the linking effect as an edge. Nodes are sorted by the weights of their links, which indicate the degree of connectivity between indices. Search for an edge with the most negligible weight and ensure there is no closed loop in the network. It is added to the MST set if all conditions are satisfied. If the network has n nodes, the MST should have n − 1 edges since there are no closed loops. This method ends with selecting the index results that have the strongest correlations with the MST.

When we use the entire period, Figure 1 , we can see that volatility has a geographical factor in its connectivity between banking markets,although with some exceptions. Europeans tended to position themselves centrally for this period, with the other blocks connecting peripherally and with less influence. Figure 2 presents a differentiated figure compared to the previous one, looking at the year 2020, which includes the initial shock of the COVID-19 pandemic. We perceive that the crisis of global proportions and caused by an external factor to the economy provides a scramble in the contagion effects between countries. We find that the COVID-19 alters significantly the connectivity and spillover effects across countries. The crisis also changes the group formation -which is mainly dye to geographical proximity and market size during normal times. Figure  3 shows that the year 2021, still under the impact of the pandemic, underwent a new change in the connectivity network between countries' markets, with a reduced level of spillover and more distant connections. 

The Heat Map analysis shows the degree of exchange of the spillover effect between the different countries, in two by two relationships (Diebold & Yilmaz (2015a) ), it is a color scale representation of the connectivity table presented in Table 2 . We replace the values with colors in the Heat Map analysis -the more intense the color, the higher the value. Next to the Heat Map we present a scale that varies by color intensity. The stronger the red tone, the greater the spillover between the banking systems of those countries. The advantage of this type of graph is that it is easier to identify connections in studies with many interconnected variables. Another characteristic is the possibility of analyzing both the received and the sent spillover. We find a higher connectivity between the European bloc countries. The 2005-2019 period analysis, as shown in Figure 4 , shows the highest levels of connection between blocks formed by geographical proximity. The 2020 map, Figure 5 , shows that Asian countries, in general, have increased the receiving of spillover effects in the crisis scenario, except for China, and to a lesser degree for Hong Kong 3 . For the year 2021, Figure 6 , when compared to the period 2005-2019, we still see an increase in the transmission of spillover from European countries to Asian countries. Figure 4 : We present the Volatility Heat Map for the period from 2005 to 2019. The more intense the color the higher the volatility spillover. We can see a darker region in the left bottom of the map and to a lesser extent in the upper right part of the map, which suggests that spillover may be proportional to geographic proximity.

We present the Volatility Heat Map for the period for the year of 2020. The more intense the color the higher the volatility spillover. We can see that there is now a darker region in the left part of the map, which suggests that the importance of geographic proximity was reduced. Figure 6 : We present the Volatility Heat Map for the period for the year of 2021. The more intense the color the higher the volatility spillover. We can see that the map is much brighter, with some small exceptions.

The analysis of the total volatility spillover effect, as shown in a timeline in Figure 7 , shows that the contagion transmission peaks between the markets occur in situations of crisis, result that is in line with that obtained in other studies, as was the case in the second half of 2008 with the subprime crisis and the first half of 2020 with the COVID-19 pandemic. The observed peaks occur with abrupt growth. The oscillation verified in 2020 is the largest in the historical series, with an increase of 99.76% in the total spillover. This effect occurred between 02/21/2020 and 03/16/2020 when the index reached a value of 79.8%. The peak observed in February 2020 exceeds by 2.8% the maximum reached during the 2008 crisis. The level of contagion before the crisis caused by the COVID-19 was one of the lowest in the historical series studied, being around a Spillover Index of 50%, giving more contrast to the COVID-19 Spillover index level. In 2021, we observed a reduction in spillover level, closing the year at a level close to the pre-pandemic level.

Countries had to take drastic measures to stop the contagion in the most intense period of infection by COVID-19 with a high number of cases, hospitalizations, and deaths. The main measures were border closures, abrupt reduction in international travel, social distancing, and lockdowns in many cases. These measures sought to reduce the contagion and pressure on each country's health system so that it would be possible to care for infected people, avoiding a collapse in the health area. Even with these measures, the spillover to banking systems increased in the COVID-19 period. This effect is due to several causes. As the severity of the pandemic increased in a country, its effects were felt acutely, and measures tended to be increasingly harsh to avoid contagion and preserve the health system. Each country had different impacts of the pandemic, and the countries looked to each other -to assess which measures worked and could help fight the pandemic. The financial market, particularly the banking system, could be severely affected by the pandemic. The risk of a sharp increase in non-performing loans and a substantial decline in bank assets was high and often difficult to measure. Uncertainty in the banking market was high, and as countries ran into problems, there was a chance that other countries might suffer from the same hardship. A vital channel -from expectations -may have operated strongly in the pandemic. As uncertainty increases in a given country, another country's risk would suffer similarly increased, leading to an increased spillover process.

J o u r n a l P r e -p r o o f 40 60 80 2 0 0 6 2 0 0 7 2 0 0 8 2 0 0 9 2 0 1 0 2 0 1 1 2 0 1 2 2 0 1 3 2 0 1 4 2 0 1 5 2 0 1 6 2 0 1 7 2 0 1 8 2 0 1 9 2 0 2 0 2 0 2 1 2 0 2 2 Figure 7 : We present the Total Spillover Effect for Volatility. The peak for the total volatility spillover effect occurs in 2020, with the beginning of the pandemic, surpassing spillover during the Global Financial Crisis. The spillover has a significant reduction as we include observations from late 2021.

The analysis of the variation in the Spillover effect during the COVID-19 crisis demonstrates that the countries that most added susceptibility to external risk in their banking markets were the ones that have historically received more negligible spillover effect, which has allowed to potentiate the impacts of global crises. On the other hand, the countries with a more historical Spillover Index were less impacted by the crisis. China and Hong Kong are the only countries that shows reduce in the spillover received during 2020 Italy was the country with the highest rate of spillovers in the year the pandemic began. For the year 2021, the countries showed a reduction in the level of spillover receipts compared to the 2005-2019 period, except for the United States, which was among the lowest spillover recipients in the period before the impact of COVID-19. The analysis of the 2021 ranking shows a generalized reduction in connectivity between banking markets, both for transmitting and receiving spillover.

We live in a connected world where financial institutions are present in several countries interacting with other financial institutions and with the real economy of each country. These financial institutions make resource allocation decisions such as investments and loans and often make global decisions from an international perspective. Resources are reallocated from one country to another according to each country's investment and earnings potential. When a country suffers 18 J o u r n a l P r e -p r o o f adverse shocks, that country's prospects can deteriorate. Investors and firms must make allocation decisions to contain losses and damages and evaluate new alternatives. Countries with similar problems or similar vulnerabilities can be seen as correlated, and decision-makers can reduce their risk exposure by making decisions that lead to a risk spillover between one country and another.

The situation of each country and banking system can change abruptly with the arrival of adverse shocks. Countries under-capitalized banking systems may be more vulnerable if a crisis could lead the economy into recession, further weakening the banking system due to expectations of rising defaults and bad loans. Countries with fiscal problems can also be seen as problematic since they will have problems developing public policies to mitigate any crises in the banking system. Likewise, countries with bank crisis resolution schemes may be less vulnerable to these shocks. In this way, different countries may suffer more from the volatility spillover effects according to their inherent vulnerabilities. These effects can even change over time as the economy changes and economic problems are mitigated or resolved, for example, by reducing fiscal risk. One of the most relevant risk assessment mechanisms in the banking system is the stress tests carried out by the authorities that oversee the financial system in each country. These stress tests are applied to large banks that could have systemic impacts if they incur financial problems. Stress tests assess the risks inherent in the loans made by these banks -especially in times of stress such as those generated by adverse shocks such as those caused by the COVID-19 pandemic. Our results suggest that in moments of exogenous shocks, the spillover between banking systems can increase, leading to moments of high volatility in some markets. These spillovers can be included in the performance of stress tests that seek to generate an early warning for financial supervision. These moments of high volatility may require more capital and assess whether, under this stressful scenario, banks have sufficient and significant capital to assess financial stability and guide banks' capital allocation and investment decisions.

The spillover between banking systems suggests that shocks from a banking system in one country can reach another country. It is crucial to assess the magnitude of the increase in risks in each case, and the financial supervisory authority can assess financial regulation measures that could be implemented. It should be noted that these moments of increased risks in the banking system are associated with the deterioration of credit conditions -with the banking system becoming more reluctant to take out loans. If the country is experiencing a recession, this movement can amplify this. This may be the case for triggering countercyclical capital requirements compensatory mechanisms. The trigger of compensatory measures is something that needs to be continually evaluated in order to improve the resilience of the financial system, as well as the economy.

An important question is whether the rapid increase in spillover between banking markets across our sample is due to the COVID-19 crisis. We recall that in 2020 the COVID-19 pandemic was the major event that took place in the world. We have witnessed the pandemic spread across all continents and countries. Millions of people were affected directly or indirectly, several countries closed down and imposed lockdowns, and several governments carried out actions to help the population, including the economy. The pandemic provoked a significant shock to health systems worldwide, which flooded with people infected needing care and assistance.

During the analyzed period, which started in 2005, only in periods of significant crisis such as the global financial crisis in 2008-2009 and the European sovereign debt crisis in 2012, the spillover was affected so much. During a crisis, the spillover increases and the connectedness increases. The intensity of this increase is an empirical question, and we can measure this increase in connectedness using our methodology. We observe an essential increase in spillover and connectedness between banking systems across the world, which suggests that exogenous shocks (such as a worldwide pandemic) can have relevant impacts on spillover levels. We include the year 2020 (with the first waves of COVID-19 contagion) and the year 2021 with the emergence of several variants of COVID-19. We observe an immediate increase in spillover in 2020 and that the spillover levels remained high for 2020 and present a reduction trend for 2021. Our results suggest that crises that have not originated in the banking sector (as it was during the global financial crisis -the subprime crisis) can significantly impact connectedness levels. Therefore, they must be accounted for during portfolio and risk management decisions. Real-time monitoring spillovers and connectedness during a crisis may be necessary to help understand the potential losses and help decision-makers design better public policies to overcome the crisis.

The rapid increase in volatility spillover is not a cyclical issue, as we see from our extensive 22 J o u r n a l P r e -p r o o f data sample (more than 15 years of observations - Figure 5 ). During this period, we do not see cyclical movements. However, we see fluctuations in response to stimuli received by the market, as is the case in 2008 under the subprime crisis or in 2011 and 2012 through the European public debt crisis. We observed in 2017-2019 a period of spillover stability (low spillover) with an immediate increase after the pandemic hit many countries across the world. Our results suggest that a global pandemic is a significant event that has increased spillover levels for the banking sector. Due to the significant expansion of their cross-border financial activities via global financial networks, an adverse shock to a major global or regional financial system might swiftly spread to local banking systems in emerging market nations as a result of advanced economies' deleveraging of internationally active banks (Park & Shin (2021) ). Demirgüç-Kunt et al. (2021) discover that while liquidity support, borrower assistance programs, and monetary easing all helped mitigate the crisis's detrimental effects, their influence differed significantly between institutions and nations. Pre-crisis vulnerabilities of countries (such as the fiscal situation) and the banking system explain, to some extent, the heterogeneity in the effects of the COVID-19 crisis.

It is necessary to analyze in more depth what are the main spillover transmission channels between banking systems in several countries. Some banks have branches in different countries. Depending on how they are managed, adverse shocks in one country are absorbed by its banking system and transmitted to others through these international branches. For example, financial losses in one country may lead banks to prepare for losses in another country or even restrict borrowing in another country if expectations are that shocks will also occur in that country. Further research can assess these effects using additional databases containing data on banks in each country, their investment strategies, and loan and liquidity management. And an essential line of future research.

The study allowed us to observe the existence of connectivity between the banking markets of the 35 countries studied, with the transmission and receiving spillover effect for volatilities. The tool used for measuring the spillover proved to be effective for observing and measuring connectivity between markets. We find that the size of the economy is one factor that influences the proximity and degree of spillover effects between countries, with a more significant relationship between economies of similar size. Another factor is geographic proximity, with more significant spillover between closer countries.

When we analyze the spillover effect in the 2005-2019 sample, countries with developed economies tend to be the most significant transmitters of shocks, while emerging countries tend to play a secondary role. Japan and the United States proved to be exceptions in this sample period, with a low spillover rate with other markets. For the 2020 period, we identified maximum spillover transmission values higher than those observed in the entire sample. Italy had the most significant spillovers during this period, which contains the initial impact of the COVID-19 pandemic, Italy had the most significant spillovers. In contrast, China had the least connectivity with the others. We remind that in the initial period of the COVID-19 crisis, Italy was the first country to reach enormous proportions of COVID-19 cases and deaths, which may be associated with the high level 23 J o u r n a l P r e -p r o o f of spillover sent to other markets. In 2020, China adopted strong protective measures for the circulation of the COVID-19 virus and economic incentives. For 2021, we observe an almost general trend towards reducing the level of spillover between the countries' banking markets. This occurred when countries went through different waves of contagion from COVID-19 and alternated between more restrictive measures and attempts to reopen.

The observations made can be used in risk diversification strategies between different world banking markets, looking for less susceptible regions to contagious relationships with the investor's primary market. A country's systemic risk mapping can be strengthened by including information on the locations from which it receives the most spillover effect. However, diversification strategy between countries may not be effective in situations of big global shocks.

The study period during the COVID-19 crisis demonstrates that the pandemic hit all markets abruptly, with the peak of contagion observed, in March 2020, higher than that observed in the 2008 crisis. In the case of a major global crisis, as noted by the impact in 2020, countries that historically have the slightest exchange of Spillover effects tend to be those that add the most external influence to their banking market. Countries with more active exchanges show a minor increase in the receipt of external influence in the shock of the crisis. In 2021, even under the impact of the pandemic, we observed a reduction in the level of spillover, closing the year at a level similar to that observed before the shock of 2020.

Why do some countries have a higher spillover level than others? There are several answers to this question. First, banks in some countries may have the same assets in their portfolios -which creates exposure to the same companies or economic sectors. If these sectors are the most exposed during the crisis, it would be natural that problems in a given country lead to spillover to the other. Second, banks may also have similar funding sources. This exposure to the same funding sources generates a common exposure that can lead to a more significant spillover effect between these countries' banking systems. Third, the intensity of the crisis may differ in each country depending on the conditions of its health system, its fiscal health, and the capacity to implement public policies that guarantee income to its most vulnerable citizens -who were left out of the labor market due to the pandemic, for example. More vulnerable countries are candidates to receive more spillover from other countries. Countries with banking systems with banks that have more relationships with banks in other countries can also generate more spillover. Several developed country banks have branches in developing countries. Shocks in the parent country can affect developing country banks -and we see an increase in spillover. Further research could exploit these potential channels as determinants of spillover across countries.

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