COVID-19 Pandemic and Financial Contagion

The original contribution of this paper is to empirically document the contagion of the Covid-19 on financial markets. We merge databases from Johns Hopkins Coronavirus Center, Oxford-Man Institute Realized Library, NYU Volatility Lab, and St-Louis Federal Reserve Board. We deploy three types of models throughout our experiments: (i) the Susceptible-Infective-Removed (SIR) that predicts the infections’ peak on 2020-03-27; (ii) volatility (GARCH), correlation (DCC), and risk-management (Value-at-Risk (VaR)) models that relate how bears painted Wall Street red; and, (iii) data-science trees algorithms with forward prunning, mosaic plots, and Pythagorean forests that crunch the data on confirmed, deaths, and recovered Covid-19 cases and then tie them to high-frequency data for 31 stock markets.


Introduction
The COVID-19 pandemic hit the world economy, without anyone knowing, at light-speed, leading to partial unemployment and factories' shutdown around the globe, leaving doctors, policymakers, businessmen, operational managers, data scientists, and citizens alike in disarray. The origin of the virus itself is not known with certainty, although most theories attach it to zoonotic transfer to the human species (Andersen et al. 2020).
As such, the COVID-19 virus outbreak represents a pandora's box. The original 45-day lock-down in most industrialized countries dated mid-March 2020 took everybody off-guard. This paper aims to address many viewpoints (e.g., business cycle analysis, operational research impediments, open-data science) during this traumatizing event.
With the quarantine in action in most industrialized countries from mid-March until the end-of-year 2020, many economist observers predict a deep recession for 2021-22. Stock markets plunged in March-April 2020, due to the shocking news of the virus spreading around the world.
Literature on the financial impacts of the COVID-19 is burgeoning. Akhtaruzzaman et al. (2020) examine how financial contagion occurs through financial and nonfinancial firms between China and G7 countries during the COVID-19 period. Ashraf (2020) finds that stock market returns declined as the number of COVID-19 confirmed cases increased. Among the main driving forces, government restrictions on commercial activity and voluntary social distancing are the main reasons behind the U.S. stock market plunge (Baker et al. 2020). On the Chinese stock market, Al-Awadhi et al. (2020) confirm that the daily growth in the total confirmed cases and total cases of death caused by COVID-19 both have significant negative effects on stock returns across all companies. Papadamou et al. (2020) suggest that Google-based anxiety regarding COVID-19 contagion effects leads to elevated risk-aversion in stock markets. Sharif et al. (2020b) analyze the connectedness between the recent spread of COVID-19, oil price volatility shock, the stock market, geopolitical risk, and economic policy uncertainty in 1 To elaborate on the notion of "contagion" in financial econometrics, usually, the definition by Forbes and Rigobon (2002) is retained as a significant increase in cross-market linkages after a shock to one country (or group of countries). According to this definition, if two markets show a high degree of co-movement during periods of stability, even if the markets continue to be positively correlated after a shock to one market, then this may not constitute contagion. According to Forbes and Rigobon (2002)'s definition, it is only contagion if cross-market co-movement significantly increases after the shock. If the co-movement does not increase significantly, then any continued high level of market correlation suggests strong linkages between the two economies that exist in all states of the world. The term interdependence is used to refer to this situation. In our setting, we merely employ financial econometrics techniques (e.g., GARCH, Dynamic Conditional Correlation (DCC), Value-at-Risk (VaR)) in order to describe the state of disarray on financial markets given the whole pandemic situation. We are not interested in measuring excess co-movements. The paper's original contribution lies in the data-scientist approach, instead mobilizing operational research techniques.
To retrieve data, we connected remotely to the servers of the John Hopkins Coronavirus Resource Center 2 , the Oxford-Man Institute Realized Library 3 , the Volatility Lab at New York University 4 , and the St-Louis Federal Reserve Board 5,6 . The time frame for the window of observations differs whether we access only recent (newest) data, such as COVID-19 cases, or whether we download the full history of data of prices for financial markets in order to document the current historical peaks. 7 The remainder of the article is structured, as follows. Section 2 details the latest medical evidence on the virus. Section 3 depicts the disarray of investors. Section 4 connects the epidemiological cases on COVID-19 to the contagion that was witnessed on financial markets from a data-science perspective. Section 5 concludes. Regarding the computational setting, the statistics are running via GNU software on an IA-ready UNIX workstation equipped with an i7-9700K @ 3.60 GHz × 8 CPU, 2 TB NVMe SSD, and 32 GiB RAM. 7 The data retrieved from the John Hopkins Coronavirus Resource Center is in daily frequency (COVID-19 reported cases). Data from the Volatility Lab NYU are presented in daily frequency (for GARCH and DCC estimates) and from the St-Louis Federal Reserve Board (VIX and Stress index). The data are only in high-frequency in the case of financial markets data from Oxford University servers. Figure 1 displays the exponentially increasing number of global COVID-19 cases that are characteristic of the pandemic (at the time of extraction from the Johns Hopkins repository). In May 2020, this highly contagious virus had spread over the five continents of the Earth and infected more than 4.2 million people in more than 187 countries (out of 198 in total). When writing the paper, the United States had the highest number of infected individuals, followed by China, Italy, and Iran.

Epidemiological
In the Appendix A, we provide additional insights on this exhaustive database, namely aggregated data that are ordered by confirmed cases, deaths, recovered cases, and active cases in Tables A1-A4. Besides, Tables A5-A7 present detailed statistics on the top-10 contributors (by country) in terms of confirmed cases, deaths, and recovered cases.

A Susceptible-Infective-Removed (SIR) Model for the World
In Figure 2, we provide the Susceptible-Infective-Removed (SIR) model by Bailey (1975) for the World.
This model supposes that we have a closed, homogeneously mixing population divided into X(t) susceptible, Y(t) infective, and Z(t) removed individuals at time t. The initial conditions are set to X(0) = N, Y(0) = a, Z(0) = 0 for some N, a. Because the population is closed, we have X(t) + Y(t) + Z(t) = N + a for all t ≥ 0, so that the epidemic is completely described by the process {(X(t), Y(t)), t ≥ 0}. The epidemic is assumed to a continuous-time Markov process on the state space: Transition probabilities are given by: All other transitions have probability ξ(δt), and the parameters β > 0, γ > 0, being known as the infection rate and removal rate, respectively. The process terminates when the number of infectives becomes zero, which will almost surely happen within finite time. Further mathematical derivation is covered, for instance, in Clancy (2014). The SIR model has been applied, among others, by Shamsi et al. (2018) for post-disaster vaccine provision. Table 1 presents the estimated parameters. According to the estimates, the "peak" of infections stemming from COVID-19 was reached on 3 March 2020, which justifies the 45-day lock-down that was implemented in most industrialized countries at the time. Figure 2 reflects the likely trends for the evolution of the epidemic.
The lock-down's intended effect is to witness a decrease in the contamination level from the COVID-19 and the number of infected. Having covered what medical science can tell us (at the time of writing) regarding the COVID-19 pandemic, we wish to envision how it impacted the world economy in the next section.

Asset Markets: The Nightmare Scenario
At the start of the global Covid-2019 pandemic in 2020, the financial markets entered a period of enormous financial stress. Corbet et al. (2020) indicate that the volatility relationship between the main Chinese stock markets and Bitcoin has evolved considerably during this tension period. Gunay (2020b) finds that the COVID-19 pandemic caused a different and more severe version of the contagion phenomenon in six different stock markets, such as the United States, Italy, Spain, China, the United Kingdom, and Turkey. Sharif et al. (2020a) assert that COVID-19 constitutes a significant threat for the U.S. stock market and carries geopolitical risk. The COVID-19 risk is perceived differently over the short-and the long-run, and it may be first viewed as an economic crisis.
The purpose of this section is to establish a quantitative assessment of the economic and financial consequences of the COVID-19 spreading worldwide, with a statistical assessment of (i) volatility, (ii) asset allocation, and (iii) risk management.

A Volatility Perspective
Things went south very quickly on stock markets. Global stock markets erased approximately six-trillion U.S. dollars in wealth in one week from 24 to 28 February due to fear and uncertainty and the rational assessment of investors that firms' profits are likely to be lower due to the impact of COVID-19. On 16 March 2020, the Dow Jones plummeted nearly 3000 points. Bonds, oil, and gold dropped in sync. During the week of 24 March 2020, the S&P 500 experienced its worst week since the 2008 sub-prime crisis. As can be expected, fear indexes exploded during that period, such as the VIX (which is computed from options on the S&P 500), or the Financial stress index computed by the St-Louis Federal Reserve board, which peaked at a year-on-year high (see Figure 3). In terms of macroeconomic fundamentals, a severe economic downturn is to be expected. Its depth can only be foreshadowed based on a preliminary inspection of industrial production data, which dropped considerablt with the 45-day lock-down that was implemented in most industrialized countries (see Figure 4). OECD countries, developing countries, and least-developed countries will experience differentiated impacts. For instance, some countries will be more severely impacted by others' closing of trading routes, depending on the price of commodities to be exported to international trade markets. Zhang et al. (2020) have already covered some ground on the COVID-19 sanitary crisis's financial aspects. By utilizing graph theory and the minimum spanning tree technique, they map the general patterns of country-specific risks and systemic risks in the global financial markets. Regional market integration/collaboration is likely to appear in the face of this major crisis. Bae et al. (2003) helps us to define contagion on financial markets by distinguishing between the terms "Epidemics" (when the virus effects are spread within geographical regions) and "Pandemics" (when its effects are prevalent across regions). The latter category is characterized by threshold events of "infection", similar to what we have witnessed in mid-March 2020. Real and financial consequences of such outbursts are to be expected.
The volatility during this window of time goes through the roof (e.g., documented as high as 49.93% in April 2020 based on a GARCH(1,1) analysis for the S&P 500 index), as presented in Figure 5. Besides, in Table 2, we verify that all of the parameters are positive and significant.
According to Bollerslev (1986), the latent volatility process can, indeed, be extracted by modeling the conditional variance in a Generalized Autoregressive Conditional Heteroskedasticity model: t is the conditional volatility and 2 t−1 the squared unexpected returns from previous period. Restrictions apply: ω >0 and α + β < 1. Table 2 contains parameter estimates for daily volatility. GARCH is now on the dashboard of all asset managers across the industry. The main parameters of interest are finding positive values (because we are dealing with variances) and statistical significance. The sum of alpha and beta shall be below unity (otherwise, it indicates the need to estimate GARCH-variants).

An Asset Manager's Perspective
For skilled traders in the derivatives markets, this pandemic might provide them opportunities to enhance their Profit & Loss statement. However, for most pension funds, mutual fund investors, and risk managers, there is "no place to hide" (Buraschi et al. 2014) in the cross-section of returns when dealing with conventional asset markets (e.g., stocks, bonds, foreign exchange, commodities) or even with gold Exchange-Traded funds. Figure 6 documents an unprecedentedly high level of correlation among international equities, peaking at 88.93% in April 2020, thereby strengthening the contagion scenario. Correlation analysis runs by construction from (−1) in blue to (+1) in red. There are opportunities for uncorrelated investment for the asset manager whenever the blue color is present (which is what he is looking for according to Markowitz portfolio theory). Only correlated market movements appear in the current context, which means that the asset manager has no solution to transfer his funds.
According to Engle and Sheppard (2001), correlations among assets can be captured through a Dynamic Conditional Correlation model. A general dynamic correlation structure follows: where S is the unconditional variance of the standardized residuals. i is a vector of ones. • is the Hadamard product of two identically sized matrices. If A, B, and ii − A − B are positive semi-definite, then Q will be positive semi-definite. R t is the time-varying correlation matrix. In Table 3, we verify that the DCC(1,1) correlation parameters are all positive and statistically significant. Table 3 presents correlation estimates (not volatility). We are interested in recovering statistically significant estimates with a sum of alpha and beta below one (otherwise, misspecification tests are required). The DCC matrix gives the level of correlation. In our case, it displays an all-time high correlation level of 88% across asset markets (henceforth, our research question of contagion due to the COVID-19 pandemic).
In the Appendix A, the interested reader may observe that the picture is the same across other asset markets (e.g., historical peak in correlations recorded for bonds and commodities in Figures A1 and A2). Foreign exchange markets are "frozen" due to the halt of international trade routes (i.e., the correlation is decreasing in Figure A3). For digital assets, such as Bitcoin, the deep price plunge that followed the aftermath of the S&P 500 market crash (as illustrated in Figure 7) tells us that they cannot be deemed as a store for value either. The correlation coefficient between SP500 and CBBTCUSD is computed as 0.83 since the beginning of the year 2020 8 . Hence, the popular wisdom that "cash is king" seems to currently prevail.

A Risk-Manager's Perspective
The Value-at-Risk (VaR), a that was concept popularized by Jorion (2000) 9 , has also known a "black-swan" (Taleb 2007) event during March-April 2020, with virtually all holdings from liquidity risks passing below the 5% threshold usually retained by risk managers. The realization of such an important risk measure from a risk management perspective is visible in Figure 8. This all circles back to the notion of systemic risk that is caused by the pandemic. Systemic risk refers to the disruption of an economy's financial system's proper functioning emanating from shocks from within or outside the financial system (Martínez-Jaramillo et al. 2010). While numerous policymakers are exploring the pandemic's economic impact, lessons that are learned from the global financial crisis demand the evaluation of financial stability concerning the effective management of the 8 Spearman rank correlation is equal to 0.84, and Kendall's tau is equal to 0.66. 9 The single-period (n = 1) 1$ VaR on percentage basis is defined by VaR % α = z α σ. VaR % 95% = (−1.645)σ and VaR % 99% = (−2.33)σ denote its 95% and 99% levels. pandemic and economy (Cukierman 2011). In the next section, we proceed to algorithmic processing of COVID-19 and financial data based on operational research techniques.

Linking the Disease to Predicted Economic Downturn
Data science comes in handy when in need for analyzing large chunks of data, as is the case with the depth of the epidemiological and clinical cases on COVID-19 on the one hand, and the heavy burden put on the servers by high-frequency financial data on the other hand.
We extract three main time-series for the world from the Johns Hopkins Coronavirus Center repository: 1.
"ts-deaths": time series data of fatal cases, and 3.
"ts-recovered": time series data of recovered cases.
These series have been thoroughly sourced by Section 2, and further documented in the Appendix A. We wish to reconstitute the series of events that stemmed from the COVID-19 outbreak to contagious effects on worldwide stock markets.
For this purpose, we encompass the closing returns from 31 stock markets based on the Oxford 'Realized Library' with an intra-daily frequency that reaches millions of transactions (2,587,175 at the time of accessing it). Tick-by-tick data are sampled over the five-minute horizon in order to avoid microstructure noise (see Barndorff-Nielsen et al. (2008) for the theory). Table 4 details the list of assets.
As a preliminary step, both databases of COVID-19 epidemiological cases and high-frequency financial data are merged by the time index.

Hierarchical Decision Tree for Visualizing the Influence of "ts-Confirmed" on Worldwide Stock Markets
In this section, we mobilize a tree algorithm with forward pruning (Breiman et al. 1984;Quinlan 1986;Smith and Nau 1994) in order to connect the epidemiological cases of COVID-19 (Section 2) to the downward market trends that were observed on stock markets (Section 3).
To feed the decision tree algorithm with stationary data, (i) COVID-19 cases are transformed to first-differences; and, (ii) stock markets data are transformed to log-returns. 10 This pre-processing step will allow for efficient splitting criteria.
The tree algorithm splits the merged data into nodes by class purity, with "COVID-19 cases" as the source and "Stock markets" returns as targets. Formally, let us write an adaptive basis-function model: where R m is the m'th region and w m is the mean response in this region. v m encodes the choice of variable to split on, and the threshold value, on the path from the root to the m'th leaf. The basis functions define the regions, and the weights specify the response values in each region (see Breiman et al. (1984); Quinlan (1986) for an introduction). Use the following split function to find the optimal partitioning of the data: with T j the set of possible thresholds for feature j by sorting the unique values of x ij to a numeric value t. The most common approach is to consider splits x ij = c k or x ij = c k for each class label c k . When growing a decision tree, we can prevent over-fitting if the extra complexity of adding an extra sub-tree is not justified. The standard approach is to grow a "full" tree, and then to perform pruning. This methodological approach prevents data fragmentation, i.e., too little data fall into each sub-tree.
In order to determine how far to prune back, the scheme is to evaluate the branches on each sub-tree and pick the tree that gives the least increase in the chosen statistical error. To measure the quality of a split, we can resort to: (i) a multinoulli modelπ c = 1 |D| ∑ i∈D I(y i = c) with D the data in the leaf by estimating class-conditional probabilities, (ii) a misclassification rate by defining the most probable class labelŷ c = arg max cπc and the corresponding error rate 1 |D| ∑ i∈D I(y i =ŷ) = 1 −πŷ, 10 We can transmit unit root tests to interested readers to ensure that the series is I(1) as such.
(iii) minimizing the entropy between the test leaf data and class label H(ß) = − C ∑ c=1π c logπ c , (or maximizing the information gain, see, e.g., Quinlan (1987)), or c , withπ c the probability of a random entry in the leaf belongs to the class c, and (1 −π c ) the probability of mis-classification.
In this paper, we favor cross-entropy and Gini measures.  Figure 9 shows the result of the COVID-19 pandemic, as measured by the confirmed cases worldwide, on stock markets' panic during 2020-01-22 to 2020-05-05 (when last accessed the JHU repository at the time of writing the paper). Figure 9 shows the connection between financial markets. At the top of the tree is the financial market from which the contagion stems at the beginning of the health crisis. At the bottom of the tree, we find spillovers from the original contagion effect.
The resulting tree and decision boundaries are quite complex, even with prunning. The "top" stock market from which the COVID-19 pandemic spread is detected to be the French CAC 40 index due to the hierarchical nature of the tree-growing process (FCHI, perhaps due to the announcement of the French president to lock-down the country on 16 March 2020).
Besides, we identify two main "paths" from which the pandemic spread to other financial markets: 1.
On the left-hand side, we have the Australian All Ordinaries index (AORD). From Australia, financial contagion is then visible on sub-trees navigating through US small caps know as Russel 2000 (RUT), the Korean Kospi index (JS11), the UK FTSE, and then at the bottom of the tree reaching India's NIFTY 50 (NSEI), Pakistan's Stock Exchange (KSE), the US Standard & Poor's 500 (SPX) or the Japanese NIKKEI (N225). Stemming from the overarching "top" of France and first "branch" Australia, we notice as well other sub-trees channeling though the US Dow Jones Industrial Average (DJI) with more pronounced regional effects on Canada's (GSPTSE) and Mexico's (MXX) stock exchanges until we reach the bottom of the tree.

2.
On the right-hand side, we identify the EURO STOXX 50 (STOXX50E). Contagion occurs immediately on the first sub-tree on the Amsterdam stock exchange (AEX) with spillovers in Switzerland (SSMI), Sweden (OMXSPI), and Norway (OSEAX), until Denmark (OMXC20) at the bottom of the tree. On the second sub-tree (far right of Figure 9), we visualize that the financial crisis ultimately reaches other European countries, such as Spain (IBEX), Belgium (BFX), and Finland (OMXHPI). Inter-regional spillovers to Brazil (BVSP, through Spain) and Singapore (STI, through EURO STOXX) are also visible at the bottom of the tree.
This first strand of the result suggests that contagion first occurred on European and Australasian stock markets, as the number of COVID-19 confirmed cases was precisely documented and raised swift public policy responses. If, instead, we plug in the time series "ts-deaths" or "ts-recovered", we verify that the decision tree that is reproduced in Figure 9 is stable, i.e., small changes to the input data (of the same information content) do not have substantial effects on the structure of the tree. 11 4.2. Experimenting Mosaic Plots with the Series "ts-Death" on 2020-03-16 Next, in Figure 10 we inspect a Mosaic plot for the day 2020-03-16 that seemed so important as to place France at the top of the hierarchical tree. Recall that the French president implemented a 45-day lock-down of the country on that date, which seems from our preliminary data analysis to have wreaked havoc on financial markets.
Mosaic graphs allow visualizing data across two or more dimensions. They are handy when attempting to capture the relationships between different variables, as in our setting. The Mosaic plot's statistical analysis as a contingency table is covered by Friendly (2002).
In Figure 10, the dimensions we are plotting are the following: • bottom: date chosen for the Mosaic is specifically 2020-03-16; • left: closing daily prices for stock markets; • top: intra-day transactions on stock markets; and, • right: number of deaths reported worldwide on that day according to JHU/CCSE repository. Figure 9. Tree for Origin "ts-confirmed" and Target "Stock markets". Note: The origin of the tree is COVID-19 confirmed cases worldwide. The Estimation period is 22 January 2020 to 5 May 2020. The first column of Table 4 provides tickers for Stock markets. The end result unequivocally paints a "red" picture of how the pandemic, and the incredibly worrying trend in deaths worldwide, has spread to financial markets, with some of them even briefly suspending trading (such as the NYSE) during these troubling events. This picture illustrates perfectly, that, in our opinion, for money managers in such a contagious financial environment with spillovers of downward closing prices on each stock market, there is "no place to hide". Had we found other colors predominant on the Mosaic (e.g., shades of blue or green), we could have advised moving the funds safely here or there, but there is not such a place (other candidates "safe-havens", such as Gold or even Bitcoin, have been discussed in Section 3).
To grasp the meaning of Figure 10 visually, the reader can view it as a carpet plot linking returns on financial markets. Usually, when such a plot is posted on Twitter about Wall Street blue chips, it shows the extent to how a piece of news (say, the Boeing 737 MAX industrial disaster) has expanded into stock markets. They are usually in a net winners or net losers situation. Against the COVID-19 pandemic, what Figure 10 shows, is that there are only losers on financial markets in such circumstances, highlighting the fact mentioned in the previous Section that there is no place to hide for asset managers to build alpha strategies.

A Final Look at the Pythagorean Forest of Influence of "ts-Recovered" on Stock Markets
If we seek to end this paper on a more positive outlook, then we might move the decision tree upside-down and present it as a forest. To that end, we employ the series "ts-recovered", which should be a reason for "rebirth" for the economy, as some patients naturally heal from the COVID-19 (in the absence of effective treatment at the time of writing, waiting for clinical experiments from Pfizer and Moderna vaccines).
In Figure 11, we reproduce a Pythagorean Forest, which visualizes how from the tree trunk of "ts-recovered" new branches and leaves can grow back on financial markets. The Pythagorean Forest stems from a decision tree model, called "random forest", where each visualization pertains to one randomly constructed tree. Its construction is covered by Beck et al. (2014).
Without loss of generality, consider Pythagorean Trees (H v , S) :, where H v = (V, E) is a binary hierarchy of V = {v 1 , . . . , v k } set of k vertices and E ⊂ V × V finite set of edges. S = (c, ∆s, θ) is the initial square with center c, length of the sides ∆s, and slope angle θ. The recursive procedure first draws square S and proceeds if the current hierarchy still contains more than a single node. Subsequently, encoding the node weights in the squares' size, the angles α and β are computed according to the normalized weight of the node opposed to the angle. The width ∆x i of a rectangle R i can be changed by modifying the corresponding angle α i accordingly. It should reflect weight w x (v i ) of a vertex v i in relation to the weight of its siblings: The width of the rectangle is ∆x i := ∆x × sin α j 2 , where ∆x is the width of the parent node.
A maximum branching factor can be implemented. The human reader automatically connects the rectangles on the curve, which is denoted as the law of continuation. Figure 11 represents another kind of tree: a "forest", so to speak since we are concerned here with patients that recovered from the COVID-19. The goal is to show by a myriad of colors how the increased number of healing is being transmitted to the various stock markets in the database under increased market gains. Although being complex to construct, such fractal images exhibit aesthetic properties, which makes these images easier to interpret. The Pythagorean Forest emphasizes the influence of the root-which is "ts-recovered"-and its hierarchical influence on subsets down to the level of unitary stock markets. The root node fills the graph with white color. Its immediate descendants can be understood as higher-level nodes of the forest.
The image shows that, among the leading directories, the most meaningful parent-child relationships are to be found with the EURO STOXX 50 (Stoxx50E) in red color; the Amsterdam (AEX), Brussels (BFX), and Australian (AORD) stock markets in orange color; the French CAC 40 (FCHI) and Dow Jones Industrial Average (DJI) in light green color; and, the Nordic stock markets of Copenhagen, Helsinki, and Stockholm (OMXC20, OMXHPI, OMXSPI) in purple colors. This finding confirms the decision tree based on "ts-confirmed", where we dated back the origins of the financial contagion to European and Australasian market, and the U.S. as a repercussion of lock-down implemented in these countries beforehand.
If we move away from the most prominent nodes to the forest's secondary level, then we can notice other sub-vertices, each displaying their own set of edges. The granularity of the results obtained with this visualization tool is remarkable without zooming too much into detail. It is perceptible how the world economy can "heal" from the Coronavirus as more patients recover from it down to the level of individual stock markets. For instance, on the forest's right-hand side, we can see the effects of recovering Amsterdam or Brussels stock exchanges on the Milan or Frankfurt market places (FTMIB and GDAXI, respectively, in light green)-hence, these nodes are connected in the sub-hierarchy of the forest.
Overall, we gained an overview of the main branches connecting the COVID-19 epidemiological cases to the world stock markets. This result's beauty is that we achieved it without restricting, a-priori, the number of vertices (e.g., arbitrary hierarchies are allowed).
To further explain our results intuitively, we point out that asset markets are susceptible to the news. Whenever pharmaceutical companies, like Pfizer, or start-ups, like Moderna, announce 95% of positive results on their COVID-19 vaccines, the financial markets react very positively with day-to-day increased returns. In our sample, the intuition is that COVID-19 cases are quickly developing worldwide, which incites stock markets to decline and be linked altogether into a recession circle. However, the extra data-science experiment illustrates that the global economy can be seen as a tree whose leaf can become green again (as patients heal, or the vaccine will be mass-administered). Therefore, financial contagion would bring a new virtuous circle of prosperous economic growth in the globalized economy. Figure 11. Pythagorean forest for series "ts-recovered" and "Stock markets". Note: the origin of the forest is COVID-19 recovered cases worldwide. The estimation period is 22 January to 5 May 2020. Tickers for Stock markets are given in the first column of Table 4.

Concluding Remarks
As a proteiform disease, COVID-19 is drowning the macro-financial environment into a recession that it is too early to foreshadow. All in all, confronting several stakeholders' views amid the COVID-19 outbreak has brought this research a myriad of facts. By merging health and stock market databases, three types of robust scientific methods have been mobilized in this paper: financial from quants' viewpoint; and, 3.
algorithmic from a data scientist's viewpoint.
The original contribution is to document the effects of the COVID-19 pandemic on financial contagion. For the wide dissemination of research results, this paper has opted for a low-key approach on the technicalities that underlie the models estimated as a methodological choice of the authors.
Whereas decision trees and mosaic plots revealed a heavy concentration of stock markets plummeting on 16 March 2020 (following a peak of infection detected on 3 March), brighter perspectives of re-birth: of the economy have been envisioned based on a Pythagorean forest that illustrates the positive effects of more patients "healing" from the disease.
Given the level of integration of the global financial system, the eminent risk of financial contagion may further accentuate the global systemic risk. While economies currently at different growth paths are faced with unique macroeconomic conditions that determine the stability and resilience of their respective financial systems, the different policy responses that are adopted by different economies in combating the pandemic will, to a large extent, determine the severity, duration, and management of both the health and consequent crisis with spillover effects expected (Battiston et al. 2012).
In this regard, while the policy response in one country may help to shield the economy from domestic adverse economic effects, cross-border financial system interactions may enhance global financial distress, as vulnerability from one economy is transmitted to other financial systems. Ultimately, interdependence and the presence of financial contagion mean that the financial system is as stable as its weakest link.
Therefore, global economies' ability to effectively manage the impending crisis will depend on: (i) the effectiveness of individual policy response and (ii) the global financial systems' ability to effectively absorb negative spillovers and adverse economic shocks. Systemic risk management will play a key role in enhancing financial systems' resilience and providing much-needed financial intermediation services to the economy. In this regard, continuous analysis and monitoring of the financial system's ability remain paramount to realize overall macroeconomic stability (Gunay 2020a).
The study implications relate to the cataclysmic impact of the COVID-19 pandemic on financial markets. The recession is expected to be severe. Financial contagion is in motion, not only across asset markets, but also across countries. The "silver bullet" to get out of the danger zone would be the swift deployment of vaccines in the years 2021-22 in order to achieve community resistance to COVID-19.
Regarding future research in this area of banking and finance, the type of data that are needed to analyze systemic risk and contagion would include (i) individual banks balance sheet and financial ratios, (ii) cross-sector loans and bonds from financial institutions to the real economy sector, and (iii) cross border loans and bonds.
The study limitations are based on the restricted data sample at the beginning of the pandemic. Several years of observations on the consequences of the COVID-19 on global economies will help to put this first set of results into perspective as data gathering evolves in the scientific community.