3.1.1 Financial data for systemic risk calculation (1998–2024).

To analyze the transmission of systemic risk across markets, this study employs daily closing prices of stock market indices from forty-six countries, covering major financial regions including North America, Europe, and Asia. This dataset spans from January 5, 1998, to September 20, 2024, enabling an extensive study of tail risk dependencies and intermarket contagion. The data is sourced from the WIND database. Due to some missing values in the initial dataset, data preprocessed was conducted, removing dates with a high proportion of missing values. After processing, a total of 40,343 daily data entries were selected.

To ensure consistency in risk measurement, daily closing prices are transformed into logarithmic returns:

(1)

where represents the closing price of market at time .

3.1.2 CCPI data (2007–2024).

In this study, we incorporate the CCPI as a measure to assess the influence of climate-related factors on systemic risk transmission across global financial markets. The CCPI, developed by Germanwatch, the New Climate Institute, and the Climate Action Network, evaluates the climate protection performance of over 60 countries, covering more than 90% of global greenhouse gas emissions. The index assesses countries on four main categories: GHG Emissions, Renewable Energy, Energy Use, and Climate Policy. These categories are weighted to form an overall CCPI score that reflects the commitment of each country and effectiveness in addressing climate change.

Our dataset for financial returns spans from 1998 to 2024, while the CCPI data begins in 2007. To ensure consistency, we apply a matched time window approach, aligning the CCPI data with the corresponding financial data from 2007 onward. This time window alignment allows us to examine how shifts in CCPI scores, reflecting changes in climate policy and emission levels, correlate with tail risk dynamics in financial markets. As shown in Fig 1, the Log Returns and CCPI vary across countries. The left side illustrates each country's log returns, capturing market volatility across different periods. The panel on the right presents CCPI scores, which reflect the climate performance of each country. Higher CCPI scores indicate stronger climate action, while lower scores suggest weaker performance. The plots highlight the relationship between financial market behavior and climate policy effectiveness over time.

Download:

• PNG
  larger image
• TIFF
  original image

Fig 1. Scatter plot of log returns and CCPI across countries.

https://doi.org/10.1371/journal.pone.0337401.g001

3.2.1 QRNN model construction.

The QRNN model takes the lagged returns of a time series as input variables, with the loss values at different quantile levels as output. The QRNN structure consists of an input layer, a hidden layer, and an output layer. The input layer receives the lagged return series as explanatory variables, the hidden layer captures the complex nonlinear relationships between the variables, and the output layer generates the VaR forecast values at specified quantile levels.

Let the target variable be and the quantile level be . The QRNN model can be represented as follows:

(2)

where is the weight connecting the input layer to the hidden layer， is the activation function of the hidden layer, is the bias term, is the activation function of the output layer.

By optimizing the loss function, the QRNN can flexibly adjust the weights to estimate the corresponding VaR values at different quantile levels.

3.2.2 Loss function and parameter optimization.

To optimize the parameters of the QRNN model, a quantile regression loss function is used, defined as follows:

(3)

where represents the quantile loss function, which measures the deviation between the predicted and actual values. The objective of this loss function is to minimize the prediction error at different quantile levels, ultimately achieving accurate estimation of VaR.

3.2.3 VaR and ES calculation.

VaR is defined as the maximum potential loss over a given time horizon such that the probability that the loss exceeds this value does not exceed 𝜏. Based on the trained QRNN model, we forecast the VaR at a specific quantile level according to the input variables. For the VaR at time , the expression is given by:

(4)

where denotes the conditional quantile function at level , represents the return series, is the lag order, and indicates the target quantile level.

To further characterize extreme losses beyond VaR, ES is employed as a supplementary risk measure, defined as:

(5)

where α denotes the quantile level and measures the expected loss conditional on returns falling below the VaR threshold at level . By calculating the conditional expected loss exceeding VaR, ES provides a more comprehensive reflection of market risk exposure.

3.2.4 Algorithm optimization: Sparrow search algorithm (SSA).

To enhance the accuracy of QRNN in estimating VaR and ES, we employ the Sparrow Search Algorithm (SSA). SSA is inspired by sparrow foraging behavior, with roles divided into producers, scroungers, and sentinels to efficiently explore and exploit the search space.

1. Step 1: Initialization
2. Initialize the positions of each sparrow in the population, where each position represents a candidate solution (parameter set) for the QRNN model.
3. Step 2: Producer Update
4. Producers search for better solutions by updating their positions as follows:

(6)

1. where is a random number between 0 and 1, is the safety threshold, and and are constants controlling exploration.
2. Step 3: Scrounger Update
3. Scroungers adjust their positions relative to the best solution found by producers:

(7)

1. where is the current worst position, K is a control parameter, and i ranks each sparrow.
2. Step 4: Sentinel Update
3. Sentinels detect poor solutions and signal other sparrows to avoid these areas, helping prevent local optima entrapment. This step does not require a formula but is crucial for the adaptive capacity of SSA.
4. Step 5: Termination
5. Repeat Steps 2–4 until the convergence criteria are met. The optimal solution found by SSA is used to fine-tune the QRNN model parameters.

Using SSA for optimization significantly improves the ability of QRNN to capture tail dependencies, leading to more accurate VaR and ES estimations for systemic risk assessment. The Sparrow Search Algorithm balances exploration and exploitation of the search space by simulating sparrow foraging behavior, helping optimize QRNN parameters to improve sensitivity and accuracy in tail risk prediction.

3.3.1 ∆CoVaR and ∆CoES in risk contagion.

∆CoVaR describes the systemic impact that one market brings to another when it is in an extreme state. It is defined as follows:

(8)

where and represent the CoVaR of market to market in extreme and median states, respectively. ∆CoVaR forms an undirected network between different markets, which is used to depict extreme tail risk contagion channels between markets.

∆CoES further enhances the characterization of extreme risk contagion. It reflects the potential loss between markets under the situation of extreme systemic risk. It is defined as follows:

(9)

where and represent the conditional expected shortfall in high-risk and median-risk states, respectively. ∆CoES provides additional information about the tail risk beyond VaR, which is used to assess the degree of systemic contagion in extreme tail risk environments.

When calculating risk contagion, to accurately reflect the heterogeneous relationships between markets, we introduce independent weighting coefficients for ∆CoVaR and ∆CoES, respectively, to capture the strength of contagion between markets. Measures the impact of market on market in terms of VaR contagion. Measures the impact of market on market in terms of expected shortfall contagion.

In the proposed tail risk network, the weight of a directed edge from market to market is defined by the magnitude of the estimated ΔCoVaR or ΔCoES, which quantifies the incremental increase in the conditional tail risk of market when market experiences an extreme downside shock. As such, the edge weight represents a pairwise and nonlinear measure of bilateral tail risk spillover rather than a correlation association. From a theoretical perspective, ΔCoVaR and ΔCoES capture conditional tail risk transmission rather than unconditional linear dependence. Unlike correlation coefficients, which measure average co-movements around the center of the distribution, ΔCoVaR focuses on how the distress of market shifts the lower tail risk distribution of market This conditional framework reflects a structural transmission mechanism under extreme states, consistent with the theory of financial contagion and tail dependence. Therefore, the bilateral relationship quantified by this study represents a directional and state-dependent risk spillover channel, instead of a symmetric linear association.

3.3.2 Cascade effect model.

When systemic risk events occur, risk contagion between markets is not static but gradually spreads over time, forming a cascade effect. To model this process, we define a dynamic contagion model to describe the state changes of markets in the process of risk contagion. Let represent the risk state of market at time . The state change is affected by external risk impacts:

(10)

where represents the risk impact on market at time due to external contagion, calculated as:

(11)

where is the total received risk impact on market at time , given by:

(12)

When exceeds , market is triggered into a risk state, forming a new source of risk contagion, thus driving further spread of risk within the network.

3.3.3 Final calculation of systemic risk contribution (SRC).

Based on the above ∆CoVaR, ∆CoES, and cascade effect models, the systemic risk contribution of market can be expressed as the sum of its own risk indicators and the additional risk from contagion by external markets:

(13)

where:

and represent the unconditional VaR and ES of market i, respectively.

denotes the risk contribution of market j to market i in terms of VaR contagion.

denotes the risk contribution of market j to market i in terms of ES contagion.

3.4.1 CCPI as an exogenous factor in risk transmission.

CCPI is a composite index that measures climate policy and performance for countries and regions, quantifying both physical risks from extreme climate events and transition risks from climate policy changes. In this study, CCPI is introduced as an external shock variable, representing how climate risk influences systemic risk transmission in financial markets. To ensure consistency in climate risk volatility within risk analysis, CCPI data is standardized and matched with financial data through a rolling time window to capture the temporal effects of climate risk.

CCPI acts as a factor influencing the propagation path of systemic risk, incorporated into the calculations of and , thus enhancing the responsiveness of the model to climate risks. Variations in CCPI reflect the dynamic changes in policy and climate factors, providing a broader perspective to capture the impact of climate risk across different time windows.

3.4.2 CCPI adjustment in ∆CoVaR^CCPI and ∆CoES^CCPI.

To precisely quantify the marginal effect of CCPI on tail risk contagion between

markets, CCPI adjustment terms are added to the calculations of and . The adjusted models are as follows:

(14)

(15)

where and represent the marginal sensitivity coefficients of CCPI on and , quantifying the amplification or mitigation effect of climate factors on tail risk contagion between specific markets. This adjustment enables the model to capture the dynamic dependency of tail risks influenced by climate factors, thus offering a more refined tail risk dependency analysis. To ensure the stability and validity of sensitivity coefficients, HAC standard error correction is performed to mitigate the effects of autocorrelation and heteroscedasticity on estimation results.

3.4.3 CCPI effect in cascade failure process.

In the dynamic risk transmission process, CCPI is further integrated into the cascade failure model to quantify the chain reaction induced by climate shocks. Specifically, whenever CCPI exceeds a certain threshold and drives market risk upward, that market will trigger tail risk state changes in other markets through accumulated risk. The triggering mechanism is given as follows:

(16)

(17)

where represents the risk impact on marketat time due to external contagion. When exceeds the of market, it triggers a tail risk state in market , forming a new source of risk contagion and driving further risk spread within the network. The fluctuations in CCPI further impact , affecting the cascading process of risk transmission.

3.4.4 Adjusted systemic risk contribution (SRC) with CCPI.

To incorporate the effect of the CCPI into the SRC calculation, we modify the original SRC formula as follows:

(18)

where:

represents the CCPI-adjusted CoVaR contribution.

represents the CCPI-adjusted CoES contribution.

This adjusted SRC formula quantifies the impact of climate change performance on systemic risk transmission by incorporating the CCPI adjustment. Changes in CCPI affect the values of ∆CoVaR and ∆CoES, thereby influencing the overall SRC calculation.

3.4.5 Systemic importance and sensitivity analysis.

In the constructed risk spillover network, CCPI is treated as a source node to evaluate its systemic importance within the transmission pathways. To measure its role in risk transmission under different market states, we apply the HITS algorithm to assess the Hub and Authority scores of the CCPI node. The Hub score represents CCPI’s ability to transmit risk to other markets, while the Authority score reflects its vulnerability as a target for risk transmission. These metrics help illustrate the dynamic influence of climate change on market structure and systemic risk.

Additionally, sensitivity analysis of the network is conducted to assess the risk transmission effect of CCPI under different market conditions. Variations in systemic importance as CCPI rises or falls provide insights into the influence of climate risk on global systemic risk across stable, volatile, and extreme conditions. This analysis offers early warning insights for policymakers to address the systemic financial risks associated with climate change.

Fig 2 illustrates the cascading process of tail risk transmission across multiple markets, incorporating financial risk and climate risk. The green halo emphasizes the climate risk exposure for each market, increasing the likelihood of triggering tail risk events and amplifying systemic risk contagion effects.

Download:

• PNG
  larger image
• TIFF
  original image

Fig 2. Tail risk cascading process under climate change (CCPI) influence.

Note:(A) Cascading Transmission Process: – Step 1: Node i triggers tail risk (TR ≥ VaR) and propagates risk to node j. – Step 2: Node j accumulates risk and transmits it to nodes k and l. – Step 3: Node k’s TR ≥ VaR, further spreading risk to nodes l and m. – Step 4: Nodes l and n are impacted by risk, propagating to node n. – Step 5: Node n is the last affected node, concluding the cascading process. (B-D) Node Status Descriptions: – Normal Node (B): Node is in equilibrium (TR = VaR). – High-Risk Node (C): Node has triggered tail risk (TR ≥ VaR). – Low-Risk Node (D): Node has accumulated risk but remains stable (TR < VaR). (E) CCPI Influence (Green Halo): – The green halo represents the Climate Change Performance Index (CCPI) of each market. – A larger or darker halo signifies superior climate governance performance, higher policy transparency, and more effective emission mitigation. – Within the cascading failure process, a higher CCPI acts as a risk buffer. It enhances market resilience, thereby reducing the probability of the node triggering a tail risk event and mitigating the intensity of risk contagion to other nodes. Pathway Indicators: – Red Solid Arrow: Indicates risk transmission between nodes (TR ≥ VaR). – Red Dashed Arrow: Indicates potential but currently inactive links. – Gray Arrow: Indicates normal linkages without risk transmission.

https://doi.org/10.1371/journal.pone.0337401.g002

4.2.1 QRNN result analysis.

To measure the SRC of major global indices, this study first employed a QRNN model, refined with the SSA algorithm, to estimate the VaR and ES for 46 global financial market indices. Given the large number of indices, we selected four representative indices based on their volatility levels to provide a clearer illustration of risk characteristics under different market conditions, covering both high and low volatility markets.

Volatility was measured by calculating the standard deviation of log returns for each index. Ultimately, Venezuela and Argentina, which exhibit the highest levels of volatility, along with Australia and New Zealand, which display the lowest levels of volatility, were selected as representative samples. Fig 4 presents a comparison between log returns shown in black and the QRNN estimated VaR thresholds shown in red for each selected market. In markets characterized by high volatility, log returns frequently approach or exceed the VaR threshold, indicating a higher degree of tail risk. The QRNN model effectively adapts to these large fluctuations, providing dynamic risk boundaries to capture extreme risk events.

Download:

• PNG
  larger image
• TIFF
  original image

Fig 4. Comparison of log returns and VaR estimates for selected markets.

Note: The subscript H represents high-volatility countries (Venezuela and Argentina), while L indicates low-volatility countries (Australia and New Zealand).

https://doi.org/10.1371/journal.pone.0337401.g004

In contrast, for low volatility markets, the VaR line remains consistently below the log returns, suggesting lower tail risk, which aligns with the stability of their economic and policy environments. This analysis highlights distinct risk characteristics between South American and Oceania markets. These regional characteristics provide valuable insights for cross-regional risk management and investment decision-making.

In the model performance evaluation, we conducted a backtesting analysis comparing the QRNN model with other commonly used risk measurement models. The in-sample data accounted for 80%, while the out-of-sample data constituted 20%. We selected five of the most commonly used VaR and ES models for comparison with the SSA-adjusted QRNN model, including EGARCH, Historical Simulation (HS), Filtered Historical Simulation (FHS), Variance-Covariance (VCV), and Extreme Value Theory (EVT). We conducted backtesting through the Kupiec likelihood ratio test.

First, we calculate the number of times each model’s predicted VaR value exceeds the actual log returns, denoted as the violation count . The violation rate is calculated as , where represents the total number of observations in the sample. Each model was evaluated under a confidence level of ninety-nine percent during the empirical analysis. The likelihood ratio statistic (LR) is used to assess whether the model’s predicted violation rate aligns with the observed violation rate:

(19)

where is the theoretical violation rate, and F is the observed violation rate.

Table 3 shows the backtesting results of various models for estimating VaR across global markets. QRNN outperforms traditional models in both in-sample and out-of-sample tests, with a lower Kupiec LR and relative error (RE), indicating superior predictive accuracy and stability. In the in-sample analysis, QRNN achieves a LR of 2.05 and an RE of 0.05, both lower than those of other models, suggesting better accuracy and error control. In the out-of-sample test, QRNN maintains its advantage, with a Kupiec LR of 1.85 and an RE of 0.03. Other models, like HS and EGARCH, show higher default rates and RE values, underscoring QRNN’s effectiveness for global market risk measurement. In addition to VaR estimates, the ES values were also analyzed to capture tail risk beyond the VaR threshold. Results indicated that the QRNN model consistently estimated ES in alignment with high volatility markets, providing further insights into extreme risk behavior in these regions.

Download:

• PNG
  larger image
• TIFF
  original image

Table 3. Model backtesting and performance evaluation.

https://doi.org/10.1371/journal.pone.0337401.t003

4.2.2 Quantifying risk spillover through ∆CoVaR and ∆CoES.

In this section, we explore the systemic risk contribution and contagion between major global indices through ∆CoVaR and ∆CoES, which represent the conditional risk transmission from one market to another. Based on the bilateral tail risk spillovers captured by ΔCoVaR and ΔCoES, the global financial system can be conceptualized as a network of conditional risk transmission. In this network, nodes represent national stock markets, while directed and weighted edges reflect the magnitude of tail-risk spillovers from one market to another. This network representation is theoretically grounded in financial network and contagion theory, where systemic risk emerges not only from individual market risk but also from the propagation of extreme shocks through interconnected channels. Consequently, the constructed network captures the structural topology of tail risk transmission, rather than merely visualizing pairwise statistical correlations.

Figs 5 and 6 present a comparative visualization of the ∆CoVaR and ∆CoES networks, illustrating the systemic risk transmission channels among global financial markets. Fig 5 reveals a dense interconnection, particularly among major financial markets, indicating strong bilateral risk spillover effects. The predominance of red links signifies intense risk transmission, suggesting that shocks originating in one market have substantial potential to propagate across the network, impacting other markets. Notably, the denser clustering of nodes suggests high interconnectedness and mutual influence within regional blocks. Fig 6 offers additional insight into expected shortfall spillovers under extreme conditions. This network structure appears similarly interconnected but exhibits some nuanced differences in the intensity and direction of risk transmission compared to ∆CoVaR. Purple links dominate, highlighting the markets where extreme negative returns contribute to systemic risks. The ∆CoES network illustrates a broader spread of potential extreme losses, pointing to markets that serve as significant sources and receivers of systemic risks under crisis conditions.

Download:

• PNG
  larger image
• TIFF
  original image

Fig 5. Visualization for ∆CoVaR network.

https://doi.org/10.1371/journal.pone.0337401.g005

Download:

• PNG
  larger image
• TIFF
  original image

Fig 6. Visualization for ∆CoVaR network.

https://doi.org/10.1371/journal.pone.0337401.g006

These networks underscore the complex nature of risk transmission pathways, with the ∆CoVaR network capturing bilateral conditional risk dependence and the ∆CoES network highlighting the impact of extreme tail events. This dual perspective provides valuable insight into the robustness and vulnerabilities within the global financial system, indicating that markets with central roles in both networks might warrant closer monitoring to mitigate systemic risks effectively. Importantly, the observed network structures should not be interpreted as correlation networks. Each edge represents a conditional amplification mechanism whereby extreme losses in one market increase the downside risk exposure of another market. This mechanism is consistent with crisis transmission channels such as capital flow reversals, investor sentiment contagion, and cross-border balance sheet exposures, which become particularly pronounced under tail risk conditions. Therefore, the network topology reflects how localized climate or financial shocks may escalate into systemic events through nonlinear and state-dependent transmission pathways. Unlike correlation networks, which are insensitive to distributional asymmetry and extreme events, this study explicitly focuses on lower tail dynamics. This distinction ensures that the identified connections reflect genuine channels of systemic risk transmission rather than average co-movements across markets.

As shown in Fig 7, the Top 10 Risk Transmitter and Top 10 Risk Recipient countries form a complex risk contagion network in global financial markets. Risk transmitter countries are typically those with high systemic importance and substantial economic influence globally, whereas risk recipient countries are often more susceptible to external economic fluctuations. This distribution pattern reflects the interconnected nature of the global economy and the differentiated roles that countries play in systemic risk transmission.

Download:

• PNG
  larger image
• TIFF
  original image

Fig 7. Top 10 risk transmitter and risk recipient countries.

https://doi.org/10.1371/journal.pone.0337401.g007

The Top 10 Risk Transmitter Countries (Fig 7(a)) are predominantly concentrated in major economies within Europe, North America, and Asia, including the European Union (EU), the United States (U.S.), Japan (JP), and Thailand (TH). The high-risk transmission capacity of these countries is closely linked to their critical positions and extensive global connections. These countries exhibit the following characteristics. Firstly, global financial centers, for instance, the EU and the U.S., serve as major financial hubs, with a vast array of multinational financial institutions and substantial capital flows. During periods of financial volatility, capital market fluctuations in these countries tend to rapidly propagate to other markets, amplifying risk transmission effects. Secondly, highly Integrated Global Supply Chains. Japan and Thailand, among other Asian economies, play crucial roles in global supply chains. Japan, for instance, is integral to high-value industries such as automotive and electronics, while Thailand serves as a manufacturing and export center in Southeast Asia. Economic disruptions in these countries can trigger chain reactions across global supply chains, further intensifying risk transmission.

From an economic perspective, this pattern can be explained by network externalities and systemic importance. Systemically important countries have an amplification effect on the global economy, as their market fluctuations impact not only their domestic economy but also the regional economies closely tied to them. The existence of these risk transmitter countries underscores the necessity of cross-national policy coordination, particularly in mitigating global financial crises and external shocks. Strengthening risk control in these countries could help reduce global contagion effects.

Conversely, the Top 10 Risk Recipient Countries (Fig 7(b)), such as Saudi Arabia (SA), the Philippines (PH), Canada (CA), and Singapore (SG), primarily act as recipients in the global financial system. These countries exhibit the following economic characteristics. Firstly, Reliance on International Markets: For instance, Saudi Arabia and Singapore have economies highly dependent on external demand and international trade. Saudi Arabia, as a major oil exporter, is highly sensitive to fluctuations in global energy markets, while Singapore, as an open economy, is particularly vulnerable to international market dynamics. Secondly, the relative Subordinate Position of Financial Markets. The financial markets of Canada and the Philippines are relatively smaller and less influential globally, making them more susceptible to the financial volatility of larger economies. This passive acceptance characteristic makes these countries more prone to absorbing external risk.

Economically, the distribution pattern of risk recipient countries reflects vulnerability, dependence and absorption of external shocks. These countries’ economic structures and smaller financial markets lead to a higher degree of external volatility. For these countries, enhancing their buffering capabilities against external risks and reducing economic dependence on global powers is essential for achieving economic stability and resilience.

Beyond aggregate network centrality, Table 4 provides evidence of bilateral tail risk transmission channels across countries based on pairwise ∆CoVaR estimates. Several salient patterns emerge. First, strong cross-country and cross-regional spillovers are evident among European markets. For instance, shocks originating from Italy and Sweden transmit significant downside risk to Finland, indicating tight financial integration and synchronized vulnerability within the European equity system. Second, pronounced transmission channels are observed from European core markets to emerging and peripheral markets. The bilateral links from Italy to Turkey and to Russia suggest that distress in Southern European markets can substantially amplify tail risk in emerging markets with closer trade and financial linkages. Third, the results highlight asymmetric spillovers from relatively diversified markets to more volatile recipients. For example, shocks from Norway and Mexico are associated with significant increases in tail risk in Argentina and Brazil, respectively, underscoring the vulnerability of Latin American markets to external financial stress. Therefore, these findings confirm that extreme risks propagate through concrete bilateral channels rather than solely through diffuse network effects. The framework allows us to explicitly identify directional, pairwise tail risk transmission mechanisms across countries, directly addressing concerns that aggregate network measures may obscure underlying bilateral contagion paths.

Download:

• PNG
  larger image
• TIFF
  original image

Table 4. Representative bilateral tail risk transmission channels.

https://doi.org/10.1371/journal.pone.0337401.t004

4.2.3 Systemic risk contribution (SRC) analysis.

This section delves into the SRC of key global markets during significant historical financial crises. By analyzing the SRC values, we aim to identify the top contributors and recipients of systemic risk during these events. The analysis focuses on eight major crises, spanning from the Mexican financial crisis to the COVID-19 outbreak, as presented in Table 5. By ranking the SRC values, we identify the top six markets contributing the most to systemic risk and the six markets contributing the least for each event. The results are presented in Table 6.

Download:

• PNG
  larger image
• TIFF
  original image

Table 5. Key financial crisis events and time periods.

https://doi.org/10.1371/journal.pone.0337401.t005

Download:

• PNG
  larger image
• TIFF
  original image

Table 6. Top 6 and bottom 6 contributors of systemic risk during financial crises.

https://doi.org/10.1371/journal.pone.0337401.t006

In the Asian financial crisis, markets such as Nigeria (NG), Lebanon (LB), and Saudi Arabia (SA) had high contributions to systemic risk, whereas Russia (RU), Brazil (BR), and Turkey (TR) showed negative contributions. This finding suggests that certain emerging markets outside of Asia were impacted, leading to challenges in maintaining financial stability. During the Russian default crisis, Nigeria (NG) and Lebanon (LB) were again significant contributors to systemic risk, reflecting the interconnectedness and vulnerabilities among emerging markets. During the Brazilian financial crisis, Australia (AU), South Africa (SA), and Canada (CA) made notable contributions to systemic risk, while Russia (RU) and Turkey (TR) had smaller contributions, highlighting the varied responses of emerging markets across different crises. Although these markets are not typically regarded as core origins of the Asian Financial Crisis, their elevated SRC values reflect an amplification mechanism distinct from crisis initiation. SRC captures the contribution of markets to tail risk propagation under extreme conditions and reflects their role in transmitting systemic stress during crisis periods. During the crisis, rising global risk aversion, capital flow retrenchment, and commodity price volatility disproportionately affected emerging and frontier markets with high external exposure and structural vulnerabilities, increasing their sensitivity to global shocks and amplifying conditional tail-risk spillovers within the global financial network.

In the Argentine financial crisis, countries such as South Africa (SA) and New Zealand (NZ) demonstrated high contributions to systemic risk, indicating that Argentina’s economic turmoil had considerable spillover effects on other South American and Oceanian nations. During the U.S. subprime mortgage crisis, New Zealand (NZ), Venezuela (VE), and Malaysia (MY) were the major contributors to systemic risk, while Argentina (AR) and Brazil (BR) had lower contributions. These results align with the global propagation path of the subprime crisis, showing how the crisis spread from the United States to the rest of the world, particularly impacting some emerging markets deeply.

During the European sovereign debt crisis, Venezuela (VE) and Nigeria (NG) had significant contributions to systemic risk, whereas Hong Kong (HK), France (FR), and others showed lower contributions. This finding highlights the differentiated impact of the crisis on European and Asian markets. In the 2018 U.S.-China trade dispute, Chile (CL) and Lebanon (LB) had substantial contributions to systemic risk, while Venezuela (VE) and Argentina (AR) had lower contributions. These findings reflect the varying impacts of the U.S.-China trade tensions on Latin American and Middle Eastern markets. Finally, during the COVID-19 outbreak and the stock market crash, New Zealand (NZ), Taiwan (TW), and other markets contributed significantly to systemic risk, while Lebanon (LB) and South Africa (SA) had negative contributions. This finding demonstrates the heterogeneous impact of COVID-19 on global financial markets, with significant disparities in systemic risk contributions across countries and regions. In summary, the systemic risk contributions of the Top 6 and Bottom 6 markets for each event reveal the heterogeneous responses of global key markets during major financial crises. These tabular results help in understanding the geographic and economic risk transmission characteristics of different financial crises and their depth of impact on the global financial system.

4.2.4 Robustness analysis.

To further test the robustness of the identification results of systemic risk contributions, this study conducts a crisis window sensitivity analysis. The Asian financial crisis is highly representative in global financial risk transmission research, and the tail risk linkages between markets were significant during this event. Therefore, this study selects it as a typical crisis scenario for robustness testing. Based on the benchmark crisis window, while keeping the window length unchanged, this study constructs several adjacent alternative windows by simultaneously shifting the crisis start and end dates forward and backward by 1 month, 2 months, and 3 months, respectively. For each alternative window, the same model settings and calculation methods as described above are used to recalculate the average SRC value of each market during the event period. The changes in the ranking of major markets under different window settings are compared to test the sensitivity of the high SRC market identification results to crisis window segmentation.

To maintain consistency with the preceding analysis, the study continues to use the value of SRC measured at time as the basis for event period aggregation within different crisis windows . the average systemic risk contribution of market

within window is defined as:

(20)

where denotes the sample length within window . Based on this measure, the study compares changes in the SRC rankings of major markets under alternative window specifications, thereby assessing the stability of the identification results for high contribution markets.

Table 7 reports the results of the robustness test for window shifting. Although the specific values of SRC in each market fluctuated to some extent as the crisis window shifted, the relative ranking of high contribution markets remained relatively stable. The core high SRC markets identified earlier maintained their high rankings under the substitution window. This finding indicates that the identification of key risk amplification nodes in this study was not driven by a mechanical division of a specific crisis interval, but rather showed strong consistency across adjacent sample windows.

Download:

• PNG
  larger image
• TIFF
  original image

Table 7. Robustness test of the SRC market identification.

https://doi.org/10.1371/journal.pone.0337401.t007

To more comprehensively examine the sensitivity of the identification results of high systemic risk contributing markets to crisis window setting, this study further supplements the analysis with robustness results under several representative crisis scenarios. We selected four representative shock events to visually compare the robustness of major high SRC markets. The results from Fig 8 show that although crisis window shifts may cause some fluctuations in the specific ranking and SRC values of some markets, the core high contribution markets generally remain at the forefront, indicating that the identification of key risk amplification nodes in this study has strong window robustness.

Download:

• PNG
  larger image
• TIFF
  original image

Fig 8. Rank stability of major high SRC markets under shifted crisis windows.

https://doi.org/10.1371/journal.pone.0337401.g008

4.3.1 The relationship between CCPI and systemic risk contribution.

To investigate the relationship between the CCPI and systemic risk contagion, a series of empirical analyses was conducted using linear regression, quantile regression, and nonlinear models across two distinct time periods, namely the period from 2007 to 2015 and the period from 2016 to 2024. The time periods were selected to capture the evolution of climate policies and their differential impacts on systemic risk. The earlier period represents the initial phase of global climate action, primarily characterized by the implementation of the Kyoto Protocol, where climate policies were less systematic, and their effects on systemic risk may have been limited. In contrast, the latter period follows the adoption of the Paris Agreement in 2015, marking a significant escalation in global climate efforts, with enhanced policy transparency, enforceability, and broader market integration. These two periods enable a comparative analysis of the temporal dynamics of CCPI’s impact on SRC. As shown in Table 8, this approach captures both temporal and distributional heterogeneity while accounting for potential nonlinear dynamics between the variables.

Download:

• PNG
  larger image
• TIFF
  original image

Table 8. Relationship between CCPI and SRC across time periods and models.

https://doi.org/10.1371/journal.pone.0337401.t008

The linear regression results indicate a significant negative relationship between CCPI and SRC across both periods. During 2007–2015, the coefficient was estimated at −0.18 with an R² of 0.40, suggesting a moderate explanatory power. For 2016–2024, the coefficient increased to −0.28, accompanied by an improved R² of 0.55. These findings highlight the growing effectiveness of climate policies in reducing systemic risks, especially after the implementation of the Paris Agreement. Introducing an interaction term between CCPI and GDP further enhances the explanatory power, with the coefficient reaching −0.35 and R² increasing to 0.65. This interaction underscores the amplified impact of climate policies in larger economies.

Quantile regression provides additional insights into the heterogeneity of CCPI’s impact across different risk levels. At the 10% quantile, the coefficient was −0.12 with an R² of 0.30, reflecting a weaker influence in low-risk markets. The impact intensifies at higher quantiles, with coefficients of −0.20 and −0.35 at the 50% and 75% quantiles, respectively, and peaking at −0.40 at the 90% quantile with an R² of 0.70. These results reveal that CCPI’s risk-reducing effect is more pronounced in high-risk environments, likely due to greater sensitivity to climate policies in such contexts. Nonlinear models further validate the robustness of these findings. The random forest model achieves an R² of 0.75 for 2007–2015 and 0.85 for 2016–2024, with further optimization increasing the R2 to 0.88. The support vector regression (SVR) results, based on an RBF kernel, yield R² values of 0.70 and 0.80 for the two periods, respectively, confirming the nonlinear nature of the relationship. The multilayer perceptron (MLP) model, leveraging neural networks with varying depths, achieves an R² of 0.83 for 2016–2024, demonstrating its capability to capture complex dynamics. The results consistently demonstrate that higher CCPI scores significantly reduce SRC. This negative relationship becomes more prominent in high-risk markets and during periods of strengthened climate policies. The findings highlight the critical role of climate performance in mitigating systemic risks and underscore the necessity of integrating climate considerations into financial stability frameworks.

4.3.2 Systemic risk transmission and dynamics: An empirical study based on key crises.

To uncover the mechanisms of global systemic risk transmission, this study analyzes key crises using risk transmission network diagrams and the data presented in Table 9. Due to space constraints and data limitations, this paper adopts the “Too Extreme to Fail” theory as the framework for analyzing systemic risk dynamics during four major crises: the 2007 global financial crisis, the 2010 European sovereign debt crisis, the 2018 trade war-induced market volatility, and the 2020 COVID-19 pandemic. Table 9 presents the performance and dynamic characteristics of SRC and climate factors in the global financial network. The SRC is calculated using a model adjusted for CCPI, while the high-risk regions, transmission paths, and network centrality metrics are derived from the risk network analysis. The market volatility index (VIX) is obtained from historical data provided by the Chicago Board Options Exchange (CBOE), and information on affected industries is derived from industry dynamics during the crises and relevant literature. Through this integration of multidimensional data, Table 9 provides an essential foundation for understanding the spatial characteristics and transmission patterns of systemic risk.

Download:

• PNG
  larger image
• TIFF
  original image

Table 9. Systemic risk contribution (SRC) and climate factors during major crises.

https://doi.org/10.1371/journal.pone.0337401.t009

2007 U.S. Subprime Mortgage Crisis: A Case of Unidirectional Linear Transmission

The global financial crisis of 2007 represents a classic example of unidirectional risk transmission and highlights the amplification effect associated with high-risk regions. The United States, as the epicenter of the crisis, exhibited significantly higher SRC values than other regions, with the financial and real estate sectors being the most heavily affected. As shown in the network diagram, the risk spreads from the United States to the European Union, eventually affecting Southeast Asia. This clear transmission path underscores the critical role of the United States as the core node in the network. During this phase, the CCPI node acted as a highly connected central node, with degree centrality and betweenness centrality values of 0.89 and 0.91, respectively, indicating its role in accelerating risk transmission across regions. The SRC value increased by an average of 25.00%, while the VIX index rose to 30.45, reflecting the market’s heightened sensitivity to the subprime mortgage crisis. The systemic importance of the United States and the unidirectional pattern of risk transmission provide empirical support for the Too Extreme to Fail hypothesis, according to which distress in risk regions can generate severe consequences for the global financial system as a whole. Fig 9 shows the risk transmission network diagrams for the 2007 Global Financial Crisis.

Download:

• PNG
  larger image
• TIFF
  original image

Fig 9. Risk trends in the U.S. subprime mortgage crisis.

https://doi.org/10.1371/journal.pone.0337401.g009

2010 European Sovereign Debt Crisis: Regional Transmission and Indirect Amplification

The 2010 European sovereign debt crisis was regional, in contrast to the global nature of the 2007 crisis. The network diagram shows that high SRC regions, such as Greece, Spain, and Italy, were concentrated within the European Union, and the risk was primarily transmitted within the Eurozone. However, despite the limited direct influence of the CCPI node, it played a significant role in amplifying the risk spillover through secondary networks, such as emerging markets. During this crisis, the SRC value increased by an average of 15.32%, with the public sector and banking industries being the most severely affected. The VIX index rose to 25.62, reflecting a notable increase in market volatility. The high degree of interdependence within the EU’s financial system further amplified systemic risk, indicating that even a regional crisis, when amplified through network structures, could potentially spill over globally. Fig 10 shows the risk transmission network diagrams for the European Sovereign Debt Crisis.

Download:

• PNG
  larger image
• TIFF
  original image

Fig 10. Risk trends in European sovereign debt crisis.

https://doi.org/10.1371/journal.pone.0337401.g010

2018 Trade War: Bidirectional Transmission and Feedback Mechanisms

The trade war of 2018 exemplified the bidirectional transmission of systemic risk in the context of a globalized economy. The network diagram reveals that the interaction between Asia and the United States significantly intensified, forming a risk transmission loop with feedback effects. During this phase, the SRC value increased by an average of 10.28%, with the manufacturing and technology sectors being most affected. The CCPI node played a pivotal role in connecting the key markets, with degree centrality and betweenness centrality values of 0.75 and 0.76, respectively, highlighting its crucial role in the risk transmission paths. The VIX index rose to 20.54, indicating heightened market sensitivity to trade tensions. The bidirectional transmission pattern increased the complexity of risk spread, which, in turn, exacerbated the difficulty of managing the crisis.

2020 COVID-19 Pandemic: Multicenter Structure and Global Amplification Effect

The 2020 COVID-19 pandemic represents a classic example of global risk transmission, with its scope and intensity surpassing all previous crises. The network diagram shows that multiple high SRC regions, such as the United States, China, and the European Union, formed a multicenter global risk transmission structure. During this phase, the SRC value increased by an average of 40.11%, with the healthcare, services, and tourism sectors experiencing the most significant impact. The CCPI node served as the central driver in the multicenter network, with degree centrality and betweenness centrality values of 0.93 and 0.95, respectively, reflecting the significant role of climate factors in risk transmission. The VIX index surged to 40.78, reaching historic levels of market panic. The transmission of risk through a multicenter structure and complex network amplification underscores the accelerated and complicated nature of systemic risk in a globalized context.

By integrating SRC calculation models, network analysis metrics, and market volatility data, this study provides a comprehensive analysis of the systemic risk dynamics during these four crises. The findings reveal that high SRC regions consistently acted as the primary origin points and amplifiers of risk during each crisis, while low SRC regions played a buffering role by absorbing external shocks to some extent. Additionally, the dynamic role of the CCPI node in each crisis demonstrates the critical influence of climate factors on systemic risk transmission. The evolution from unidirectional transmission to bidirectional feedback and finally to multicenter diffusion demonstrates the increasing complexity of risk transmission in a globalized and interconnected network. This study further validates the “Too Extreme to Fail” theory, offering a new perspective for understanding systemic risk transmission mechanisms and providing targeted empirical support for policymakers and risk managers.