Identification of systemically important banks in China based on Merton-Shapley model and a comparison between different indicators

Abstract

Accurately measuring systemic risk in the banking industry and identifying systemically important banks are significant parts of macro-prudential supervision. However, there is a lack of research on measuring systemic risk and identifying important banks under the same framework. And there are relatively few studies comparing different indicators of systemically important banks in the context of China's banking industry. Therefore, this paper first constructs a new Merton model to measure the dynamically evolving systemic risk of China's banking system. Then combine the Merton model with the Shapley value to construct the Merton-Shapley framework, and propose a new indicator MShv to identify systemically important banks. At last, use the data of China's banking industry from 2006 to 2019 to conduct an empirical study. The research results show that the systemic risk in China peaked in 2008 and 2015 near the stock market crash, after 2008 the risk appeared a fluctuating decline. And it is found that MShv can accurately identify important banks and simultaneously is conducive to policy implementation. By a comparison between MShv and other systemic risk contribution indicators such as ΔCoVaR, MES, and SRISK, we find that there are many differences for different indicators in the applicability of identifying systemically important banks, the information reflected, and so on. Regulators can consider using several indicators synthetically to supervise banks during different risk periods, in order to maintain the stability of the financial system.

Systemically important banks; Merton model; Shapley value; Indicator comparison; Macro-prudential supervision.

1. Introduction

The U.S. subprime mortgage crisis broke out in 2008, caused the global financial system to be in trouble at the same time, and had a serious negative impact on the real economy, which is regarded as systemic risk. Since then, the systemic risk of the financial industry has become a hot topic both between academic researchers and regulators of various countries. Banks play an essential role in the financial system, and the systemic risk of the banking industry has attracted more attention.

In order to enhance the soundness of the banking industry, in the post-crisis era, the Financial Stability Board (FSB) has carried out fundamental reforms to the international financial regulatory framework and proposed Basel III (BCBS, 2010). Basel III claimed that the financial crisis in 2008 fully exposed the significant impact on the financial system due to the interconnectedness of financial institutions, and the traditional micro-prudential supervision framework has been unable to effectively prevent risks. Consequently, Basel III has established the dominant position of the macro-prudential regulation framework in financial supervision reform and emphasized the supervision of the overall stability of the financial system. For systemically important institutions, macro-prudential regulation also requires setting higher capital and liquidity requirements. So, it is necessary to measure the contribution of individual institutions to systemic risk and identify institutions with large risk contributions. In summary, the measurement of overall systemic risk in the banking industry and the identification of systemically important banks are important contents in macro-prudential supervision, the two complement each other and jointly promote the stability of the financial system.

In terms of systemic risk measurement, many scholars use the structured method based on Merton's capital assets pricing model (Merton, 1973), which uses both balance sheet data and high-frequency financial market data, having the advantages of being forward-looking and accurate. The method is also known as the Contingent Claims Analysis (CCA). Based upon the Merton model, Lehar (2005) constructed a portfolio method that can continuously evaluate the total risk of the banking system along the time dimension, so as to capture the period of systemic risk increase. Varotto and Zhao (2018) extended Lehar's research by introducing market-based time-varying default triggers. Different from Lehar (2005), Yuan and Liu (2019) used the GARCH process to estimate the volatility of banks' asset returns and proposed a new CCA method based on time-varying volatility. In the way of introducing the copula function, Gray and Jobst (2010) proposed an extension framework named the Systemic Contingent Claims Analysis (SCCA) and measured the joint default risk based on extreme value theory. Liu et al. (2019) constructed a different SCCA method based on the Gumbel Copula model and applied it to the systemic risk measurement of China's securities companies.

As for the identification of systemically important banks, most research has been carried out relying on the contribution of banks to the banking industry's systemic risk to conduct identification. With the above research idea, it is usually to use the time-series data of the stock market to establish models which assess the systemic risk contribution of banks, such as CoVaR, ΔCoVaR, MES, SES, SRISK, and other indicators. Adrian and Brunnermeier (2016) built the Conditional Value at Risk (CoVaR) indicator based on VaR, which measures the risk of the whole banking system when a particular bank is in trouble, then ΔCoVaR was proposed to measure the marginal contribution of a bank to systemic risk. On the basis of Expected Loss (ES), Acharya et al. (2017) put forward Systemic Expected Shortfall (SES) and Marginal Expected Loss (MES) to evaluate the marginal risk contribution of banks when the market is in crisis. Brownlees and Engle (2017) improved the estimation method of MES, and by making use of the improved method, they proposed a systemic risk index method named SRISK that accounts for factors such as bank size and leverage ratio.

Many scholars have improved and applied these methods, and a considerable amount of literature thus has been published (Chen and Wang, 2014; Engle and Ruan, 2019; Fang et al., 2020; Foggitt et al., 2019; Ouyang et al., 2022; Wang et al., 2018). Among all of these improved methods or indicators, a method that combines the tail risk measurement and network model is particularly striking. In recent years, "too-connected-to-fail" has attracted increasing attention, which indicates that systemic risk depends not only on financial institutions themselves but also on the interconnection between them. Introducing the network model makes it possible to take the correlation between financial institutions into account. Härdle et al. (2016) used CoVaR to measure tail risk and introduced tail correlation among financial institutions, proposing tail-event driven network risk. They defined two indicators of Systemic Risk Receivers and Systemic Risk Emitters to assess the systemic importance of financial institutions. Similarly, Torri et al. (2021) extended ΔCoVaR to network form and constructed a method based on the conditional tail risk network. Naeem et al. (2022) combined CoVaR and network model to measure systemic risk spillover, the differences between this work and the above two studies are that the authors used neural network quantile regression to predict risk and aimed at measuring the risk of different industries in the United States.

In addition to the above-mentioned literature, some interesting literature has emerged in the field of systemic risk research during the past two years, either focusing on new phenomena or using other methods. Tao et al. (2022) and Su et al. (2022) compared the financial market performance or risk spillovers of Pakistan and European countries before and after the COVID-19 pandemic. Unexpectedly, the European stock market had higher returns after the COVID-19 pandemic. They also found Poland became the main source of net return shocks to other Eastern European economies. Some scholars carried out research based on the Granger causality test. For example, Cincinelli et al. (2022) studied the Granger causality between individual factors (such as leverage) and systemic risk; Foglia et al. (2022) studied the risk spillovers among financial institutions based on the Granger causality test under the two specific conditions of downside and upside, in order to learn the heterogeneity in different situations. Other scholars proposed new methods, such as building a multilayer spillover network based on variance decomposition (Wang et al., 2021) or building financial conditions indexes using weighted arithmetic mean and principal component analysis to measure risk (Wang and Li, 2021).

In conclusion, the existing literature usually only focuses on the measurement of overall systemic risk or the evaluation of individual banks' systemic risk contribution. There is a small body of literature that is concerned with both aspects simultaneously, up to now Fan et al. (2013) and Brunnermeier and Cheridito (2019) have conducted related research, which, however, remain narrow in lacking an empirical comparative analysis of different systemic risk contribution indicators. Foglia and Angelini (2021) proposed a new measurement considering the time and cross-section dimensions of systemic risk and made an empirical comparison among CoVaR, MES, and SRISK, which is similar to our work. The difference mainly lies in the method of developing the new measurement. Foglia and Angelini (2021) built the systemic risk indicator based on the volatility of specific asset returns and three-way factorial analysis. In terms of evaluating banks' contribution to systemic risk, methods like CoVaR and MES have some defects, being unable to well characterize the systemic importance of banks and be well used for supervision (Benoit et al., 2013; Liu and Ouyang, 2019). CoVaR is a "bottom-up" measurement method, which is of non-additivity so that the sum of individual banks' contribution to systemic risk is not equal to the risk of the entire banking system. Additivity means that systemic capital requirements can be allocated easily according to the contribution to systemic risk, which makes it to be more conducive to implementing macro-prudential supervision. Although MES meets additivity, the sum of which can't indicate the systemic risk of the whole banking system. It ignores the factor of bank size and measures the systemic risk contribution of unit assets. Similarly, SES has the same limitations. In addition, the current literature does not pay much attention to the empirical comparison of existing indicators. A large body of literature has compared the definitions, models, advantages, and defects of various indicators at the theoretical level (Benoit et al., 2017; Bisias et al., 2012; Jobst, 2014), while the number of research using actual data for comparison is limited. The research about the applicability of each indicator to assess the systemic importance of banks in China's financial system is relatively rare, furthermore related studies have inconsistent conclusions (Chen et al., 2019; Kleinow et al., 2017; Lin et al., 2018). Therefore, it becomes an important issue to empirically compare these indicators and evaluate their effectiveness in identifying systemically important banks.

Considering the above deficiencies, this paper combines the Merton model and Shapley value method. On the basis of the traditional Merton model, introduce the correlation of bank asset returns to measure the dynamic evolution of systemic risk, then make use of the Shapley value method to attribute systemic risk to individual banks according to the risk contribution, and propose the systemic risk contribution indicator Metrics Combined Merton Model and Shapley Value (MShv), identifying banks with systemic importance. Lastly, this paper conducts an empirical comparison between the proposed MShv and other traditional systemic risk contribution indicators such as ΔCoVaR, MES, and SRISK.

The Shapley value is a general solution for attributing the total revenue to each player in a cooperative game. By analogy with this idea, the method can be used to allocate systemic risk, and the systemic risk contribution of individual banks can be obtained by risk attribution. It meets additivity and other excellent properties, making the sum of systemic risk contributions equal to the risk of the whole system. The Shapley value is also robust to modeling and parameter uncertainty and it can be adapted to various risk measurement models to realize risk attribution (Tarashev et al., 2016). Tarashev et al. (2016) first demonstrated that the Shapley value can be used as a method for risk contribution allocation, and used two tail-risk measures, VaR and ES, to conduct empirical research.

The first contribution of this paper is to construct the Merton-Shapley framework and propose a new indicator MShv to measure the systemic risk contribution so that it is possible to measure the systemic risk and identify systemically important banks under the same framework. The second contribution is to empirically compare the indicator MShv and other systemic risk contribution indicators such as ΔCoVaR, MES, and SRISK. Specifically, we conduct a comparison on the systemic importance evaluation of banks obtained by these indicators, as well as their correlation and stability, studying the applicability of each indicator in China's financial system. This paper provides a reference for regulators to grasp the evolutionary law of systemic risk, take corresponding measures in the period of risk accumulation, put forward strict regulation requirements for systemically important banks, and comprehensively make use of various indicators to control systemic risk. Thus, more fine regulation can be achieved.

This paper is organized as follows: the Merton-Shapley framework which can simultaneously dynamically measure systemic risk and identify systemically important banks is proposed in Section 2. Other indicators of systemic risk contribution are introduced in Section 3. The data used and the empirical results are presented in Section 4. Section 4.1 describes the data and sample. Section 4.2 and Section 4.3 give the results of the evolution of systemic risk in China's banking industry and the analysis of the identification of systemically important banks respectively. In Section 4.4 an empirical comparison between different systemic risk contribution indicators is conducted. Section 5 draws the conclusions.

2. Merton-Shapley framework

The systemic event occurs when a large number of financial institutions default concurrently, we define the possibility of this event as systemic risk. When the market value of a bank's assets is lower than the book value of its liabilities, the financial institution is deemed to be in default (namely bankruptcy). In addition to tradable securities, a bank's investment portfolio also includes non-tradable assets. Therefore, the actual market value of a bank's assets cannot be observed and needs to be estimated. Firstly, this paper proposes a systemic risk measurement model for the banking industry based on the Merton model. In the first step, we estimate the market value of bank assets and introduce an asset return correlation to obtain the time series of asset value and liability value. Then, a Monte Carlo simulation is performed to judge the default status of individual banks, so we can further estimate the systemic risk of the banking industry, see Section 2.1. Secondly, we combine the Merton model with the Shapley value to construct the Merton-Shapley framework, for details see Section 2.2. Finally, the MShv systemic risk contribution indicator is defined, see Section 2.3.

2.1. Systemic risk measurement model of banking industry based on Merton model

On the basis of the Black-Scholes option pricing model, the Merton model (Merton, 1973) made further assumptions, regarding the company's equity value $E_i\left(t\right)$ as a call option, whose underlying asset price is the company's asset value $A_i\left(t\right)$ and exercise price is equal to the face value of the liability at the maturity date $D_i\left(T\right)$. Assuming that the liabilities increase at a risk-free interest rate (Lehar, 2005), the expression is shown as:

$$D_i\left(t\right)=D_i\left(0\right)\exp \left(rt\right)=D_i\left(T\right)\exp (-r\left(T-t\right)).$$ (1)

In Eq. (1), $r$ is the risk-free interest rate. According to Merton's call option theory, $E_i\left(t\right)$ is expressed as:

$$E_i\left(t\right)=A_i\left(t\right)N\left(d_{1t}\right)-D_i\left(T\right)\exp \left(-r\left(T-t\right)\right)N\left(d_{2t}\right)$$ (2)

$$d_{1t}=\frac{\mathit{ln}\left(A_i\left(t\right)/D_i\left(t\right)\right)+\left({{\sigma }_i}^2/2\right)T}{{\sigma }_i\sqrt{T}}.$$ (3)

$$d_{2t}=\frac{\mathit{ln}\left(A_i\left(t\right)/D_i\left(t\right)\right)-\left({{\sigma }_i}^2/2\right)T}{{\sigma }_i\sqrt{T}}.$$ (4)

In Eq. (2)- Eq. (4), ${\sigma }_i$ is the volatility of asset returns, $N\left(x\right)$ is the cumulative probability distribution function of standard normal distribution, and the maturity period $T$ is usually assumed to be 1 year.

Supposing that the asset value $A_i$ of bank $i$ follows the geometric Brownian motion, its drift rate is ${\mu }_i$, and its volatility is ${\sigma }_i$. Then $A_i$ can be expressed as:

$$d{A}_i={\mu }_i{A}_{i}dt+{\sigma }_i{A}_{i}dz.$$ (5)

In Eq. (5), $dz=\epsilon \sqrt{dt}$, $\epsilon \sim N\left(\mathrm{0,1}\right)$. This paper models the dynamic evolution of assets as a sequence in discrete time. The calculation formula of asset value can be obtained by deriving Eq. (5):

$$A_i\left(t\right)=A_i\left(0\right)\exp [\left({\mu }_i-{{\sigma }_i}^2/2\right)t+{\sigma }_i{z}_t].$$ (6)

First, read the opening asset value $A_i\left(0\right)$ from the balance sheet, calculate the equity value sequence $E_i\left(t\right),t=\mathrm{0,1},\dots ,T$ through the stock price and the number of equities, and obtain the liability value sequence $D_i\left(t\right),t=\mathrm{0,1},\dots ,T$ according to Eq. (1). Then, as long as the initial values of drift rate ${\mu }_i\left(0\right)$ and volatility ${\sigma }_i\left(0\right)$ are assumed, the estimation of asset value ${\hat{A}}_i\left(t\right),t=\mathrm{0,1},\dots ,T$ can be obtained according to Eq. (2)-Eq. (4). Since the drift rate and volatility are assumed, the estimated value of the asset can't be directly used for further calculation.

Second, we use the estimation method proposed by Duan, 1994, 2000 to estimate the asset drift rate ${\hat{\mu }}_i$ and volatility ${\hat{\sigma }}_i$, as shown in (7):

$$L\left({\mu }_i,{\sigma }_i;\hat{A}\left(0\right),{\hat{A}}_i\left(1\right),...,\hat{A}\left(T\right)\right)=-\frac{T}{2}\mathit{ln}\left(2\pi {\sigma }_i^{2}h\right)-\frac{1}{2}\sum _{t=1}^{T-1}\frac{{\left(R_i\left(t\right)-\left({\mu }_i-{\sigma }_i^2/2\right)h\right)}^2}{{\sigma }_i^{2}h}-\sum _{t=\mathit{1}}^T\mathit{ln}\left({\hat{A}}_i\left(t\right)\right).$$ (7)

In Eq. (7), $R_i\left(t\right)=\mathit{ln}\left({\hat{A}}_i\left(t\right)/{\hat{A}}_i\left(t-1\right)\right)$, $h=1/T=1/52$.

In the next step, use the iteration method to obtain the solution. ${\hat{\mu }}_i$ and ${\hat{\sigma }}_i$ are used as the new initial value, until the difference between the estimated value and the initial value is small enough (less than 1e-4), the iteration stops. Then we obtain the converged estimates of drift rate ${\mu }_i$ and volatility ${\sigma }_i$. Substitute the estimated ${\mu }_i$ and ${\sigma }_i$ into Eq. (6), and the dynamic sequence of the bank's asset $A_i\left(t\right),t=\mathrm{1,2},\dots ,T$ can be calculated.

According to the influence of bank's correlation on systemic risk which is presented by Basel III, this paper introduces the correlation variable of bank asset returns, using the EWMA model to calculate the covariance of asset returns for the estimation of correlation variable. The process is shown in Eq. (8) and Eq. (9).

$${\sigma }_{ij}\left(t\right)=\lambda {\sigma }_{ij}\left(t-1\right)+\left(1-\lambda \right)\mathit{ln}\left(\frac{A_i\left(t\right)}{A_i\left(t-1\right)}\right)\mathit{ln}\left(\frac{A_j\left(t\right)}{A_j\left(t-1\right)}\right).$$ (8)

Following the RiskMetrics framework (Gupton et al., 1997), in Eq. (8), the attenuation factor $\lambda$ is set to 0.94. Perform Cholesky decomposition on the variance-covariance matrix of asset returns ${\Sigma }_t$ that is just calculated, introduce the variance-covariance matrix after Cholesky decomposition in Eq. (6), and re-estimate the asset value, then the asset value estimated by introducing asset correlation is:

$$A_i^s\left(t\right)=A_i\left(0\right)\exp [{\mu }_{i}t+Chol{\left({\Sigma }_t\right)}^T{\epsilon }_t\sqrt{t}-\frac{1}{2}{{\sigma }_{ii}}^{2}t].$$ (9)

In Eq. (9), $Chol\left({\Sigma }_t\right)$ is the upper triangular matrix obtained by Cholesky decomposition of ${\Sigma }_t$. After Eq. (9) is obtained, the asset value $A_i^s\left(t\right)$ is calculated by Monte Carlo simulation; in every year of the sample period, there are 10000 simulations carried out.

To accurately measure the systemic risk, given the threshold $\theta$, calculate the probability of the event that the sum of defaulted bank assets in the banking system exceeds a certain proportion $\theta$ of the sum of all bank assets, judging whether a bank defaults according to the market value of assets and the value of liabilities. The formula for calculating systemic risk is as follows:

$$S{R}_t=P\left[Crsis\right]=P\left[{\sum }_i\left(A_i^s\left(t+1\right)|A_i^s\left(t+1\right)<D_i\left(t+1\right)\right)>\theta {\sum }_{i\in N}{A}_i^s\left(t+1\right)\right]\text{.}$$ (10)

In Eq. (10), $N$ is the set of all banks in the system, ${\sum }_i\left(A_i^s\left(t+1\right)|A_i^s\left(t+1\right)<D_i\left(t+1\right)\right)$ is the sum of default banks' assets, and ${\sum }_{i\in N}{A}_i^s\left(t+1\right)$ is the sum of all banks' assets in the sample. The systemic risk $S{R}_t$ is estimated according to the joint process of banks’ asset value within 6 months. $S{R}_t$ changes with time, so we can measure the systemic risk dynamically.

2.2. Shapley value

The Shapley value method was first proposed by Lloyd S. Shapley in 1953, it can be used to fairly and reasonably attribute the total benefit to each player in a cooperative game of transferable utility (Shapley, 2016). In the game, each player faces complex cooperative strategy choices, and characteristic functions are proposed to measure the interests of the players when they choose different cooperative strategies. Define the set of players in the game as $N$, $S1$ and $S2$ as any cooperative alliance, and the characteristic function $v$ satisfies the properties shown in Eq. (11):

$$\{\begin{array}{l}v(\varnothing )=0\text{,}\\ v\left(S1\cup S2\right)\ge v\left(S1\right)+v\left(S2\right),S1\cap S2=\varnothing \text{.}\end{array}$$ (11)

Based on the characteristic function $v$, we define the value ${\phi }_i$, which attributes the total benefits of cooperation to each player, so that the distribution of the interest obeys the symmetry axiom, the efficiency axiom, the null player axiom, and the additivity axiom (Shapley, 2016). It is proved that there is a unique solution in the game space which obeys all the above axioms. ${\phi }_i$ is equal to the average of the benefit increment generated by every player $i$ to all cooperative alliances they participate in, that is, the marginal benefit contribution of the player $i$, which can be expressed as:

$${\phi }_i=\frac{1}{n}\sum _{nr=1}^n\left[\frac{1}{c\left(nr\right)}\sum _{i\notin R,\left|R\right|=nr}\left[v\left(R\cup \left\{i\right\}\right)-v\left(R\right)\right]\right]$$ (12)

In Eq. (12), $N$ is the set of all players, $n$ is the number of elements of the set $N$. $i\notin R$ represents that set $R$ is all subsets of the set $N$ without the player $i$, $\left|R\right|$ represents the number of elements in the set $R$, and $c\left(nr\right)=n!/[\left(n-nr-1\right)!nr!]$ is the number of all subsets $R$, whose elements number is equal to $nr$. $v$ is the characteristic function and $v\left(R\right)$ is the interests of cooperative alliance $R$.

Since attributing total risk to each bank is similar to allocating total benefits to each player in a cooperative game, we use the Shapley value method to calculate the marginal contribution of individual banks to the systemic risk and put forward a new indicator in Section 2.3.

2.3. MShv: the systemic risk contribution indicator

Based on the Merton model in Section 2.1 and the Shapley value method in section 2.2, under the Merton-Shapley framework, the MShv indicator is further proposed to measure the systemic importance of individual banks.

The Merton-Shapley framework first calculates the expected capital shortfall of the bank set $R$ under the condition of systemic risk occurrence. The capital shortfall is the characteristic function $v$, which is used to measure the risk of a bank set. Then the characteristic function under the Merton-Shapley framework is shown as:

$$v_R\left(t\right)=E\left[{\sum }_{i\in R}{D}_i\left(t+1\right)-re\times A_i^s\left(t+1\right)|Crsis\right]$$ (13)

In Eq. (13), $re$ is the proportion of assets that can be recovered for debt repayment in case of bank bankruptcy. According to Huang et al. (2009), the average value of the asset recovery rate is 0.45. When bank $i$ meets the condition of $A_i^s\left(t+1\right)<D_i\left(t+1\right)$, that is, when bank $i$ goes bankrupt, the above capital shortfall will occur, otherwise the capital shortfall is 0.

In accordance with the Shapley value method, due to adding bank $i$, the average value of the risk increments of all other bank sets is the bank's contribution to systemic risk. Therefore, the systemic risk contribution indicator MShv of bank $i$ can be expressed as:

$$MSh{v}_i=\frac{1}{n}\sum _{nr=1}^n\left\{\frac{1}{c\left(nr\right)}\sum _{i\notin R,\left|R\right|=nr}E\left[\sum _{j\in R\cup \left\{i\right\}}{D}_j\right(t+1)-re\times A_j^s(t+1\left)\right|\sum _k\left(A_k^s\right(t+1\left)\right|A_k^s(t+1)<D_k(t+1))>\theta \sum _{k\in N}{A}_k^s(t+1\left)\right]\right\}-\frac{1}{n}\sum _{nr=1}^n\left\{\frac{1}{c\left(nr\right)}\sum _{i\notin R,\left|R\right|=nr}E\left[\sum _{j\in R}{D}_j\right(t+1)-re\times A_j^s(t+1\left)\right|\sum _k\left(A_k^s\right(t+1\left)\right|A_k^s(t+1)<D_k(t+1))>\theta \sum _{k\in N}{A}_k^s(t+1\left)\right]\right\}$$ (14)

In Eq. (14), $N$ is the set of all banks in the sample, $n$ is the total number of all banks, and the meanings of the rest variables are the same as in Eq. (10) and Eq. (12).

3. Other indicators of systemic risk contribution

In current research on systemic risk contribution of financial institutions, ΔCoVaR, MES, and SRISK are the three most widely used indicators, and they are highly recognized by the academic community. ΔCoVaR is the difference between the Conditional Value-at-Risk of the financial system when a specific financial institution is facing difficulties and in a normal condition, which is equal to the quantile regression result of the VaR, as shown in Eq. (15):

$$\Delta CoVa{R}_q^i=CoVa{R}_q^{X^i=Va{R}_q^i}-CoVa{R}_q^{X^i=Media{n}^i}.$$ (15)

Use quantile regression to estimate ΔCoVaR, the conditional VaR (CoVaR) is the Value at Risk under the condition of $X^i=Va{R}_q^i$, so ΔCoVaR is equal to the quantile regression result of VaR,

$$\Delta CoVa{R}_q^i={\hat{\beta }}_q^i(Va{R}_q^i-Va{R}_{50\%}^i).$$ (16)

In Eq. (16), ${\hat{\beta }}_q^i$ is the regression coefficient estimated from quantile regression, $Va{R}_q^i$ and $Va{R}_{50\%}^i$ are respectively the q^th-quantile and 50% quantile of institution $i$’s returns.

The Marginal Expected Loss (MES) is the equity loss of the bank when the market falls, which is equal to the partial derivative of the system's ES concerning the institution $i$’s weight, that is:

$$ME{S}_t^i=\frac{\partial E{S}_t^m}{\partial w_t^i}=-E_{t-1}(r_t^i|r_t^m<-Va{R}_q).$$ (17)

In Eq. (17), $r_t^m$ is the returns of the whole system, and $r_t^i$ is the returns of institution $i$.

SRISK is the long-term capital shortfall of individual institutions. When the market index falls by 40% within 6 months, a long-term capital shortfall will occur. This indicator depends on factors such as leverage ratio, liabilities, and Long-Term Marginal Expected Shortage (LRMES). Its expression is as:

$$SRIS{K}_t^i=\mathit{max}(0,-k{D}_t^i+\left(1-k\right)E_t^i\left(1-LRME{S}_t^i\right)).$$ (18)

In Eq. (18), $D_t^i$ represents the book value of the institution $i$'s debt, $W_t^i$ represents the market value of its equity, and $k$ is the prudent capital ratio between 0 and 1.

As for specific explanations of these formulas, see Adrian and Brunnermeier (2016), Acharya et al. (2017), Brownlees and Engle (2017) for more details.

The DCC-GJR-GARCH model can accurately and reasonably estimate the volatility of the return series. Based DCC-GJR-GARCH model, this paper calculates the variance and covariance of banks’ stock returns, then calculates the above three indicators according to their definitions.

4. Data and empirical results

4.1. Data

This paper studies the evolution trend of systemic risk and the identification of systemically important banks in China's banking industry. For better achieving research purposes, the research period is set from 2006 to 2019, covering two big events of the global financial crisis and the stock market crash in 2015. The sample consists of 16 Chinese commercial banks listed before 2015, after taking the research period and data volume into account. The risk-free rate is set to the one-year treasury bond rate. Since some banks are listed on the A-share market and H-share market at the same time, this paper comprehensively considers the closing price of A-share and H- share to calculate the equity value of banks. The circulating value of H-share needs to be converted into RMB according to the exchange rate.

The weekly data of stock closing price is used in the calculation of overall systemic risk of the banking industry and systemic importance indicator MShv, and the post-adjusted stock closing price data is used in the calculation of other indicators. The stock closing price data comes from Python's Tushare financial database, and the balance sheet data is obtained from the annual financial reports of each bank.

This paper compares MShv with these three indicators introduced above empirically. To meet data integrity and the requirements of quantile regression, the research period was adjusted to 2008–2019. Due to the late listing time of CEB and ABC, the sample becomes unbalanced panel data. The daily stock return rate of banks is calculated by the logarithmic rate of return, and the market rate of return is calculated by the CSI 300 financial index. The other parameters involved are set as: quantile $q=0.05$, capital adequacy ratio $k=8\%$ (according to Basel III), and the crisis will happen if the stock market fell by $C=40\%$ in the next 6 months.

4.2. Evolution of systemic risk in China's banking industry

We use the method proposed in Section 2.1 to measure the overall systemic risk of the banking industry. The systemic risk is defined as the probability of an event that the sum of default bank assets exceeds a certain percentage $\theta$ of all bank's total assets. Assuming that systemic event occurs when $\theta$ is equal to 10%, 20%, and 30% respectively, systemic risk $S{R}_t$ from 2006 to 2019 under the three thresholds are obtained, as shown in Figure 1.

Figure 1.

Systemic risk evolution from 2006 to 2019 under different thresholds.

It can be seen from Figure 1 that when $\theta$ is equal to 10%, the systemic risk is large, the evolution of systemic risk under this threshold is analyzed below. From 2006 to 2007, the systemic risk was relatively small. During the financial crisis, the systemic risk rose sharply, peaked in 2008, and then decreased. Under the influence of the European sovereign debt crisis, the systemic risk increased to a certain extent in 2010, then decreased, and remained at a low level after then. In 2015, China's stock market fluctuated abnormally, and the systemic risk increased substantially again. The high risk continued until 2016 when the financial institutions experienced a liquidity crisis. After 2017, the risk fell to the lowest level in the sample period, at which time there was almost no systemic risk.

The above evolution patterns were basically in line with the actual economic condition. Dynamically measuring systemic risk enables regulators to actively take corresponding policies to prevent crisis, in the period of obvious accumulation or increase of systemic risk.

As the threshold $\theta$ increases to 20% and above, the systemic risk drops to almost zero in years other than 2008, reflecting how serious and risky the crisis was in 2008, which makes it more prone to happen large-scale default events. Although other years excluding 2008 also have high systemic risk when $\theta$ is smaller, it is not easy for a large number of banks to default jointly, such as in 2015 and 2016. In regulatory practice and risk prevention, it is of great importance to set appropriate thresholds $\theta$ according to specific requirements, so as to avoid overestimating or underestimating the risks and judge the accumulation of systemic risk reasonably.

4.3. Identification of systemically important banks

By using the new indicator MShv proposed in Section 2.3, this paper identifies systemically important banks and analyses the results. In the case of risk stress testing, we make use of the Shapley value method to conduct risk attribution on the systemic risk calculated from the Merton model, then the systemic risk contribution indicator MShv of individual banks can be obtained. The systemic risk contribution of 16 listed banks during the sample period is presented in Table 1. We use the abbreviation of bank name to represent a bank, refer to Appendix for the full name of a bank.

Table 1.

Annual average MShv of listed banks (unit: 10 billion RMB).

Type	Bank	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019
State-owned	BOC	25.78	15.39	36.15	38.73	43.70	46.66	50.95	26.68	51.44	65.21	69.81	76.01
	ICBC	36.04	40.05	48.77	50.11	57.34	64.95	69.84	76.75	88.95	86.62	93.09	98.50
	BCM	8.62	9.58	13.88	14.82	17.15	19.25	21.63	8.73	23.22	30.62	32.77	34.40
	CCB	27.92	31.62	40.12	39.81	45.24	51.32	56.42	58.76	66.04	75.86	79.11	82.35
	ABC				35.83	43.55	46.78	53.54	57.16	64.47	72.04	71.24	80.36
National joint-stock	PAB	0.21	0.56	0.67	2.83	4.35	3.03	1.33	4.07	7.68	10.36	11.59	11.39
	SPDB	0.51	1.69	6.31	2.50	7.79	10.86	13.47	8.38	17.48	20.55	21.49	20.86
	CMBC	2.18	2.82	6.10	7.12	7.64	8.72	11.88	3.63	16.45	22.02	21.08	21.11
	CMB	5.45	2.32	8.79	9.03	10.42	12.82	15.01	17.57	21.23	21.79	22.56	24.09
	HXB	0.64	0.77	3.34	3.93	4.53	4.75	5.68	2.87	6.15	8.05	9.04	9.54
	CIB	0.81	1.37	0.95	4.09	3.35	6.26	2.70	6.57	18.92	22.86	23.41	22.29
	CNCB	4.09	5.32	7.82	7.73	10.18	10.37	12.69	4.82	15.81	19.68	19.47	21.77
	CEB				4.43	6.07	7.89	8.80	3.04	7.46	14.59	14.90	14.88
Urban comm-ercial	NJCB	0.28	0.35	0.60	0.79	1.02	1.24	1.52	0.78	0.93	0.44	1.17	4.41
	NBCB	0.29	0.30	0.69	0.97	0.95	1.35	1.71	1.28	1.73	2.63	3.69	3.92
	BOB	1.45	0.53	2.19	2.76	2.45	4.21	4.83	2.61	5.77	7.55	8.50	9.44

According to the nature and the controlling style of banks, 16 banks are divided into three categories: state-owned banks, national joint-stock banks, and urban commercial banks, so that we can illustrate clearly the difference in systemic risk contribution of listed banks in China. From the data in Table 1, it is apparent that the contribution of different types of banks to systemic risk varies greatly. On the whole, the systemic importance of urban commercial banks is the lowest, national joint-stock banks are in the middle, and state-owned banks are the most important. Among these banks, four major state-owned banks (ICBC, CCB, ABC, and BOC) have the largest contribution to systemic risk, which is significantly larger than other banks. They are systemically important banks in China. Once they fall into crisis, there is gonging to have a serious adverse impact on the financial system. As the above analysis shows, it is not difficult to conclude that the systemic risk contribution of individual banks is affected by the size of banks. Generally, the larger the size, the higher the systemic importance. However, there is no strict positive correlation between them. For a bank having a larger size, the level of systemic importance may be lower. The systemic importance is also affected by the correlation between banks, leverage of banks, and other factors. It is not advisable to only pay attention to "too-big-to-fail" in regulatory practice.

The contribution of banks to systemic risk is not a fixed value. As time goes by, the size of banks, the relationship between banks, the risk of the whole banking system, and other factors are changing, with the ranking of systemic importance varying, as shown in Figure 2.

Figure 2.

Changes in the systemic importance ranking of listed banks from 2008 to 2019.

For different types of banks, changes in the systemic importance ranking are significantly distinct from each other. The systemic importance ranking of four major state-owned banks in China has hardly changed, while the national joint-stock banks and urban commercial banks have great fluctuations, which is caused by the differences in the nature, size, and business development of banks. As mentioned above, ICBC, ABC, BOC, and CCB rank in the top four, the ranking of systemic importance remains within this range. The ranking of the four banks' systemic importance is the most stable, their position of systemically important banks is obvious. ICBC and CCB have always ranked first and second. Before the listing of ABC, BOC ranked third. In 2013, BOC's ranking decreased slightly to fourth, and the rank of ABC rose from fourth to third, its systemic importance has increased at that time. Generally speaking, the ranking of the four major state-owned banks is steady, and they are always the most important banks.

On the contrary, the systemic importance ranking of joint-stock banks fluctuates greatly, such as CNCB, CMBC, and CIB. What leads to this fluctuation is that joint-stock banks have developed rapidly in recent years, actively reformed and innovated, thus their instability and uncertainty are strengthened, facing more fierce competition. The ranking of CNCB has declined significantly, while CIB shows a trend of decline first and then rise. Some joint-stock banks have a strong development momentum and may become systemically important banks in the next few years. Compared with the national joint-stock banks, the ranking of the three urban commercial banks is relatively stable, but the change range is still greater than that of state-owned banks. Urban commercial banks have always been in the last few, and there is still a large gap between them and the national joint-stock banks.

For regulators, they should regularly assess the systemic importance of banks and keep abreast of changes in systemically important banks. Although both international and domestic regulatory agencies have released the list of systemically important banks, the regulatory agencies usually use the index evaluation method to identify systemically important banks. The index evaluation method needs to give weight to each index, which has a certain subjective risk preference and does not make use of high-frequency data of the financial market, lacking the reflection of market risk and being not able to forward-look risk. In contrast, the MShv indicator proposed in this paper belongs to the model method, does not involve subjective factors, and uses high-frequency data of the stock market, making it reflect the actual condition better.

It is more important that regulators usually only release the ranking and the group of systemically important banks, however, the method proposed in this paper can provide more information about systemically important banks. For example, every year's level of systemic importance and how the level of systemic importance changes will help regulators to better grasp the variation and development of systemically important banks, so as to achieve more fine supervision.

According to the above results, in addition to the identified systemically important banks, regulators should pay special attention to joint-stock banks whose systemic importance fluctuates greatly, especially banks whose systemic importance has risen sharply. Such banks are very likely to become systemically important banks in the future. Then regulators should reasonably formulate macro-prudential supervision policies to them and adjust promptly when changes happen. Moreover, the MShv indicator is additive, allowing regulatory capital to be allocated directly based on the risk contribution, which is more conducive to the implementation of macro-prudential regulatory measures related to capital requirements.

4.4. Empirical comparison of systemic risk contribution indicators

According to the definition of each indicator, the systemic risk contribution corresponding to ΔCoVaR, MES, SRISK, and MShv can be calculated respectively. The daily systemic risk contribution of each bank is aggregated to obtain the annual contribution, and then we can compare the systemic importance rating results of different indicators. Table 2 shows the four banks with the largest contribution to systemic risk evaluated by the four indicators of ΔCoVaR, MES, SRISK, and MShv. It is generally believed that the greater the contribution, the greater the systemic importance.

Table 2.

Comparison between the four banks with the largest contribution to systemic risk evaluated by each indicator.

Year	ΔCoVaR		MES		SRISK		MShv
2008	CMB	SPDB	SPDB	PAB	ICBC	CCB	ICBC	CCB
	CIB	HXB	CIB	NBCB	BOC	BCM	BOC	BCM
2009	CMB	SPDB	NBCB	HXB	CCB	ICBC	ICBC	CCB
	CMBC	CIB	CIB	NJCB	BOC	BCM	BOC	BCM
2010	CNCB	CIB	NBCB	CNCB	CCB	BOC	ICBC	CCB
	BOB	HXB	NJCB	BOB	BCM	ICBC	BOC	BCM
2011	HXB	CIB	NBCB	HXB	ABC	CCB	ICBC	CCB
	SPDB	CMB	CIB	PAB	BOC	ICBC	BOC	ABC
2012	HXB	NBCB	NBCB	NJCB	ABC	CCB	ICBC	CCB
	NJCB	CMB	HXB	PAB	BOC	ICBC	ABC	BOC
2013	PAB	CIB	PAB	CIB	ABC	BOC	ICBC	CCB
	CMBC	SPDB	SPDB	CMBC	CCB	ICBC	ABC	BOC
2014	HXB	CMBC	PAB	NBCB	ABC	ICBC	ICBC	CCB
	CNCB	CIB	CIB	CNCB	BOC	CCB	ABC	BOC
2015	BOB	HXB	NBCB	NJCB	ABC	CCB	ICBC	CCB
	NJCB	CCB	PAB	CEB	ICBC	BOC	ABC	BOC
2016	NBCB	NJCB	NBCB	NJCB	ABC	BOC	ICBC	CCB
	HXB	CMB	CNCB	PAB	ICBC	CCB	ABC	BOC
2017	CMB	NBCB	NBCB	NJCB	ABC	BOC	ICBC	CCB
	NJCB	PAB	PAB	CMB	ICBC	CCB	ABC	BOC
2018	CCB	PAB	PAB	NBCB	ABC	BOC	ICBC	CCB
	CMB	ICBC	CMB	NJCB	ICBC	CCB	ABC	BOC
2019	PAB	CMB	PAB	NBCB	ABC	BOC	ICBC	CCB
	NBCB	CIB	NJCB	CMB	ICBC	CCB	ABC	BOC
Accuracy	7.1%		0%		100%		100%

The International regulator FSB has been updating the list of global systemically important banks (G-SIBs) every year since 2011. Four banks including BOC, ICBC, ABC, and CCB have been selected as G-SIBs. Using the list of G-SIBs as a reference standard to compare the ability of the above four indicators to assess the systemic importance of banks, the identification accuracy of systemically important banks is summarized in Table 2. MShv and SRISK can accurately identify systemically important banks, and the top 4 banks whose contributions are the largest are all in the G-SIBs list, with an identification accuracy rate of 100%. While ΔCoVaR and MES cannot identify accurately, with an accuracy rate of below 10%.

Identification accuracy preliminarily shows that MShv and SRISK are suitable for measuring systemic importance, while ΔCoVaR and MES are not suitable. This paper conducts specific analyses of the systemic importance rating results to further illustrate the four indicators' applicability in China's financial system.

The systemic importance ranking measured by ΔCoVaR is the opposite of empirical judgment. Joint-stock banks and urban commercial banks such as CIB, HXB, NJCB, and NBCB contribute more to systemic risk, while state-owned banks contribute less. Actually, according to its definition, ΔCoVaR measures the spillover risk of individual banks to the entire banking system. State-owned banks have a lower ability to cause losses to the system, while joint-stock banks have a larger spillover to the risk of the financial system when they are in crisis. This is due to that joint-stock banks usually carry out innovative inter-bank business more actively, with a high proportion of inter-bank business, which makes it prone to occurring liquidity problems. Once a default caused by liquidity problems occurs, the entire banking system will fall into crisis through the joint-stock bank's close business ties with other banks. However, state-owned banks adopt a more stable business model and have a more comprehensive risk management system.

As mentioned in Section Introduction, the conclusions of the indicator comparisons between the existing literature are inconsistent with each other. The main controversy lies in whether ΔCoVaR can accurately identify systemically important banks. This paper's results show that ΔCoVaR is not suitable for identifying systemically important banks and further explain the reasons based on its definition. Other scholars have come to the opposite conclusion may be due to miscalculation or confusion of the directionality of ΔCoVaR. Although systemically important banks cannot be accurately identified, the risk spillover effect represented by ΔCoVaR is a factor that has to be considered in supervision. Supervisors need to pay special attention to banks with high-risk spillover effects to prevent large-scale risk contagion caused by small-size institutions.

For indicator MES, in three types of banks, the average MES of urban commercial banks is the highest, and the average of state-owned banks is the lowest. Among them, CCB, BOC, ICBC, and ABC ranked the last four. In terms of its definition, MES is the systemic risk contribution of a financial institution's unit assets under a stress scenario, which represents the systemic vulnerability of a financial institution faced with crises. It shows that when the stock market index falls significantly, state-owned banks have the smallest marginal expected losses and can better withstand risks, while urban commercial banks are more vulnerable and will incur greater losses in the face of crises. Similar to ΔCoVaR, the systemic fragility represented by MES cannot be ignored in regulation.

Different from the above two indicators, in the results obtained by SRISK and MShv, large state-owned banks have the largest contribution to systemic risk, followed by national joint-stock banks and urban commercial banks, indicating that these two indicators can fully reflect the information of the bank's size. Size is generally considered to be an important factor that affects the contribution of financial institutions to systemic risk.

Table 3 below illustrates the correlations between the systemic importance rating results of each indicator and their evaluation stability, which are both calculated by the Kendall harmony coefficient. When we compare the correlations between four systemic importance rankings obtained by the above indicators, it is found that the correlation between the ranking based on MShv and the ranking based on SRISK is the highest. Since the correlation coefficient reaches 0.9466, there is a significant correlation between MShv and SRISK. The correlation coefficients between MShv and ΔCoVaR or MES are low and the correlation relationships are not significant, which further verifies that the two sets of indicators reflect the information of different dimensions. In order to judge the evaluation ability of indicators, we usually also pay attention to their evaluation stability. The evaluation stability (namely consistency) of MShv is 0.9730, which means that MShv can evaluate the systemic importance of banks with consistency.

Table 3.

Correlations between systemic importance ratings of four indicators and their consistency.

Indicator	ΔCoVaR	MES	SRISK	MShv
ΔCoVaR	1∗∗∗ (0)
MES	0.8397∗∗∗ (4.72e-05)	1∗∗∗ (0)
SRISK	0.3567 (0.1750)	0.2229 (0.4067)	1∗∗∗ (0)
MShv	0.3582 (0.1731)	0.1967 (0.4653)	0.9466∗∗∗ (2.88e-08)	1∗∗∗ (0)
Consistency	0.7601∗ (0.0884)	0.8789∗∗ (0.0343)	0.9822∗∗ (0.014)	0.9730∗∗ (0.0152)

Notes: Consistency measures whether each indicator can obtain consistent evaluation on systemic importance in different years. We use ${\chi }^2$ tests to illustrate its significance. ∗∗∗, ∗∗ and ∗ denote significance at the 1%, 5% and 10% level, respectively. The data in brackets are p values.

Given all of that, the MShv indicator proposed in this paper is suitable for the identification of systemically important banks, with high accuracy and high evaluation stability. Compared with other indicators, MShv combines the Merton model and the Shapley value method, which can simultaneously measure the systemic risk of the banking industry and identify systemically important banks under the same framework. Other indicators can only measure the systemic risk contribution of individual banks, and cannot effectively identify systemically important banks (except SRISK).

5. Conclusions

Under the background of the continuous promotion of the macro-prudential supervision system, this paper constructed a Merton-Shapley framework. First, we measured the overall systemic risk of the banking industry based on the Merton model, then effectively attributed the systemic risk to individual banks according to their contribution by combining with the Shapley value method, and put forward a new indicator MShv to evaluate the systemic importance of banks. Thus realized researching the measurement of systemic risk and the identification of systemically important banks simultaneously under the Merton-Shapley framework. Through empirical research on 16 listed banks in China, this paper obtained the dynamic evolution trend of the systemic risk in China's banking industry from 2006 to 2019 and the level of the systemic importance of each bank. Then we compared MShv with several mainstream systemic risk indicators such as ΔCoVaR, MES, and SRISK, and discussed the disputes about the comparison results in the existing literature. The main conclusions are summarized as follows:

• (1)The systemic risk of China's banking industry peaks near the financial crisis in 2008 and the stock market crash in 2015. After 2008, it presents a fluctuating downward trend, but the risk still increases in some years.
• (2)The indicator MShv can accurately identify systemically important banks. ICBC, CCB, ABC, and BOC are systemically important banks. However, the level of the systemic importance of banks is not static and immutable. The systemic importance ranking of state-owned banks and urban commercial banks is relatively stable. The state-owned banks have always been the most systemically important, while urban commercial banks have always been the least systemically important. On the contrary, the ranking of national joint-stock banks fluctuates greatly, especially CNCB, CMBC, and CIB, among which the ranking of CIB has risen significantly in recent years.
• (3)Different systemic risk contribution indicators reflect the information of different dimensions, emphasizing different aspects of systemic risk (such as importance, spillover effects, and vulnerability). ΔCoVaR mainly reflects the spillover risk of an individual institution to the financial system, that is, the ability of an institution to cause losses to the system when it is in crisis. MES lays stress on the systemic vulnerability of financial institutions, that is, the extent to which they can withstand shocks and resist risks. MShv and SRISK reflect the systemic importance well, they are suitable for identifying systemically important banks, while ΔCoVaR and MES are not. However, the above types of indicators can be comprehensively used in supervision.

The indicator MShv proposed in this paper can reasonably attribute systemic risk to individual banks. Due to its good properties such as additivity, MShv can directly allocate systemic capital requirements based on the risk contribution obtained from risk attributing. It is exactly this obvious advantage of MShv that makes it distinct from other indicators.

This paper provides a possible framework or reference for regulators to implement macro-prudential regulation. Based on the Merton-Shapley framework, risk supervision can be carried out from the perspective of the overall systemic risk and individual institutions' systemic importance. According to the research results, the following policy recommendations are made to the regulators: (1) Track the dynamic evolution of systemic risk, especially pay attention to the period when systemic risk continues to accumulate or increase, and take timely measures to control the risk. (2) For individual institutions, it is of significance to pay attention to the changes in the level of systemic importance. In addition to formulating corresponding regulatory policies for the identified systemically important banks, regulators should also highly regard national joint-stock banks with rapidly rising systemic importance. They should timely adjust regulatory requirements to these banks, such as imposing higher capital requirements. The method proposed in this paper can reflect more information about systemically important banks (like the level of systemic importance, its changes, and the bank's potential losses), not only limited to their ranking and grouping. Grasp the changes in systemically important banks, then regulators can conduct supervision more precisely. (3) Reallocate capital to banks in the system based on the systemic risk contribution obtained from MShv. Through the redistribution of capital, important banks can hold assets in proportion to their risk contributions, so they have more adequate assets without being insolvent when they are in a crisis, realizing a significant reduction in systemic risk. (4) In regulatory practice, different indicators like MShv, CoVaR, and MES can be comprehensively applied. Not only should regulators pay attention to banks with high systemic importance, but also banks with large risk spillover effects or high systemic vulnerability. Different policies should be formulated in accordance with the characteristics of banks. For instance, banks with large spillover effects or high vulnerability should be urged to improve their risk management system, standardize innovative financial business, and especially strengthen the supervision of the interbank innovative business.

The Merton-Shapley framework proposed in this paper is a market-based approach, using daily stock data and having advantages such as being forward-looking. But as the business connections among financial institutions continue to deepen, it is difficult to accurately describe the complex connections among them by just considering the correlations of their asset returns. Therefore, in future work, we can try to extend the Merton-Shapley framework to the network form, in order to include the complex associations among financial institutions. In addition, our research on systemic risk focuses on the banking industry. It may be a good improvement to extend the model to other financial institutions (such as securities companies, insurance companies, and so on) and compare the risk characteristics of different institutions, thereby studying the risk profile of the financial system from a comprehensive perspective. We also realize that the extension of the sample period to post-COVID-19 is worth further study and will provide more interesting conclusions. Due to the particularity of the COVID-19 pandemic and the fact that no similar large-scale public health event has seriously affected industrial production and economic development since modern times, for the sake of taking particularity into account, the systemic risk study of the COVID-19 pandemic period can be carried out independently. It may be important to consider the epidemic prevalence, the release of lockdown announcements, and other special external factors, besides using a generic systemic risk measurement method. In future work, we will focus on the period of the COVID-19 epidemic to study the evolution of systemic risk and the changes in individual banks’ systemic importance, and the influence of external factors and possible interactions.

Declarations

Author contribution statement

Hong Fan: Conceived and designed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Yating Zhao: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Funding statement

Prof. Hong Fan was supported by National Natural Science Foundation of China [71971054], Natural Science Foundation of Shanghai [19ZR1402100].

Data availability statement

Data will be made available on request.

Declaration of interests statement

The authors declare no competing interests.

Additional information

No additional information is available for this paper.

Appendix.

Table A1.

Abbreviation of bank name and corresponding full name of bank.

Abbreviation of bank name	Bank name
BOC	Bank of China
ICBC	Industrial and Commercial Bank of China
BCM	Bank of Communications
CCB	China Construction Bank
ABC	Agricultural Bank of China
PAB	Ping An Bank
SPDB	Shanghai Pudong Development Bank
CMBC	China Minsheng Banking Corporate
CMB	China Merchants Bank
HXB	Huaxia Bank
CIB	China's Industrial Bank
CNCB	China CITIC Bank
CEB	China Everbright Bank
NJCB	Bank of Nanjing
NBCB	Bank of Ningbo
BOB	Bank of Beijing