# 基于银企间多层金融网络的系统性风险传导机制及建模研究Systematic Risk Contagion Mechanism and Modeling Based on Multi-Layer Financial Network between Banks and Firms

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Although the various relationships in the financial system have improved the convenience of fi-nancial services, they also make the risk contagion more complicated. This paper is devoted to the construction of a multi-layer financial network between banks and firms, including interbank lending, bank-firm lending and inter-firm guarantee relationships. Based on the balance sheet and off-balance-sheet business of banks and firms, we explain the relationship of rights and responsi-bilities between the various entities and clarify the risk components. Considering factors such as individual risk, credit risk and market liquidity risk, we describe the risk contagion mechanism from the perspective of layered conduction and step-by-step infection, and propose the contagion effect in the network structure. At the same time, based on the Debtrank algorithm, we construct a methodological approach to the individual and overall risk status in the risk conduction process.

1. 引言

2. 基于银企间多层金融网络的模型构建

2.1. 银企间网络模型的构成要素

${A}_{ji,\gamma }={\left\{{a}_{ji,\gamma }\right\}}_{N*N\left(M\right)}$ 来表示各节点之间的关系， $\gamma$ 表示不同层：银行间同业拆借层(第1层)、银企间借贷层

(第2层)、企业担保层(第3层)； ${a}_{ji,\gamma }$ 表示第 $\gamma$ 层上的第i个节点拥有第j个节点的债权金额，相当于i的风险敞口，按惯例方向是从节点j指向节点i；统一定义 ${a}_{ii,\gamma }=0$ 表示不存在自己对自己的债权。

Figure 1. Simplified network structure

2.2. 银行和企业两类主体的微观结构

${L}^{OF}$ 和权益 ${E}_{f}$ ；显然两张资产负债表中，企业的银企间负债与银行的银企间资产是相互对应的；权益 ${E}_{f}$ 作为资产缓冲器， ${E}_{f}\left(0\right)={\varphi }_{4}{V}_{f}\left(0\right)$ ；且 ${V}^{LF}\text{+}{V}^{OF}={L}^{BF}+{L}^{OF}+{E}_{f}$ 关系恒定；另外，由于担保业务属于表外业务，而企业对外提供担保实际上形成了或有负债，因而一旦企业被要求履行担保义务时，体现在资产负债表上为资产受损，这里假定流动性资产受损。

Table 1. Simplified bank balance sheet

Table 2. Simplified firm balance sheet

3. 基于银企间多层金融网络的风险传导机制

3.1. 简化的风险传导机制

Figure 2. Simplified risk conduction mechanism diagram

3.2. 银行同业拆借层的风险传导机制

Figure 3. Risk contagion mechanism of the interbank lending layer

3.3. 银企间借贷层的风险传导机制

Figure 4. Risk contagion mechanism of the lending layer between banks and firms

3.4. 企业担保层的风险传导机制

Figure 5. Risk contagion mechanism of the firm guarantee layer

3.5. 分步骤的风险传导机制

(1) (2) (3) (4)

Figure 6. Steps of the risk contagion mechanism

f5多次受到风险的传导。

4. 基于银企间多层金融网络的模型思路分析

4.1. 对风险状态的测度思路

4.2. 基于Debtrank算法的风险测度模型构建

${H}_{i}\left(t\right)=\mathrm{min}\left\{1,{H}_{i}\left(t-1\right)+\underset{{C}_{j}\left(t-1\right)=D}{\sum }{W}_{ji}{H}_{j}\left(t-1\right)\right\}$ (1)

${S}_{i}\left(t\right)=\left\{\begin{array}{l}D,{H}_{i}\left(t\right)>0;{S}_{i}\left(t-1\right)\ne I\\ I,{S}_{i}\left(t-1\right)=D\\ {S}_{i}\left(t-1\right),\text{otherwise}\end{array}$ (2)

Debtrank算法是一种受反馈中心性启发的新颖度量方法，能够量化在外部冲击下，特定节点产生财务困境并将风险扩散至整个网络的程度。Battiston等(2012) [39] 将整个网络归一化，定义整个市场的总资

$L{O}_{f}=m{V}^{OF}\left(0\right)+\underset{{E}_{b}\left(t-1\right)\le 0}{\sum }{a}_{fb}\left(t\right)+{a}_{kf,3}\left(t\right)+\frac{1-q}{q}{V}^{OF}\left(t\right)$ (3)

${E}_{f}\left(t\right)={V}^{LF}\left(t\right)+{V}^{OF}\left(t\right)-\underset{b=1}{\overset{N}{\sum }}{a}_{fb}-{L}^{OF}\left(t\right)-L{O}_{f}$ (4)

${W}_{kf,3}\left(t\right)=\left\{\begin{array}{l}\frac{\frac{1}{q}{a}_{kf,3}\left(0\right)}{{E}_{f}\left(0\right)},{E}_{k}\left(t-1\right)>0\\ 0,{E}_{k}\left(t-1\right)\le 0\end{array}$ (5)

${H}_{f}\left(t+1\right)=\mathrm{min}\left\{1,{H}_{f}\left(t\right)+\underset{k=1}{\overset{M}{\sum }}{W}_{kf,3}\left[{H}_{k}\left(t\right)-{H}_{k}\left(t-1\right)\right]\right\}$ (6)

${S}_{f}\left(t\right)=\left\{\begin{array}{l}U,{H}_{f}\left(t\right)=0\\ D,{H}_{f}\left(t\right)\in \left(0,1\right)\cap {S}_{f}\left(t-1\right)=\left\{U,D\right\}\\ I,{H}_{f}\left(t\right)=1\cap {S}_{f}\left(t-1\right)=\left\{U,D\right\}\end{array}$ (7)

${v}_{f}=\frac{\underset{k}{\sum }{a}_{kf,3}}{\underset{f}{\sum }\underset{k}{\sum }{a}_{kf,3}}$ (8)

${R}_{f}=\underset{f}{\sum }{H}_{f}\left(T\right){v}_{f}-\underset{f}{\sum }{H}_{f}\left(1\right){v}_{f}$ (9)

${a}_{jb}\left(t+1\right)=\left\{\begin{array}{l}{a}_{jb,\gamma }\left(t\right)\frac{{E}_{j}\left(t\right)}{{E}_{j}\left(t-1\right)},{E}_{j}\left(t-1\right)>0\\ {a}_{jb}\left(t\right)=0,{E}_{j}\left(t-1\right)\le 0\end{array}$ (10)

${a}_{fb}\left(t+1\right)=\left\{\begin{array}{l}{a}_{fb}\left(t\right)\frac{{E}_{f}\left(t\right)}{{E}_{f}\left(t-1\right)},{E}_{b}\left(t-1\right)\ge {\phi }_{3}{V}_{b}\left(0\right)\\ {a}_{fb}\left(t\right),{E}_{b}\left(t-1\right)<{\phi }_{3}{V}_{b}\left(0\right)\end{array}$ (11)

$L{O}_{b}=\frac{1-q}{q}\left\{m\left[{V}^{OB}\left(0\right)+{a}_{fb}\left(0\right)\right]+\underset{{E}_{j}\left(t-1\right)\le 0}{\sum }{a}_{jb}\left(t\right)\right\}$ (12)

${E}_{b}\left(t\right)=\underset{j=1}{\overset{N}{\sum }}{a}_{jb}\left(t\right)+\underset{f=1}{\overset{M}{\sum }}{a}_{fb}\left(t\right)+{V}^{OB}\left(t\right)-{L}^{JB}\left(t\right)-{L}^{OB}\left(t\right)-L{O}_{b}$ (13)

${W}_{jb,\gamma }\left(t\right)=\left\{\begin{array}{l}\frac{\frac{1}{q}{a}_{jb,\gamma }\left(0\right)}{{E}_{b}\left(0\right)},{E}_{j}\left(t-1\right)>0\\ 0,{E}_{j}\left(t-1\right)\le 0\end{array}$ (14)

${H}_{b,1}\left(t+1\right)=\mathrm{min}\left\{1,{H}_{b,1}\left(t\right)+\underset{j=1}{\overset{N}{\sum }}{W}_{jb}\left[{H}_{j}\left(t\right)-{H}_{j}\left(t-1\right)\right]\right\}$ (15)

${H}_{b,2}\left(t+1\right)=\mathrm{min}\left\{1,{H}_{b,2}\left(t\right)+\underset{f=1}{\overset{M}{\sum }}{W}_{fb}\left[{H}_{f}\left(t\right)-{H}_{f}\left(t-1\right)\right]\right\}$ (16)

${S}_{b}\left(t\right)=\left\{\begin{array}{l}U,{H}_{b}\left(t\right)=0\\ D,{H}_{b}\left(t\right)\in \left(0,1\right)\cap {S}_{b}\left(t-1\right)=\left\{U,D\right\}\\ I,{H}_{b}\left(t\right)=1\cap {S}_{b}\left(t-1\right)=\left\{U,D\right\}\end{array}$ (17)

${v}_{b}=\frac{\underset{j}{\sum }{a}_{jb,\gamma }}{\underset{b}{\sum }\underset{j}{\sum }{a}_{jb,\gamma }}$ (18)

${R}_{b}=\underset{b}{\sum }{H}_{b}\left(T\right){v}_{b}-\underset{b}{\sum }{H}_{b}\left(1\right){v}_{b}$ (19)

5. 结论

NOTES

1通常担保分为一般担保和连带担保。当事人在保证合同中约定，债务方不能履行债务时，由保证方承担保证责任的，为一般保证。连带责任保证的债务方在主合同规定的债务履行期届满没有履行债务的，债权方可以要求债务方履行债务，也可以要求保证方在其保证范围内承担保证责任。如果保证合同中没有写明是哪种担保模式，则默认为是连带担保。

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