Research on Risk Contagion among Financial Submarkets in China Based on Complex Networks
<p>The dynamic correlation test in first stage.</p> "> Figure 1 Cont.
<p>The dynamic correlation test in first stage.</p> "> Figure 2
<p>The dynamic correlation test in second stage.</p> "> Figure 3
<p>Stage 1: Complex Network Diagram of Financial Markets.</p> "> Figure 4
<p>Stage 2: Complex Network Diagram of Financial Markets.</p> "> Figure 5
<p>Stage 1: Minimum Spanning Tree Diagram.</p> "> Figure 6
<p>Stage 2: Minimum Spanning Tree Diagram.</p> ">
Abstract
:1. Introduction
2. Theoretical Model Analysis
2.1. Introduction to DCC-GARCH Model
2.1.1. ARCH Model
2.1.2. GARCH Model
2.1.3. DCC-GARCH Model
2.2. Application of GARCH Family Model
2.3. Complex Network Theory
2.3.1. Degree and Degree Distribution
2.3.2. Degree and Degree Distribution
2.3.3. Clustering Coefficient
2.4. Minimum Spanning Tree Model
2.4.1. Krustal Algorithm
2.4.2. Minimal Tree Diagram Model
- does not contain directed rings;
- There is a node , which is not the end point of any arc, and other nodes in V are the end points of a unique arc, then is a tree graph with as the root.
2.5. Basic Algorithm
- From all arcs with as the end point, take the shortest one, and if is not the root node for a certain point and there is no incoming edge, the minimum tree graph cannot be generated, and the algorithm ends; if the root is removed If all nodes other than nodes have incoming edges, a subgraph with the smallest weight can be obtained, and the arc set in the subgraph is the shortest arc set;
- After completing step 1, to obtain the shortest arc set, it is necessary to check whether there are directed cycles and contraction points in the connected graph. There are three cases: if there is no directed loop and no shrinkage points, the calculation is over, and the smallest tree graph with as the root is generated in step 1; if there is no directed loop but there are shrinkage points, it is necessary to expand the contraction point; if there is a directed loop, the directed loop needs to be contracted into a point to generate a new graph ;
- The directed loop in the original graph is contracted into a point. At this time, the edges belonging to the directed loop in the original graph G are contracted, while other arcs remain, thus obtaining a new graph . Compared with the original graph , in the new graph , the direction of the length change of the arc with the contraction point as the end point remains unchanged, and the nature of whether to generate the minimum tree graph remains unchanged. At the same time, the operation of step 1 needs to be performed on the new graph until there is no directed cycle in the graph.
- If the original graph has a directed cycle, and the minimum tree graph of the new graph has been obtained, then all arcs in also belong to . We can expand a contraction point of graph into a directed ring and remove arcs with the same end point in , so that all other arcs belong to .
3. Empirical Analysis
3.1. Analysis of Sample Data of China’s Financial Market
3.1.1. Data Description
3.1.2. DCC-GARCH Pre-Modeling Test
ADF Test
Arch Test
3.2. Analysis of DCC-GARCH Model
3.2.1. Dynamic Correlation Analysis among Financial Sub-Markets in the First Stage
3.2.2. Dynamic Correlation Analysis between Financial Sub-Markets in the Second Stage
3.3. Complex Network Analysis
3.3.1. Data Processing
3.3.2. Two-Stage Complex Network Diagram
3.3.3. Two-Stage Complex Network Topology Parameter Analysis
3.3.4. Two-Stage Minimum Spanning Tree Diagram Analysis
4. Discussion
5. Conclusions
5.1. Empirical Conclusions
5.2. Recommendations
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Primary Market | Secondary Market | Specific Index |
---|---|---|
capital market | stock market | CSI 300 Index |
bond market | Chinese bond index | |
money market | interbank market | Inter-bank overnight rate |
Foreign exchange market | US dollar to RMB | US dollar to RMB exchange rate |
commodity market | metal market | south China Metal Index |
energy market | south China Energy Index | |
agricultural products market | agricultural products index | |
gold market | AU9995 gold spot price | |
real estate market | Shanghai Real Estate Sector Index |
Market | Mean | Standard Deviation | Skewness | Kurtosis | Jarque-Bera | p |
---|---|---|---|---|---|---|
stocks | 0.000 | 0.016 | −0.147 | 7.681 | 1120.128 | 0.000 |
bonds | 0.000 | 0.012 | −0.542 | 10.200 | 2699.559 | 0.000 |
currency | 0.000 | 0.009 | 0.034 | 8.063 | 1305.579 | 0.000 |
exchange | 0.000 | 0.119 | 1.030 | 13.419 | 5743.428 | 0.000 |
metals | 0.001 | 0.014 | −0.319 | 6.963 | 820.360 | 0.000 |
energy | 0.001 | 0.002 | −0.098 | 5.109 | 228.446 | 0.000 |
agricultural products | 0.000 | 0.014 | −0.218 | 6.662 | 692.681 | 0.000 |
gold | 0.000 | 0.008 | 1.590 | 25.943 | 27,317.020 | 0.000 |
real estate | 0.000 | 0.001 | 0.781 | 17.752 | 11,204.740 | 0.000 |
Market | ADF | Prob. * |
---|---|---|
stocks | −35.736 | 0.000 |
bonds | −25.418 | 0.000 |
currency | −25.401 | 0.000 |
exchange | −33.304 | 0.000 |
metals | −34.580 | 0.000 |
energy | −34.790 | 0.000 |
agricultural products | −36.773 | 0.000 |
gold | −34.404 | 0.000 |
F-Statistic | 24.344 | Prob.F (1,1219) | 0.000 |
Obs * R-Squared | 23.907 | Prob.Chi-Square (1) | 0.000 |
Real Estate | Gold | Currency | Stocks | Foreign Exchange | Bonds | Agricultural Products | Energy | Metals | |
---|---|---|---|---|---|---|---|---|---|
real estate | 1.000 | −0.090 | 0.010 | 0.260 | −0.110 | −0.040 | 0.080 | 0.090 | 0.100 |
gold | −0.090 | 1.000 | 0.170 | −0.030 | −0.040 | 0.070 | 0.010 | 0.040 | 0.040 |
currency | 0.010 | 0.170 | 1.000 | −0.040 | −0.050 | 0.030 | 0.020 | 0.020 | 0.010 |
stocks | 0.260 | −0.030 | −0.040 | 1.000 | 0.010 | 0.010 | 0.020 | 0.070 | 0.060 |
foreign exchange | −0.110 | −0.040 | −0.050 | 0.010 | 1.000 | −0.010 | 0.010 | 0.020 | 0.020 |
bonds | −0.040 | 0.070 | 0.030 | 0.010 | −0.010 | 1.000 | −0.020 | 0.000 | −0.010 |
agricultural products | 0.080 | 0.010 | 0.020 | 0.020 | 0.010 | −0.020 | 1.000 | 0.430 | 0.320 |
energy | 0.090 | 0.040 | 0.020 | 0.070 | 0.020 | 0.000 | 0.430 | 1.000 | 0.730 |
metals | 0.100 | 0.040 | 0.010 | 0.060 | 0.020 | −0.010 | 0.320 | 0.730 | 1.000 |
Real Estate | Gold | Currency | Stocks | Exchange | Bonds | Agricultural Products | Energy | Metals | |
---|---|---|---|---|---|---|---|---|---|
real estate | 1.000 | −0.010 | 0.080 | 0.150 | 0.070 | 0.000 | 0.030 | 0.020 | 0.000 |
gold | −0.010 | 1.000 | −0.050 | −0.030 | 0.040 | 0.090 | 0.010 | −0.060 | −0.100 |
currency | 0.080 | −0.050 | 1.000 | 0.080 | −0.030 | 0.020 | −0.010 | −0.020 | −0.010 |
stocks | 0.150 | −0.030 | 0.080 | 1.000 | −0.170 | 0.010 | 0.040 | 0.020 | 0.070 |
exchange | 0.070 | 0.040 | −0.030 | −0.170 | 1.000 | −0.040 | 0.020 | 0.060 | −0.030 |
bonds | 0.000 | 0.090 | 0.020 | 0.010 | −0.040 | 1.000 | 0.060 | −0.010 | −0.060 |
agricultural products | 0.030 | 0.010 | −0.010 | 0.040 | 0.020 | 0.060 | 1.000 | 0.360 | 0.240 |
energy | 0.020 | −0.060 | −0.020 | 0.020 | 0.060 | −0.010 | 0.360 | 1.000 | 0.540 |
metal | 0.000 | −0.100 | −0.010 | 0.070 | −0.030 | −0.060 | 0.240 | 0.540 | 1.000 |
Real Estate | Gold | Currency | Stocks | Exchange | Bonds | Agricultural Products | Energy | Metals | |
---|---|---|---|---|---|---|---|---|---|
real estate | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 |
gold | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 |
currency | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
stocks | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
exchange | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
bonds | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |
agricultural products | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
energy | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 |
metals | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 |
Real Estate | Gold | Currency | Stocks | Exchange | Bonds | Agricultural Products | Energy | Metals | |
---|---|---|---|---|---|---|---|---|---|
real estate | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
gold | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 |
currency | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
stocks | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 |
exchange | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
bonds | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |
agricultural products | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 |
energy | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
metals | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 |
Average Clustering Coefficient | Average Path Length | Diameter | |
---|---|---|---|
Stage 1 | 0.444 | 1.861 | 3.111 |
Stage 2 | 0.350 | 1.694 | 3.444 |
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Xu, Y.; Zhao, Y.; Liu, M.; Xie, C. Research on Risk Contagion among Financial Submarkets in China Based on Complex Networks. Entropy 2022, 24, 1120. https://doi.org/10.3390/e24081120
Xu Y, Zhao Y, Liu M, Xie C. Research on Risk Contagion among Financial Submarkets in China Based on Complex Networks. Entropy. 2022; 24(8):1120. https://doi.org/10.3390/e24081120
Chicago/Turabian StyleXu, Yuhua, Yue Zhao, Mengna Liu, and Chengrong Xie. 2022. "Research on Risk Contagion among Financial Submarkets in China Based on Complex Networks" Entropy 24, no. 8: 1120. https://doi.org/10.3390/e24081120
APA StyleXu, Y., Zhao, Y., Liu, M., & Xie, C. (2022). Research on Risk Contagion among Financial Submarkets in China Based on Complex Networks. Entropy, 24(8), 1120. https://doi.org/10.3390/e24081120