A new Copula-CoVaR approach incorporating the PSO-SVM for identifying systemically important financial institutions

Figures & data

Figure 1. The flow chart of PSO-SVM-Copula-CoVaR model.

Source: Authors.

Table 1. Basic information of financial institutions.

Number	Code	Full name of the institution	Abbreviation
1	000001.SZ	PingAn Bank	PAB
2	002142.SZ	Bank of Ningbo	BONB
3	600000.SH	Shanghai Pudong development Bank	SPDB
4	600015.SH	HuaXia Bank	HXB
5	600016.SH	China Minsheng banking Corp., Ltd	CMBC
6	600036.SH	China merchants bank	CMB
7	601009.SH	Bank of Nanjing	BONJ
8	601166.SH	Industrial Bank	IB
9	601169.SH	Bank of Beijing	BOBJ
10	601288.SH	Agricultural Bank of China	ABC
11	601328.SH	Bank of communications	BOCOM
12	601398.SH	Industrial and commercial Bank of China Ltd.	ICBOC
13	601939.SH	China construction bank	CCB
14	601988.SH	Bank of China	BOC
15	601998.SH	China CITIC bank	CNCB
16	601818.SH	China Everbright Bank	CEBB
17	000686.SZ	Northeast securities	NES
18	000728.SZ	Guoyuan securities	GYS
19	000783.SZ	Changjiang securities	CJS
20	600030.SH	CITIC securities	CITICS
21	600109.SH	Sinolink securities	SLS
22	600837.SH	Haitong securities	HTS
23	601318.SH	Ping An insurance (group) Co. of China, Ltd.	PAICOC
24	601601.SH	China Pacifific insurance (group) Co., Ltd.	CPIC
25	601628.SH	China life insurance (group) co., Ltd.	CLIC
26	600643.SH	Shanghai Aj Group Co., Ltd	SAGC
27	000563.SZ	Shanxi International Trust & Investment Corp., Ltd.	SITI
28	601099.SH	The Pacific Securities Co., ltd	PSC

Source: Authors.

Table 3. CoVaR results of different marginal distribution estimation methods (calculation results based on Shanghai Securities Composite Index).

Institutions	GJR-GARCH	Kendisty	PSO-SVM
PAB	−0.0272	−0.0782	−0.0782
BONB	−0.0333	−0.0305	−0.0303
SPDB	−0.017	−0.0234	−0.0232
HXB	−0.0142	−0.0227	−0.0227
CMBC	−0.0121 (#4)	−0.0267	−0.048
CMB	−0.03	−0.0758	−0.0758
BONJ	−0.0291	−0.026	−0.0254
IB	−0.0232	−0.1018	−0.1018
BOBJ	−0.0109 (#2)	−0.0207	−0.0207 (#5)
ABC	−0.0112 (#3)	−0.0153 (#2)	−0.0153 (#2)
BOCOM	−0.0136	−0.0178 (#4)	−0.0179 (#4)
ICBOC	−0.0143	−0.017 (#3)	−0.017 (#3)
CCB	−0.0131 (#5)	−0.0199	−0.0474
BOC	−0.0103 (#1)	−0.0148 (#1)	−0.0149 (#1)
CNCB	−0.0173	−0.0234	−0.023
CEEB	−0.0168	−0.0214	−0.0214
NES	−0.0353	−0.037	−0.0369
GYS	−0.0308	−0.0357	−0.0357
CJS	−0.0308	−0.0819	−0.0819
CITICS	−0.0368	−0.0328	−0.0328
SLS	−0.0412	−0.0424	−0.0424
HTS	−0.0281	−0.0319	−0.0321
PAICOC	−0.027	−0.082	−0.082
CPIC	−0.0436	−0.0875	−0.0875
CLIC	−0.0484	−0.0812	−0.0812
SAGC	−0.0277	−0.039	−0.039
SITI	−0.0353	−0.0892	−0.0892
PSC	−0.0338	−0.0335	−0.033

Notes: #1–#5 are financial institutions ranked 1 to 5, respectively, in the calculation results.

Source: Authors.

Table 2. Mean square error of different marginal distribution methods.

Institutions	GJR-GARCH	Kendisty	PSO-SVM
PAB	0.0037	0.0014	0.0001
BONB	0.0018	0.0013	0.0002
SPDB	0.0061	0.0022	0.0002
HXB	0.0096	0.0033	0.0005
CMBC	0.0094	0.0056	0.001
CMB	0.004	0.0014	0.0002
BONJ	0.0023	0.0024	0.0001
IB	0.0033	0.0015	0.0001
BOBJ	0.0094	0.0045	0.0001
ABC	0.0145	0.0272	0.0004
BOCOM	0.0114	0.0072	0.0002
ICBOC	0.0068	0.0108	0.0001
CCB	0.0053	0.0059	0.0005
BOC	0.0188	0.0191	0.0003
CNCB	0.0106	0.005	0.0007
CEEB	0.0193	0.0102	0.0002
NES	0.0085	0.0016	0.0004
GYS	0.006	0.0014	0
CJS	0.0077	0.0019	0.0001
CITICS	0.003	0.0012	0.0001
SLS	0.0037	0.0013	0
HTS	0.0093	0.0016	0.0001
PAICOC	0.0038	0.0012	0
CPIC	0.0107	0.0032	0.0007
CLIC	0.0073	0.0011	0
SAGC	0.0064	0.0015	0.0001
SITI	0.0078	0.0025	0.0005
PSC	0.0026	0.0011	0.0002

Notes: Bold value is the minimum value.

Source: Authors.

Table 4. CoVaR results of different marginal distribution estimation methods (calculation results based on Shenzhen Securities Component Index).

Institutions	GJR-GARCH	Kendisty	PSO-SVM
PAB	−0.0272	−0.0781	−0.0781
BONB	−0.0332	−0.0302	−0.0299
SPDB	−0.0169	−0.0231	−0.0228
HXB	−0.0142	−0.0225	−0.0224
CMBC	−0.012 (#4)	−0.0592	−0.0592
CMB	−0.0299	−0.0271	−0.0268
BONJ	−0.0291	−0.0258	−0.0251
IB	−0.0231	−0.0269	−0.027
BOBJ	−0.0108 (#2)	−0.0205	−0.0204 (#5)
ABC	−0.011 (#3)	−0.0149 (#2)	−0.0149 (#2)
BOCOM	−0.0134	−0.0176 (#4)	−0.0175 (#4)
ICBOC	−0.0141	−0.0165 (#3)	−0.0165 (#3)
CCB	−0.013 (#5)	−0.0195 (#5)	−0.0474
BOC	−0.0103 (#1)	−0.0146 (#1)	−0.0146 (#1)
CNCB	−0.0172	−0.0232	−0.0227
CEEB	−0.0167	−0.0212	−0.021
NES	−0.0352	−0.037	−0.0369
GYS	−0.0307	−0.0357	−0.0358
CJS	−0.0307	−0.0346	−0.0347
CITICS	−0.0367	−0.0328	−0.0327
SLS	−0.0411	−0.0423	−0.0423
HTS	−0.028	−0.0812	−0.0812
PAICOC	−0.0269	−0.0819	−0.0819
CPIC	−0.0435	−0.0875	−0.0875
CLIC	−0.0482	−0.0812	−0.0812
SAGC	−0.0277	−0.0389	−0.0389
SITI	−0.0352	−0.0794	−0.0794
PSC	−0.0337	−0.0333	−0.0327

Notes: #1–#5 are financial institutions ranked 1 to 5, respectively, in the calculation results.

Source: Authors.

Table A1. Six different copula functions.

Copula	Definition of $C(u_1,u_2;\theta )$	$\theta$ limits
Gaussian	${\Phi }_{\theta }\left({{\Phi }^{-1}(u}_1),{{\Phi }^{-1}(u}_2);\theta \right)$	$[-1,1]$
T	$T_2(T_v^{-1}(u_1),T_v^{-1}(u_2);\theta ,v)$	$[-1,1]$
Clayton	${\left(u_1^{-\theta }+u_2^{-\theta }-1\right)}^{-1/\theta }$	$(0,\infty )$
Gumbel	$\exp \left\{-{\left[{(-ln{u}_1)}^{\theta }+{(-ln{u}_2)}^{\theta }\right]}^{1/\theta }\right\}$	$[1,\infty )$
Frank	$-\frac{1}{\theta }\mathrm{l}\mathrm{n}[1+\frac{(e^{-\theta u_1}-1)(e^{-\theta u_2}-1)}{e^{-\theta }-1}]$	$(-\infty ,\infty )\setminus \left\{0\right\}$
Joe	$1-{\left({\left(1-u_1\right)}^{\theta }+{\left(1-u_2\right)}^{\theta }-\left(1-u_1\right){\left(1-u_2\right)}^{\theta }\right)}^{1/\theta }$	$[1,\infty )$

Source: Authors.

Table A2. Descriptive statistics of financial institutions’ yield series.

Institutions	Mean value	Maximum	Minimum	Standard deviation	Skewness	Kurtosis	The value of JB
PAB	−0.0004	0.1004	−0.1002	0.0217	0.4291	3.2719	1048.0822
BONB	0	0.1004	−0.0998	0.021	0.3585	2.7689	749.5641
SPDB	0	0.1003	−0.1002	0.0161	0.5181	6.9072	4464.9874
HXB	0	0.1005	−0.1003	0.0159	0.5266	7.2739	4944.0742
CMBC	0	0.1001	−0.0999	0.0156	0.7018	10.0187	9365.2931
CMB	−0.0005	0.1003	−0.0991	0.0184	0.3989	3.2757	1041.2027
BONJ	0	0.1003	−0.0996	0.018	0.3873	4.4822	1894.4847
IB	−0.0006	0.1005	−0.1002	0.0187	0.4973	4.8305	2226.9294
BOBJ	0	0.0996	−0.0997	0.0145	0.5356	8.5778	6838.5964
ABC	0	0.1012	−0.099	0.0119	0.6253	12.5867	14638.5466
BOCOM	0	0.101	−0.0999	0.0136	0.9544	12.7164	15128.866
ICBOC	0	0.0853	−0.099	0.012	0.2323	8.8938	7258.5516
CCB	0	0.1004	−0.0994	0.0142	0.5048	8.1101	6112.7821
BOC	0	0.1014	−0.1004	0.0118	0.8192	15.4914	22201.6703
CNCB	0	0.1009	−0.1003	0.0173	0.8425	8.1371	6319.3392
CEEB	0	0.1014	−0.0992	0.0156	0.929	7.4127	5344.8072
NES	0	0.1005	−0.1001	0.0248	0.2152	3.7053	1274.4205
GYS	0	0.1005	−0.1001	0.0241	0.2447	3.7559	1313.9505
CJS	0	0.1007	−0.1008	0.0241	0.3832	3.9736	1499.8072
CITICS	−0.0008	0.1004	−0.1001	0.0235	0.4675	4.2214	1711.8527
SLS	−0.0005	0.1005	−0.1003	0.0282	0.2921	2.8126	756.0823
HTS	−0.0007	0.1005	−0.1001	0.023	0.4589	4.5373	1962.1611
PAICOC	−0.0002	0.0964	−0.1	0.0191	0.2638	3.0363	870.1473
CPIC	0	0.102	−0.1001	0.0255	0.4426	3.8837	1453.0792
CLIC	−0.0005	0.1004	−0.1001	0.0223	0.6184	4.2513	1794.9185
SAGC	0	0.1005	−0.1002	0.0254	0.1512	3.3439	1032.7094
SITI	0	0.1017	−0.1007	0.0267	0.2726	3.3897	1079.7279
PSC	0	0.1001	−0.1001	0.0218	0.2471	2.2402	482.4474

Source: Authors.