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Risk contagion in financial markets based on copula model

Li Ma
Li Ma
, 
Fahad Abdullah Alqurashi
Fahad Abdullah Alqurashi
 und 
Mohammed Helmi Qeshta
Mohammed Helmi Qeshta
   | 30. Dez. 2021
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Online veröffentlicht: 30. Dez. 2021
Seitenbereich: 565 - 572
Eingereicht: 16. Juni 2021
Akzeptiert: 24. Sept. 2021
DOI: https://doi.org/10.2478/amns.2021.1.00076
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© 2021 Ma et al., published by Sciendo.
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

S&P 500 daily yield (January 2015 to June 2019)
S&P 500 daily yield (January 2015 to June 2019)

Fig. 2

SSE 300 Financial Daily Yield (January 2015 to June 2019)
SSE 300 Financial Daily Yield (January 2015 to June 2019)

Four-stage K-S test of the marginal distribution

K-S K-S probability
Bp1 0.011 1
Bp2 0.012 1
Bp3 0.197 0.0523
Bp4 0.079 0.3508
Sh1 0.011 1
Sh2 0.009 1
Sh3 0.189 0.0704
Sh4 0.084 0.2909

Estimated values of the parameters of each marginal distribution model before the crisis broke out

BP1 μ1 ϕ1,1 ϕ1,2 ω1 α1 β1 ν1
0.0005 -0.0474 -0.0637 4.83E-05 0.1287 0.0538 3.3915
(0.0002) (0.0449) (0.0328) (8.53E-06) (0.0839) (0.1311) (0.2186)
Sh1 μ2 ϕ2,6 ω2 α2 β2 ν2
0.0019 -0.0762 1.86E-06 0.0457 0.9537 8.1928
(0.0007) (0.0456) (4.32E-06) (0.0215) (0.029) (2.9599)

SH1 and BP1Granger causality test

Lag length Null hypothesis F P In conclusion
1 SH1 is not a Granger reason for BP1 1.08434 0.29825 Accept
BP1 is not a Granger reason for SH1 0.63241 0.42686 Accept
2 SH1 is not a Granger reason for BP1 0.87401 0.41793 Accept
BP1 is not a Granger reason for SH1 2.1805 0.1141 Accept

Parameter estimation of each marginal distribution model in the first stage after the outbreak of the crisis

BP2 μ3 ϕ3,1 α3 β3 ν3
0.0002 0.1511 2.15E-06 0.0863 0.9107 7.4628
(0.0005) (0.0607) (2.43E-06) (0.0366) (0.037) (4.0494)
Sh2 μ4 ϕ4,5 ω4 α4 β4 ν4
0.0006 -0.1208 0.0003 0.0145 0.6166 8.394
(0.0013) (0.0494) (0.0005) (0.0513) (0.6567) (4.7757)

Parameter estimation of each marginal distribution model in the third stage after the outbreak of the crisis

BP4 μ7 ω7 α7 β7 ν7
8.33E-05 5.89E-05 0.0316 0.8417 10.24
(0.002) (5.59E-05) (0.0643) (0.1244) (11.2066)
Sh4 μ8 ωs α8 β8 ν8
0.0037 -7.38E-06 -0.0019 1.0107 19.81
(0.0018) (1.12E-05) (0.0359) (0.0521) (35.4823)

SH4 and BP4Granger causality test

Lag length Null hypothesis F P In conclusion
1 SH4 is not a Granger reason for BP4 3.76151 0.05459 Accept
BP4 is not a Granger reason for SH4 0.10389 0.74773 Accept
2 SH4 is not a Granger reason for BP4 2.99813 0.0534 Accept
BP4 is not a Granger reason for SH4 0.04023 0.96058 Accept

SH2 and BP2Granger causality test

Lag length Null hypothesis F P In conclusion
1 SH2 is not a Granger reason for BP2 0.08311 0.77329 Accept
BP2 is not a Granger reason for SH2 5.77063 0.01678 Refuse
2 SH2 is not a Granger reason for BP2 0.17162 0.84236 Accept
BP2 is not a Granger reason for SH2 3.17334 0.043 Refuse

Parameter estimation of each marginal distribution model in the second stage after the outbreak of the crisis

BP3 μ5 ω5 α5 β5 ν5
-0.0055 0.0015 -0.1642 0.4349 20.02
(0.0073) (0.0007) (0.0363) (0.4032) (90.079)
Sh3 μ6 ω6 α6 β6 ν6
-0.007 0.0004 -0.2405 1.0267 21.6
(0.0047) (0.0002) (0.0806) (0.171) (103.3)

SH3 and BP3Granger causality test

Lag length Null hypothesis F P In conclusion
1 SH3 is not a Granger reason for BP3 2.65028 0.11119 Accept
BP3 is not a Granger reason for SH3 0.00298 0.95676 Accept
2 SH3 is not a Granger reason for BP3 0.97062 0.38804 Accept
BP3 is not a Granger reason for SH3 1.084 0.34847 Accept

Correlation structure between the Standard & Poor’s 500 Index and the SSE 300 Financial Index

k v Date τ ρ Z statistics
1 490 2017/2/12 0.0382 0.0573 -2.5852
2 868 2018/9/18 0.1563 0.2308 0.2257
3 913 2018/11/28 0.1303 0.191 0.0056
4 1048 2019/6/29 0.1271 0.1901
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