Financial market openness and risk contagion: A time-varying Copula approach
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1 ½ 31 ½ 4 Ò Vol.31, No Systems Engineering Theory & Practice Apr., 11 : (11) : F83.9 ÞÁã : A Ùî Copula ÃÑè öü», è ( Ã, 3118) ý î Copula Ñè Á ö ù ÁË ùñ öü» Ã. AR(1)-GJR(1,1)-t º Á þ Ë, î SJC Copula þ Ñ í, Á ö ù ßÁ ù Á ù ù Ð ù 1 æ 1 11 Ñ öü. Ý ÂÄ : Ñè Á ö ù ßÁ Á ùè ç í³, Ð ùñ ç í ÃáÑè Ç Æ Û ; ÁË ù ç í Ãè. ³ öü»; ÃÑè; î Copula Financial market openness and risk contagion: A time-varying Copula approach WANG Yong-qiao, LIU Shi-wen (College of Finance, Zhejiang Gongshang University, Hangzhou 3118, China) Abstract The paper proposes a time-varying Copula to study financial contagion issues between China mainland and major international stock markets in the opening process of Chinese capital markets. By modeling marginal distributions as AR(1)-GJR(1,1)-t and dependence relations as time-varying SJC Copula, the paper analyzes time-varying co-movements between China mainland and US, UK, Japan, HK stock markets in the interval from Jan to Nov 1. The empirical results show that: the lower-tail dependence with US, UK and Japan still stays in a weak level, while the lower tail dependence with HK steadily keeps increasing in the opening process; the upper-tail dependence with all international major stock markets shows a consistent low level. Keywords financial contagion; capital market openness; time-varying Copula 1 Á ö ù Å, Ðè ñ ù Ǒ º Ãù Đ è. Ãù ñ î, öü Í ù Ñ, Ǒð Á ö ù à í è [1]. á Á Ä Ã º Ä, Á ù Ñè, æä ö ù ¾ðè ù. Ñè Á ö ù º ù Ñ öü, óá Ãù öüëë à ã»â à ٵ Ý ûþ. Ãù ÑöÜ» àß ³ ß [] GARCH Ǒñ º [3] VAR àßǒ Æ ÂÙ [1] Ò [4]. Åàß ðó, í îñáð, ùöîñ, Ë í. ó ù þú : á : è (1YJC7965); (Y785); Ô» ( à ) ß¼:,, Ð ÃöÜ Ò Ã, wangyq@amss.ac.cn; è, µ, Ð ÃöÜ Ò.
2 ½ 4, : Ùî Copula ÃÑè öü» 779 ó Ñè Á Ãù ÁË Ãù Ñ öü», Í ÆÑèÄ Ùµ Þ. î Copula àß Ñè Á ù ÁË ù Ñ ö Ü. Õ àß ³, àß Û : èð Copula ø Ãù Ñ í, ³ àß ³ Í Òê í, GARCH º VAR º ³ Á þ, ÍÅ» È ù Ñ ê í ç í½ǒ; ð î ÍÅ» Ñè Á Ãù º Ãù Ñ Þ. Copula ø Ǒ Joe-Clayton (SJC) Copula, Í à ç í ç í. : ½ ¼«î SJC Copula ø Ç Ã, ½ 3 î SJC Copula ÝÒ ßÁ â Á Ãî 1 Nikkei5 Ð µ Ñ í, ½ß Ó. î Copula Ò.1 SJC Copula Sklar ùò [5], è N á µǒ N Ë ø è Copula ø. Â Ë ð, à Copula ø ð è. ð Copula ø ãäåá Ñ í, Copula ø Ǒ Ǒí ø. Copula ø á Ç Ò Ǒß. æ Ç, Õ ß Ç èá Ë, ¾ Õ ß Ç Copula ø. Copula ø ß» Ò Ãù Ñ ç í, ç í è Ãù ( Ç), ð è ù (ù Ç).  Ãù Ñ Copula ø Ǒ C(u, v), à ç í ç í ÇǑ λ L C(u, u) = lim u u, λ U = lim u 1 1 u + C(u, u) 1 u Copula ø Copula, t-copula, Gumbel Copula, Clayton Copula, Frank Copula. Å Copula ø Ù Ãù Ñ öü î Û, Copula t-copula ß È Ãù Ñ ê í, Gumbel Copula ß È ç í, Clayton Copula ß Èç í, Frank Copula ø ç í ç í ß È. Joe [6]  Joe-Clayton Copula ø ( ß JC Copula) Ãù Ñ í, ø» { { } C JC (u, v) = 1 1 [1 (1 u) κ ] γ + [1 (1 v) κ ] γ 1/γ 1/κ 1}, κ 1, γ > () Copula ø ³, JC Copula ø Û, î ç í ç í. ç í ç í Ǒ λ L = 1/γ, λ U = 1/κ. JC Copula è, ç í î, JC Copula ø ðê. Ǒ, Patton [7]  JC Copula ø ( ß SJC Copula) ǑÜù Ñ í : C SJC (u, v) = C JC (u, v) + C JC (1 u, 1 v) + u + v 1 Ù SJC Copula Í î ç í, Í Òê ç í, ¾ Ù Ã ù Ñù Ã Ñ öü».. î SJC Copula Ãù Ñ í³ Íá Ä Ã Þ Þ, Á î Copula º Ãù Ñ ê í [8]. î Copula ºíõ, è ð î, è ð î [9 1]. à î SJC Copula Ãù Ñ í. t î á Ëçø ÇǑ f 1 f, ø Ǒ F 1 F, ø Ǒ θ 1 θ ( î, θ 1t θ t ), SJC Copula î Ǒ θ ct = {κ t, γ t }, à (1) (3)
3 78 Ò ½ 31 Ä Ǒ f(x 1t, x t ; θ 1, θ, θ ct ) = f 1 (x 1t ; θ 1 ) f (x t ; θ ) c(f 1 (x 1t ; θ 1 ), F (x t ; θ ); θ ct ) (4) c(u, v) = C(u,v) u v Ǒ Copula ç. îñë Ǒ (x 1t, x t ), t = 1,,,T. ù θ 1, θ θ c ½ Õ Çî, ½ [11], ½è Ë ½ Õ Ç ˆθ 1 arg max θ 1 T log f 1 (x 1t ; θ 1 ), ½ Copula ½ Õ Ç ˆθ ct arg max θ ct T ˆθ argmax θ T log f (x t ; θ ) (5) log c (F 1 (x 1t ; ˆθ 1 ) F (x t ; ˆθ ) ); θ ct ½ Çî, Á T Ç T, ð ½. Patton [7] ç í ½ ½ Copula ø î Ç, λ L t = Λ ω L + β L λ L t 1 + α L 1 q u t j v t j (7) q j=1 ( ) λ U t = Λ ω U + β U λ U t 1 + α U 1 q u t j v t j (8) q Λ( ) Ǒ Logistic ø Λ(x) = 1/(1 + e x ). Λ( ) ðǒå Ý < λ L t < 1, < λu t < 1. u t = F 1 (x 1t ; ˆθ 1 ), v t = F (x t ; ˆθ ). Þà ÕÙ ARMA(1, q) º, q è 1. Ù JC Copula ç í èè, î κ t γ t Ä γ t = 1/ log λ L t κ t = 1/ log ( λ U t ). Ä, î κ t γ t Ñ Ä ó ω L, β L, α L, ω U, β U, α U Õ Ç. 3 Ý î SJC Copula º ÝÒ (SSEC) ßÁ â (DJIA) Á Ãî (FTSE1) 5 (Nikkei5) Ð µ (HSI) Ñ öü ³. ÙÕ ù Ö³, ÝÒ ãäë» ù. ßÁ ð º ÄÆ, Ç Áã ãä. ÐðÁË Ã ±, Ð Ä ö Ä ç, µ ãä ö ù Ð ù Ñ. 3.1 þ Ǒ, ü îñǒ 1 4 æ Ù 9 ãð Á ù Đî, Ù Å, Ñè Ǒ³, Ùñ. Î, Á Ä WTO, QFII QDII ë, Í è Á ù Ñè. ü Ñè Á ù ÁË ù Ñ öü Ò. þ Ç ï Ä 1. ÝÒ, ÁËù þ ÄÝ Û Ôôíç. Jarque-Bera ÇÄ þ Û ê. Ä 1 Ç SSEC DJIA FTSE1 Nikkei5 HSI ÁÇ« ô Jarque-Bera (6)
4 ½ 4, : Ùî Copula ÃÑè öü» Ë Ç Â, AR(1)-GJR(1,1)-t º þ Ë, Æ» R t = µ + φr t 1 + ε t σt = ϕ + Gσt 1 + LI ( ε t 1 )ε t 1 + Aε t 1 ν σt (ν ).ε t iid t ν I (x) Ǒ ø, x > î, I (x) = 1, x î, I (x) =. þ Ë Ç Â Ä. þ L Ǒ, Ä ù à î Ö. Ä Ë Ç SSEC DJIA FTSE1 Nikkei5 HSI µ φ ϕ..... G A L ν Diehoid [1] Ë ½ Ù : èð Ù, ð Ù. Ljung- Box Ù ÂÄ, 5% Û 5 îñë Đ ³, Ǒ Ë ð. Kolmogorov-Smirnov Ù ð, Ù Î Ë ð Ð [,1], 5 Ë 5% Û ÄÙ. ÂÄ AR(1)-GJR(1,1)-t º þ Ë. 3.3 Ý ÒØ [13] Ǒ Á ù Ñè ð Ð Ñè Ñè Æ Đ. 1 1 Á WTO û à â Ä Ë Ñè, ð Á ù âñè Ñ. 3 7 ½èµ QFII ð Ù, Áã Á Ñ ÁË ù, 6 11 Á˽è QDII ÃÁã Á Ñ ÁË ù, 5 7, ½ Í Ëð Á ù åáëþ. Ó Á ù Ñè ûþ, ð ÁÑ ÑèÁË ù Áã. Ó Áã Ǒ º Ö Á ù Ñè Ǒ, Ë Á ù º ù Ñ öü Ç Đ,» öü Ñè Þ. 3.4 Copula î Ç Ë Ç,. ½ àß î SJC Copula 6 î ½ Õ Ç. Ǒ, SJC Copula º Ǒ ½ Ç. Ç Â º AIC Ä 3. Ä 3 Copula Ç SSEC-DJIA SSEC-FTSE1 SSEC-Nikkei5 SSEC-HSI ω L β L α L ω U β U α U AIC λ U.1.93 λ L AIC (9)
5 78 Ò ½ ç í ÝÒ Ó ÁË Ñ î ç í 1. Û Á ö ù ßÁ Á ù Ñ ç í Ñè, ßÁ DJIA ç í.5 Ñ ¾, Á FTSE1 ç í.1 Ñ, ä ÑǑÚ Ý Û. Ð 1 ÛÛ : Á ç í è ³, Ú ÄÝ, î Å Û. AIC ² ÇÃǑ ³î SJC Copula, SJC Copula Í» Á ö ù ß ù Ñ ç í. Á î ç í ê Ù, Ù ç í à á Ù. Ä Á ù ß ù Ñ öü ³, ù, Á ù ß ù î Ý ÇÝæ Î. ä ç í Þ,  Âê. Ù [14] î Copula à ßÙÝ ß Ñ ä ç í Ç, Þê. áâï [15] î t-copula àßùý ß ù ä í Ç. ÁË è Á ö ù ß ù Ñ ½ Í öü. Á ù ù Ñ ç í.15 Ѿ, ô Ä., ß ù. ç í î Û, ûú Û Þ. AIC ² ÇÃÄ î SJC Copula Á ù ùñ ç í Â, Á ù ù Ñ ç í Ùî. Ä Á ù ù Ñ öü ß ù Ö, û Đ èù, Á ù ù î Ý ÇÝæ Í, Ǒá Á ö ù Ñè Ç, ù öü ³ ûú Û Ç. Á ö ù Ð ù ç í Ò Ú ÄÝ, àð ÝÅ Ç. 5 Í 6 QDII ë Á ù Ð ù Ñ ç í ÝÅ. Ñè Á ö ù Ð ù ç í ÄÝ î, ½Ó½ É Ý ô, Ôî.84. û î SJC Copula» È Á ö ù Ð ù Ñ ç í Þ, AIC ² Çà Âèç. Ä á Á ù Ñè, Á ù Ð ù Ñ öü ÄÝ Û, Á ö ù Ð ù î Ý ÇÝæ Î Ä î Ç - - Ä Ç 1 ÝÒ ÁË ù Ñ ç í 3.6 ç í ÝÒ Ó ÁË Ñ î ç í. Û, Á ù Ñè Á ö ù ßÁ Á ù ç í Ǒ ( Ù ), Ä Á ù ß ù ù î Î., ß ù ù Ú Á ù, Á ù 7 ù îßá ù± ä è Ǒ. ÁË Á ù
6 ½ 4, : Ùî Copula ÃÑè öü» 783 ÁË ù Ñ í Copula t-copula, Å ç í. ³ß ù ù, Á ö ù Ð ù ç í, Ǒ Ù, è.1 Ѿ. Á ù ÑèÄ ù, ûú ÄÝ. Ä Á ö ù Ð ù î Î Ǒ. Ó [16] Gumbel Copula ǑÜ ÝÒ Ð µ Ñ öü, Ç ç í ÂǑ.9, Âê. Ù Á ö Ð ç Ä Æ» îù, Ä ù î» µ, ³ß ù ù, Á ö ù Ð ù ÑÄÝ ç í Ä î Ç - - Ä Ç ÝÒ ÁË ù Ñ ç í 4 î SJC Copula º Ñè Á ù ÁË ùñ öü, î öü Þ, SJC Copula ê ç í. Ý ÂÄ, Á ö ù ßÁ Á ù Ñí ç í ç í, Á ù î ù Ç Í, Đ öü»³ ; ö ù Ð ù Æ Ç.  ÁË Ã Đ. Ù Á ö ù ßÁ Á ù Ñ ç í, Å ùñ öü. Á ö Ð ù Ñ ÙĐ ç í, Çð ç í Á ö ù ÑèÄ Ö, Á ö ù Ð ùñ ½ èî ûã Ùµ öü, í» ù î Ç. Ð ÃöÜ Æ, Ù Á ö ù Ð ùñ ç íî Û, ÆÄÝ Ö,  ó àß Ç Ñ í, Í öü. Đ Þ [1] Hong Y M, Liu Y H, Wang S Y. Granger causality in risk and detection of extreme risk spillover between financial markets[j]. Journal of Econometrics, 9, 15(): [] King M, Wadhwani S. Transmission of volatility between stock markets[j]. Review of Financial Studies, 199, 3(1): [3] Tse Y K. A test for constant correlations in a multivariate GARCH model[j]. Journal of Econometrics,, 98(1):
7 784 Ò ½ 31 [4] Longin F, Solnik B. Extreme correlations of international equity markets[j]. Journal of Finance, 1, 56(): [5] Sklar A. Fonctions de répartition àn dimensions et leurs marges[j]. Publ Inst Statist Univ Paris, 1959(8): [6] Joe H. Multivariate Models and Dependence Concepts[M]. London: Chapman & Hall, [7] Patton A J. Modelling asymmetric exchange rate dependence[j]. International Economic Review, 6, 47(): [8], áâï. î ³ [J]. Ò, 8, 8(8): Gong P, Huang R B. Analysis of the time-varying dependence of foreign exchange assets[j]. Systems Engineering Theory & Practice, 8, 8(8): [9] Rodriguez J C. Measuring financial contagion: A Copula approach[j]. Journal of Empirical Finance, 7, 14(3): [1] Harvey A. Tracking a changing Copula[J]. Journal of Empirical Finance, 1, 17(3): [11] Patton A J. Estimation of multivariate models for time series of possibly different lengths[j]. Journal of Applied Econometrics, 6, 1(): [1] Diebold F X, Gunther T, Tay A S. Evaluating density forecasts with applications to financial risk management[j]. International Economic Review, 1998, 39: [13] ÒØ. Á ù Ñèð üâ [J]. º Ä, 3(3): Ba S S. Review on the choices of the opening path of Chinese capital markets[j]. World Economics, 3(3): [14], Ù. ä ù öü ùñ í [J]. º Ä, 1(3): Wu J L, Zhang E H. Subprime mortgage crisis, market risk and dependence between stock markets[j]. World Economics, 1(3): [15], áâï. ä Á ùãǒ Ý Ù ß ù [J]. Òñ, 9, 1(): 1 3. Gong P, Huang R B. Empirical analysis of sub-prime mortgage crisis s impacts on Chinese stock market Based on the interaction between Chinese and American stock markets[j]. Management Review, 9, 1(): 1 3. [16] Ó,. Ý µ Copula ç ³ [J]., 6, 4(5): Li Y, Cheng X J. Copula dependence analysis between SSEC and HSI[J]. System Engineering, 6, 4(5): 88 9.
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