12 Copula-SV-GPD 71 5 GARCH SV Copula GARCH 6-8 SV SV-t ARCH 9 10 Copula Copula-SV POT Copula-SV Copula- GARCH 1 1 SV-t SV Copula SV SV-t EVT 11 9 y t

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1 JOURNAL OF MANAGEMENT SCIENCES IN CHINA Vol 15 No 12 Dec Copula-SV-GPD 周孝华, 张保帅, 董耀武对于多元金融资产组合, 针对资产收益的厚尾性波动的异方差性及资产间的非线性相关结构等特征, 采用 SV-t 模型与极值理论结合刻画单个资产收益的波动性及尾部分布特征, 应用 Copula 函数处理多元资产间的相关性, 并结合 Monte Carlo 模拟对投资组合进行风险测度通过对华安创新基金的实证分析结果表明, 基于 SV-GPD 的边缘分布模型能有效地刻画金融资产收益时序并较为精确地处理资产收益尾部的异常变化, 相比其他风险度量模型具有更好的优越性, 基于 Copula-SV-GPD 模型的多元资产组合对风险测度能力更强, 能有效地管理投资风险 Copula; SV-GPD; Monte Carlo 模拟 ; VaR F A VaR value at risk Copula VaR VaR Copula VaR Copula Copula 90 3 VaR Copula CDJXS zhxiaoh@ yahoo com cn

2 12 Copula-SV-GPD 71 5 GARCH SV Copula GARCH 6-8 SV SV-t ARCH 9 10 Copula Copula-SV POT Copula-SV Copula- GARCH 1 1 SV-t SV Copula SV SV-t EVT 11 9 y t y t = ln p t - E p ln p t t -1 [ p t - ] 1 1 VaR p t y t y t ~ N 0 σ 2 t σ 2 t y t t - 1 POT GARCH SV SV-t Copula y t = ε t e h t / ln σ t = μ + ln σ t -1 - ω + τη t 2 h t = ln σ 2 t Copula η t ~ nid 0 σ 2 ε η t ~ t 0 1 υ ε t η t < 1 SV-t SV-t Copula SV ε t υ t Copula 1 SV-GPD Taylor SV-t μ τ υ QML Monte Carlo GMM VaR MCMC Markov Chain Monte Carlo

3 F u y 18 u G ξ β y MCMC { F u y G ξ β y = ξ y 1 β - ξ ξ 0 MCMC 1 - e - y β ξ = 0 6 ξ β ξ 0 Gibbs MCMC SV-t y x F - σ /ξ ξ < 0 y 0 - β /ξ BUGS G ξ β y Kim 18 GPD 19 GPD 1 + μ ~ i i N τ 2 ~ Beta ~ IGamma υ ~ χ SV-GPD z EVT SV-GPD VaR N L 12 u POT N 1 + u L - z ξl -1 /ξl z < u L β L F Z = Φ z u L z u R 1 - NR u N 1 + z - u R ξr -1 /ξr R z > u β R SV-t 7 Z t μ^ t σ^ t ξ L β L u L N L Z t-n+1 Z t = X t-n+1 - μ^ t-n+1 X u z t - μ^ t ξ R β R σ^ t-n+1 σ^ t u R N R u z 3 u Z t ξ β VaR u Pareto Z t F Z = 20 P Z z Z u F u F Z F u F u y = p Z - u y Z > u F u y = = F u + y - F u 1 - F u F z - F u 1 - F u 4 5 Z t 2 Copula VaR 0 y z F - u z F Copula F u Copula VaR

4 12 Copula-SV-GPD 73 Copula Monte Carlo 2 1 Copula VaR Copula C 0 22 Kendall 1 n 0 1 F 1 F n 0 1 Sklar 1959 K 1 Copula Copula Copula Copul N Copula F n F x 1 F x 2 C Σ u 1 u N = Φ Σ Φ -1 u 1 Φ -1 u N F x n Copula 8 C F x 1 x 2 x n = C F x 1 F x 2 F x n F x 1 F x 2 F x n Copula C n Copula F 1 F 2 F n 2 3 Monte Carlo VaR F F 1 F 2 F n n Sklar Copula Copula 0 1 n VaR VaR n 0 Copula Monte Carlo X Monte Carlo Y F x G y Copula C F x G y VaR P δx δ Y > γ = dc F x G y δ X γ r i1 r i2 r it i = 1 N α Copula Copula Copula 2 2 Copula τ Spearman ρ Copula 23 Copula Σ Φ Σ Σ N Φ -1 Copula VaR n i F 1 F n Copula C u 1 u n u 1 = F 1 x u n = F n x u 1 u n 0 1 Copula Monte Embrechts 21 Carlo VaR Copula Copula C u 1 u n u 1 u n 2 F 1 F n u 1 u n x 1 x n

5 x 1 = F -1 1 u 1 x n = F -1 u n n 3 i λ i 0 1 z = n λ i x i i = 1 1 K-S 4 1 ~ 3 SV-GPD GPD 1 α VaR P L > VaR = α GPD QQ GPD 3 SV-GPD 3 1 Copula β L K-S Table 1 Top ten portfolio s weight of Hua An Innovation Fund % % K-S R it 2 ~ 7 1 SV-GPD Fig 1 QQ fitting results for GPD distribution of up tail 2 overflow data for Pudong Development Bank 2 Table 2 Marginal distribution parameters for Pudong Development Bank μ 2 34 β R φ ξ R τ u L υ u R 1 60 ξ L K-S t Copula Copula 21 3 Copula GPD QQ

6 12 Copula-SV-GPD 75 3 Copula Table 3 Estimates of interrelated parameters matrix for multivariate normal Copula function VaR Copula-SV-GPD Monte Carlo VaR Copula-GARCH-t Copula-SV-t VaR VaR 4 4 VaR Table 4 VaR of the single stock and portfolio 5 3 VaR Table 5 VaR of the investment portfolio for three models VaR VaR / VaR 90% VaR 95% VaR 99% Copula-GARCH-t Copula-SV-t Copula-SV-GPD VaR VaR VaR % 5 3 VaR 3 Copula Copula-SV-GPD VaR VaR SV-GPD GARCH-t SV-t VaR Copula-SV-GPD Monte Carlo VaR Kupiec 24

7 LR LR = - 2ln 1 - p T-N p N + 2ln 1 - N /T T-N N /T N T N N /T = p p LR Copula Copula-SV-GPD 1 χ 2 Kupiec SV-GPD 6 T = Table 6 Failures measurement of portfolio when T = SV % < N < < N < 36 4 < N < Monte Carlo SV Copula Copula 1 Longin F Solnik B Extreme correlation of international equity markets J Journal of Finance Ang A Bekaert G International asset allocation with regime shifts J Review of Financial Studies Copula J Zhang Yaoting Copula technology and financial risk analysis J Statistics Research in Chinese 4 Rodriguez J C Measuring financial contagion A copula approach J Journal of Empirical Finance Consigli G Tail estimation and mean - VaR portfolio selection in markets subject tofinancial instability J Journal of Banking & Finance J Li Xiumin Shi Daoji Research and analysis on Shanghai and Shengzhen stock market s relate structure J Journal of Ap-

8 12 Copula-SV-GPD 77 plied Statistics and Management in Chinese 7 Copula-APD-GARCH J Ren Xianling Ye Mingque Zhang Shiying Analysis on portfolio effective frontier based on Copula-APD-GARCH model J Chinese Journal of Management in Chinese 8 Copula-GARCH LPM J Liang Jianfeng Chen Jianping Liu Jingjun Hedging with LPM based on Copula-GARCH method J Journal of Systems Engineering in Chinese 9 GARCH SV VaR J Yu Suhong Zhang Shiying Song Jun Comparison of VaR based on GARCH and SV models J Journal of Management Sciences in China in Chinese 10 Copula-SV J Zhan Xueli Zhang Shiying Analysis on financial investment portfolio s risk based on Copula-SV model J Journal of System & Management in Chinese 11 Bekiros S D Georgoutsos D A Estimation of value-at-risk by extreme value and conventional methods A comparative evaluation of their predictive performance J Journal of International Financial Markets Institutions and Money Ramazan G Faruk S Extreme value theory and Value-at-Risk Relative performance in emerging markets J International Journal of forecasting J Wei Yu Research on extreme value risk measurement and posterior estimate in stock market J Journal of Management Sciences in China in Chinese 14 Copula VaR J Fu Qiang Xing Linlin Calculate on condition VaR based on extreme value theory and copula function J Journal of System Engineering in Chinese 15 J Li Yuelei Zhang Wei Xiong Xiong et al Investigation on prevention ofmanipulation in the stock index future markets based on method of extreme correlation J Journal of Management Sciences in China in Chinese 16 EVT-VaR J Lin Yu Huang Dengshi Wei Yu Study on financial markets dynamic EVT-VaR measuring based on fated-tail distribution and long memory volatility J Journal of Management Sciences in China in Chinese 17 EVT-POT-SV-MT J Dong Yaowu Zhou Xiaohua Jiang Ting Extreme risk measurement based on EVT-POT-SV-GED model J Journal of Industrial Engineering /Engineering Management in China in Chinese 18 Kim S Shephard N Chib S Stochastic volatility Likelihood inference and comparison with ARCH models J Review of Economic Studies Dempster M A H Risk Management Value at Risk and Beyond M Cambridge Cambridge University Press Stuart Coles An Introduction to Statistical Modeling of Extreme Values M London Springer 2001

9 Embrechts P Kluppelburg C Mikosch T Modelling Extremal Events for Insurance and Finance M Berlin Springer Copula-Garch J Wei Yanhua Zhang Shiying Analyses on financial market correlation Copula-Garch model and applying J System Engineering in Chinese 23 Embrechts P McNeil A Straunmn D Correlation Pitfalls and alternatives J Risk Kupiec P Techniques for verifying the accuracy of risk measurement models J Journal of Derivatives Risk measurement of financial portfolio based on Copula-SV-GPD model ZHOU Xiao-hua ZHANG Bao-shuai DONG Yao-wu School of Economics and Business Administration Chongqing University Chongqing China Abstract In view of the characteristics of fat tail fluctution heteroscedasticity and nonlinear correlation of the combination of multiple financial portfolios this paper combines the SV-t models with the EVT to depict the single asset return volatility and tail characteristics and applies the Copula function to treat with the non-linear structures among assets and measures the risk of portfolio by Monte Carlo simulation By empirical research of Hua An Innovation Fund it is found that the risk measurement model can effectively manage investment risk based on Copula-SV-GPD method which could effectively depict the time series of returns of financial assets and accurately treat abnormal changes of the tail Key words Copula SV-GPD Monte Carlo Simulation VaR

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untitled 2005 1 Frechet 2 31999-2003 1993-1998 4 Pearson GPD 500 200122 0216840-1002 han.gf@shfe.com.cn Abstract We examine the tail characteristics of and tail dependence between return series of copper futures