The return of financial asset usually has a characteristic of fluctuation clustering with sharp peaks and fat tails, not complying with the normal distribution. Therefore, the nonlinear correlation should be considered when measuring the risk of an investment portfolio. In this respect, copula functions provide a fairly new approach for connecting the marginal distributions of nonlinear series in the high-dimensional risk assessment of portfolio. However, it is noteworthy that two challenging problems exist in this field:one is how to choose or construct an appropriate copula function, the other is how to estimate model parameters. To address these issues, a novel M-Copula-SV-t model is proposed in this paper. Specifically, SV-t model is first employed to fit the marginal distributions of financial time series, where MCMC method with Gibbs sampling are used to estimate marginal parameters; then an M-Copula function consisted of linearly combined Archimedean Copulas is designed to jointly connect these marginals. where joint model parameters are estimated by MLE and BFGS algorithm; afterwards Monte Carlo technique is adopted to simulate optimal portfolios under minimal values of VaR and CVaR. The model feasibility and effectiveness is fruther vertified by taking an example of four exchange rates, where the empirical results indicate that our mixture modeling outperforms other individual Archimedean Copula modeling in dealing with the issue of dimensionality curse, and capturing asymmetry and tailed fatness of portfolio analysis. Therefore, our proposed model contributes to the literature of intra-market portfolio management, and provides valuable suggestions for international investors with respect to short-term decisions.
[1] Nelsen R B. An introduction to copulas[M]. New York:Springer, 2006.
[2] Yang Lu, Hamori S. Gold prices and exchange rates:A time-varying copula analysis[J]. Applied Financial Economics, 2014, 24(1):41-50.
[3] Aloui R, Hammoudeh S, Nguyen D K. A time-varying copula approach to oil and stock market dependence:The case of transition economies[J]. Energy Economics, 2013, 39:208-221.
[4] Dajcman S. Tail dependence between Central and Eastern European and major European stock markets:A copula approach[J]. Applied Economics Letters, 2013, 20(17):1567-1573.
[5] Wang K, Chen Y, Huang S. The dynamic dependence between the Chinese market and other international stock markets:A time-varying copula approach[J]. International Review of Economics & Finance, 2011, 20(4):654-664.
[6] Miguel-Angel C, Eduardo P. Modelling dependence in Latin American markets using copula functions[J]. Journal of Emerging Market Finance, 2012, 11(3):231-270.
[7] Chen Wang, Wei Yu, Lang Qiaoqi, et al. Financial market volatility and contagion effect:A copula-multifractal volatility approach[J]. Physica A:Statistical Mechanics and its Applications, 2014, 398:289-300.
[8] Gülp?nar N, Katata K. Modelling oil and gas supply disruption risks using extreme-value theory and copula[J]. Journal of Applied Statistics, 2014, 41(1):2-25.
[9] Wu C, Lin Z. An economic evaluation of stock-bond return comovements with copula-based GARCH models[J]. Quantitative Finance, 2014, 14(7):1283-1296.
[10] 姚登宝,刘晓星,张旭.市场流动性与市场预期的动态相关结构研究——基于ARMA-GJR-GARCH-Copula模型分析[J]. 中国管理科学,2016,24(2):1-10.
[11] 姬强,刘炳越,范英.国际油气价格与汇率动态相依关系研究:基于一种新的时变最优Copula模型[J]. 中国管理科学,2016,24(10):1-9.
[12] Chen Jianli, Liu Zhen, Li Shenghong. Mixed copula model with stochastic correlation for CDO pricing[J]. Economic Modelling, 2014, 40:167-174.
[13] Choro?-Tomczyk B, Karl Härdle W, Overbeck L. Copula dynamics in CDOs[J]. Quantitative Finance, 2014, 14(9):1573-1585.
[14] Liao G, Pan T, Chang L, et al. Portfolio value-at-risk by Bayesian conditional EVT-copula models:Taking an Asian index portfolio for example[J]. Journal of Statistics and Management Systems, 2012, 15(2-3):345-367.
[15] Wang Zongrun, Chen Xiaohong, Jin Yanbo, et al. Estimating risk of foreign exchange portfolio:Using VaR and CVaR based on GARCH-EVT-Copula model[J]. Physica A:Statistical Mechanics and its Applications, 2010, 389(21):4918-4928.
[16] 李战江,迟国泰,党均章.基于copula的追随者银行的企业项目总体风险评价模型[J]. 中国管理科学,2015,23(1):99-110.
[17] 张晨,杨玉,张涛.基于Copula模型的商业银行碳金融市场风险整合度量[J]. 中国管理科学,2015,23(4):61-9.
[18] 叶五一,李潇颖,缪柏其.基于藤Copula方法的持续期自相依结构估计及预测[J]. 中国管理科学,2015,23(11):29-38.
[19] 林宇,陈王,王一鸣,等.典型事实、混合Copula函数与金融市场相依结构研究[J]. 中国管理科学,2015,23(4):20-9.
[20] 周孝华,张保帅,董耀武.基于Copula-SV-GPD模型的投资组合风险度量[J]. 管理科学学报,2012,15(12):70-78.
[21] 马锋,魏宇,黄登仕.基于vine copula方法的股市组合动态VaR测度及预测模型研究[J]. 系统工程理论与实践,2015,35(1):26-36.
[22] 苟红军,陈迅,花拥军.基于GARCH-EVT-COPULA模型的外汇投资组合风险度量研究[J]. 管理工程学报,2015,(1):183-193.
[23] Hu Ling. Dependence patterns across financial markets:A mixed copula approach[J]. AppliedFinancial Economics, 2006, 16(10):717-729.
[24] 吴吉林,陈刚,黄辰.中国A, B, H股市间尾部相依性的趋势研究——基于多机制平滑转换混合Copula模型的实证分析[J]. 管理科学学报,2015,18(2):50-65.
[25] Sklar M. Fonctions de répartition à n dimensions et leurs marges[M].Paris:Institute of Statistics of the Université Paris, 1959.
[26] Clark P K. A subordinated stochastic process model with finite variance for speculative prices[J]. Econometrica, 1973, 41(1):135-155.
[27] Taylor S J. Modelling financial time series[M]. New York:Wiley, 1986.
[28] Hull J, White A. The pricing of options on assets with stochastic volatilities[J]. The Journal of Finance, 1987, 42(2):281-300.
[29] Harvey A, Ruiz E, Shephard N. Multivariate stochastic variance models[J]. The Review of Economic Studies, 1994, 61(2):247-264.
[30] Jacquier E, Polson N G, Rossi P E. Bayesian analysis of stochastic volatility models[J]. Journal of Business & Economic Statistics, 2002, 20(1):69-87.
[31] Kim S, Shephard N, Chib S. Stochastic volatility:Likelihood inference and comparison with ARCH models[J]. The Review of Economic Studies, 1998, 65(3):361-393.
[32] Meyer R, Yu Jun. BUGS for a Bayesian analysis of stochastic volatility models[J]. The Econometrics Journal, 2000, 3(2):198-215.
[33] Rockafellar R T, Uryasev S. Conditional value-at-risk for general loss distributions[J]. Journal of Banking & Finance, 2002, 26(7):1443-1471.
[34] Kupiec P H. Techniques for verifying the accuracy of risk measurement models[J]. Journal of Derivatives, 1995, 3(2):173-184.
