Abstract: It is well known that financial return has sharp-peaks, fat-tails, heteroscedasticity and long memory. Considering three features, the paper constructs a risk measure model based on the ARFIMA-GARCH-Copula for financial portfolio,which is composed by Shanghai Stock index return and Shenzhen Component Index return equal weight. First the classical R/S analysis is adopted to test the long memory of a single asset. Second, the paper adopts different GARCH models to fit each asset return series. Third, it selects Copula function to describe the relational structure between each asset. Fourth, it uses Monte Carlo method to produce each return sequence of the assets. And then it calculates the VaR of financial portfolio. The empirical results show that there is apparent long memory property in the Shanghai and Shenzhen stock market which has symmetrical tail correlation. Kupiec test results show that the model of ARFIMA-GARCH-Copula is more efficient than GARCH-Copula model in measuring the portfolio risk.

Key words: ARFIMA, GARCH, copula function, value at risk(VaR), kupiec test

摘要： 金融资产收益率不仅具有尖峰厚尾性、异方差性,还具有长记忆性。基于此,本文建立ARFIMA-GARCH-Copula模型来研究沪深股市的相关结构和等权重投资组合风险值VaR,利用上证指数和深成指数收益率的组合来进行实证研究。首先采用经典R/S分析法检验各个资产收益率的长记忆性,经过分数阶差分后选用GARCH模型建模得到边缘分布。然后选择Copula函数来刻画两资产之间的相关结构,建立联合分布模型。进而采用Monte Carlo方法模拟产生各资产的收益率序列,计算出投资组合的风险值VaR。实证研究表明:沪深股市具有长记忆性,且两者具有对称的尾部相关性;Kupiec检验说明ARFIMA-GARCH-Copula模型较之于GARCH-Copula模型能更准确地度量投资组合风险。

关键词: ARFIMA, GARCH, Copula函数, VaR风险值, Kupiec检验