基于高维动态藤Copula的汇率组合风险分析

Risk analysis of Foreign Exchange Portfolios Based on High-dimensional Dynamic Vine Copula

以Pair Copula为简单构造模块的高维动态藤Copula结构能够克服二元Copula面临的"维度诅咒"问题,对多元变量之间的非线性相依进行动态化描述,是Copula函数研究的学术前沿。本文选取美元、欧元、日元、港币及英镑五种汇率的日间对数收益率数据实证研究,对其进行AR-GJR-GARCH模型过滤,过滤所得新息序列用GPD模型拟合,之后进行概率积分变换,采用高维动态C藤和D藤Copula对变换后序列建模,运用蒙特卡罗方法计算组合风险VaR,对其进行UC回溯测试,并与相应的静态方法作比较。结果表明:高维动态C藤Copula结构计算出来的VaR表现最好,对其进行分解发现美元的边际风险最低,通过蒙特卡罗选择权重组合发现最大限度持有美元将会产生最小VaR。该结论为量化风险指标、合理配置资产,及风险监管提供了一种新的模型与方法。

The structure of high-dimensional dynamic vine copula can overcome‘dimensional curse'faced by bivariate Copula and dynamically describe nonlinear dependence between multi-variables,and represents the academic frontier.Five kinds of foreign exchange log-returns,including USD,EUR,JPY,HKD and GBP,are selected to make empirical analysis,Time series are fitted with AR-GJR-GARCH and GPD models.After probability integral transform,high-dimensional dynamic C and D vine copulas are modelled.Then,portfolio VaR sets are got by Monte-Carlo method,tested by UC back testing,and compared to the corresponding static research.The results show that VaR based on high-dimensional dynamic C vine copula performs the best,and marginal risk of USD is considered as the least by VaR decomposition,the more USD the lest risk.The conclusions provide a new model and method to quantify risk,reasonably allocate asset portfolio,and for authorities to regulate risk.