基于M-Copula-SV-t模型的高维组合风险度量

High-dimensional Portfolio Risk Measurement Based on M-Copula-SV-t Model

为解决非线性相关的高维投资组合风险度量问题,本文构建了一个基于M-Copula-SV-t风险度量模型。利用SV-t模型来拟合金融时序的边缘分布,并结合MCMC和Gibbs抽样法对边缘模型进行参数估计;采用由阿基米德族Copula线性组合构成的M-Copula函数联合边缘分布,并通过极大似然估计和BFGS算法对联合模型进行参数估计,进而利用Monte Carlo技术对最优风险投资组合进行风险测度;最后以典型汇率构建四维国际投资组合为例,检验所构建模型的可行性和有效性。实证结果表明,与单一Copula函数相比,由Gumbel Copula、Clayton Copula和Frank Copula线性组合所构成的M-Copula函数能够更为有效地刻画资产收益率的相依结构和尾部特征,建立在M-Copula函数基础上的风险度量结果也更为精确;由模型所计算的最优投资组合权重为外汇组合投资提供了重要参考。

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.