双边Burr分布及其在金融市场风险预测与优化中的应用

doi:10.12341/jssms22415

系统科学与数学 ›› 2023, Vol. 43 ›› Issue (2): 505-530.DOI: 10.12341/jssms22415

双边Burr分布及其在金融市场风险预测与优化中的应用

陈振龙^1,2, 金上^1,2

1. 浙江工商大学统计与数学学院, 杭州 310018;
2. 浙江工商大学统计数据工程技术与应用协同创新中心, 杭州 310018

收稿日期:2022-06-03 修回日期:2022-09-09 出版日期:2023-02-25 发布日期:2023-03-16
通讯作者: 金上,Email:shangjin2058@163.com
基金资助:
浙江省自然科学基金项目(LY21G010003),国家自然科学基金项目(11971432),浙江省自然科学基金项目(LQ22G010001),浙江省哲学社会科学规划领军人才培养项目(22YJRC07ZD-2YB),浙江省重点建设高校特色优势学科(浙江工商大学统计学)和统计数据工程技术与应用协同创新中心资助课题.

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陈振龙,金上. 双边Burr分布及其在金融市场风险预测与优化中的应用[J]. 系统科学与数学, 2023, 43(2): 505-530.

CHEN Zhenlong, JIN Shang. Two-Sided Burr Distribution and Its Application in Risk Prediction and Optimization of Financial Market[J]. Journal of Systems Science and Mathematical Sciences, 2023, 43(2): 505-530.

Two-Sided Burr Distribution and Its Application in Risk Prediction and Optimization of Financial Market

CHEN Zhenlong^1,2, JIN Shang^1,2

1. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018;
2. Collaborative Innovation Center of Statistical Data Engineering, Technology & Application, Zhejiang Gongshang University, Hangzhou 310018

Received:2022-06-03 Revised:2022-09-09 Online:2023-02-25 Published:2023-03-16

考虑到金融数据具有非对称、尖峰厚尾特征,文章将具有尖峰厚尾特征的Burr分布拓展至双边Burr (TSB)分布,给出了其重要的数字特征、极大似然估计、最小二乘估计以及加权最小二乘估计,并通过数值模拟验证了这三种参数估计方法的有效性.其次,文章基于TSB分布构建GJR-GARCH模型,旨在研究TSB分布相比于常见分布在度量金融风险方面的优势.实证结果表明,与正态分布、t分布、GED分布、双边Weibull分布和双边Lomax分布相比,基于该分布的GJR-GARCH模型具有最高的VaR预测精度.另外,文章将基于TSB分布的GJR-GARCH模型与Copula函数结合来构建均值-CVaR模型以研究多元投资组合的风险优化,实证研究亦表明能够刻画非对称特征的该模型具有更好的CVaR预测效果.最后,稳健性检验结果证实TSB分布对于金融风险预测以及投资组合优化的改进效果不依赖于波动率模型和Copula函数的设定.

关键词： 非对称, 双边Burr分布, 参数估计, VaR, 投资组合

Considering that financial data usually has asymmetry, leptokurtosis and fat tail, this paper extends the Burr distribution with the leptokurtosis and fat tail to the two-sided Burr (TSB) distribution, and gives its important statistical properties, maximum likelihood estimation, least squares estimation and weighted least squares estimation, and verifies the effectiveness of above three estimation methods by numerical simulation. Secondly, this paper constructs GJR-GARCH model based on TSB distribution to investigate the advantages of TSB distribution in terms of measuring financial risk compared with common distributions. The empirical results show that the GJR-GARCH model based on TSB distribution has the highest VaR prediction accuracy compared with the normal distribution, t distribution, GED distribution, two-sided Weibull distribution and two-sided Lomax distribution. Furthermore, the mean-CVaR model is established by combining the GJR-GARCH model based on TSB distribution and the Copula function and then used to study the risk optimization of portfolio. The empirical research also indicates that the model which can describe the asymmetric characteristic has better CVaR prediction effect. Finally, the robustness test results confirm that the improvement effect of TSB distribution on financial risk prediction and portfolio optimization does not depend on the setting of volatility model and Copula function.

Key words: Asymmetry, two-sided Burr distribution, parameter estimation, VaR, portfolio

MR(2010)主题分类:

62P20
91B28

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