摘要
资产收益率分布假设对期权定价、对冲,风险度量和组合资产优化的结果有着重要影响.但由于资产收益率的"程式化性质",经典正态分布假设不能很好拟合实际收益率分布.广义双曲线分布,作为子分布及极限分布非常丰富的分布族,在资产收益率分布拟合中已取得良好效果.在讨论第三类修正贝塞尔函数和广义逆高斯分布性质基础上,借助于正态均值-方差混合理论,得到广义双曲线分布及其极限分布.在McNeil,Frey和Embrechts(2005)算法框架内,以及WenBo Hu(2005)算法改进基础上,对参数估计的算法做了实质性改进:用两个重要参数χ和ψ的线性关系,代替了一个包含第三类修正贝塞尔函数的方程,避免了对该方程数值求解.在实证部分,选择了3个主要指数,利用GH分布的两个子分布和两个极限分布对过滤后的指数收益率进行拟合,并对它们的拟合优度和收敛速度做了比较.
Hypotheses of asset return distribution play an important role on the theory of pricing,hedging,risk measure and portfolio optimization.But the classical hypothesis that returns obey normal distribution is bad to fit the empirical financial data due to so-called ＇stylized properties＇.Generalized Hyperbolic Distribution（GH）,as a rich family of distributions, have achieved excellent effects since it was introduced into finance by Eberlein and Keller（1995）.This paper introduces the properties of Modified Bessel Function of the Third Kind（MBTK） and Generalized Inverse Gaussian Distribution,resorts to the concept of normal mean-variance mixture,and deduces the GH distribution and its limit distributions.Under the framework of McNeil,Prey,and Embrechts（2005）,Wenbo Hu（2005） gives his improved algorithm,but we think it still has some drawbacks.This paper provides a key improvement on that,substituting linear equation of parametersχandψfor an equation including MBTK in Wenbo Hu＇s algorithm,and avoiding the numerical solution for that equation.In empirical examples section,we choose 3 stock indexes as examples and fit them with GH distribution and its limit distributions.Finally,we compare the goodness-of-fit of different distributions and give our conclusions.
出处
《数学的实践与认识》
CSCD
北大核心
2010年第21期26-34,共9页
Mathematics in Practice and Theory
关键词
广义双曲线分布
广义逆高斯分布
EM算法
拟合优度检验
generalized hyperbolic distribution
generalized inverse gaussian distribution
expectation-maximization algorithm
goodness-of-fit test
