The sum of two independent polynomially-modified hyperbolic secant random variables with application in computational finance  

作　　者：A.A.L.Zadeh Hojatollah Zakerzadeh Hamzeh Torabi 

机构地区：[1]Department of Statistics Yazd University,Yazd,Iran

出　　处：《International Journal of Modeling, Simulation, and Scientific Computing》2021年第4期201-214,共14页建模、仿真和科学计算国际期刊（英文）

摘　　要：In this paper,by reshaping the hyperbolic secant distribution using Hermite polynomial,we devise a polynomially-modified hyperbolic secant distribution which is more flexible than secant distribution to capture the skewness,heavy-tailedness and kurtosis of data.As a portfolio possibly consists of multiple assets,the distribution of the sum of independent polynomially-modified hyperbolic secant random variables is derived.In exceptional cases,we evaluate risk measures such as value at risk and expected shortfall(ES)for the sum of two independent polynomially-modified hyperbolic secant random variables.Finally,using real datasets from four international computers stocks,such as Adobe Systems,Microsoft,Nvidia and Symantec Corporations,the effectiveness of the proposed model is shown by the goodness of Gram–Charlier-like expansion of hyperbolic secant law,for performance of value at risk and ES estimation,both in and out of the sample period.

关 键 词：Expected shortfall Gram–Charlier-like expansions heavy tailed distributions value at risk 

分 类 号：O17[理学—数学]