Generalized Skew-Slash Logistic Distribution And Its Application In Risk Estimation

In the financial market,when investors buy stocks or bonds,they are most concerned about the logarithmic return of stocks,which is an index reflecting the level of stock return.In addition,by using VaR and CVaR to measure the risk of stock logarithmic return,we can manage the risk of financial assets,In the past,many scholars usually assumed that the data obeyed the normal distribution when studying the logarithmic return,but in fact,the distribution of stock logarithmic return is asymmetric,with the characteristics of skewness,peak and thick tail.It is not appropriate to use the normal distribution to simulate.In 1985,Azzalini's skew distribution can well fit the data of skewness,peak and thick tail Since then,scholars have continuously studied various skew distributions,such as skew t distribution,skew Cauchy distribution,skew Logistic distribution and so on.Based on the generalized skew Logistic distribution(GSL)studied by Asgharzadeh et al.,this paper defines a new class of generalized skew-slash Logistic distribution(GSSL)by introducing a slash parameter.The content is mainly divided into the following two parts:In the theoretical part,firstly,the definition of GSSL distribution is given,the density function comparison diagram between this distribution and GSL distribution is drawn,and some basic properties of GSSL distribution are proved.Then,according to the double and triple series expansions of GSL distribution's density function and distribution function,the double and triple series expansion of density function and distribution function of GSSL distribution are obtained,and the quadruple series expansion of density function and distribution function is further deduced.Then the moment generating function of GSSL distribution is discussed in detail,its n-order moment is given,and the formulas of mean,variance,skewness and kurtosis are obtained.Finally,the maximum likelihood estimation method is used to estimate the parameters,and the changes of the estimated values of each parameter under different sample sizes are studied,It shows that the maximum likelihood estimation effect of GSSL distribution is very good.In the empirical part,this paper uses GSSL distribution,GSL distribution and normal distribution to fit and compare the distribution of log return of Shanghai Stock Exchange Index in China.From the perspective of intuition and statistical test,it shows that the log return of stock does not obey the normal distribution and has the characteristics of skewness,peak and thick tail.Then the maximum likelihood estimation method is used to obtain the estimated values of the parameters of GSSL distribution and GSL distribution,which shows that GSSL distribution is more suitable for fitting the distribution of log return of stocks than GSL distribution.Finally,we compare the VaR and CVaR of the three distributions to estimate the log return of stocks,and get the conclusion that under the condition of minimum probability,the risk estimated by GSSL distribution is greater and can better describe the risk of tail.