Research On PET Distribution And Its Application In Financial Risk Measurement

A large number of empirical analyses show that the data of return on financial assets has the characteristics of "peak and thick tail",which is difficult to describe the normal distribution.The parameters in the Edgeworth expansion of the distribution function directly correspond to skewness and kurtosis,which can more directly reflect the peak and tail characteristics of the data.In this paper,a new distribution,the positive Edgeworth expanded truncated distribution(PET distribution),is proposed.The probability density function of PET distribution,the expression of distribution function,the moment of PET distribution,the moment generating function,the maximum likelihood estimation,Fisher information matrix and the related theorems of PET distribution are given.The parameter estimation and mean square error of PET distribution can be obtained by random simulation test.The simulation results show that the larger the sample size,the closer the fitting parameter estimates are to their true values.The normal distribution,PET distribution and PES distribution were used to fit the stock price and return data of Ping An Bank,and the AIC value was compared and analyzed.The results show that PET distribution can describe the financial data better.In this paper,APARCH model was constructed by combining the APARCH model with PET distribution.The fitting effect of APARCH-PET,APARCH-Normal and APARCH-PES models was compared and analyzed with the stock yield data of China Merchants Bank of Shanghai Main Board.By comparing AIC and BIC,it can be concluded that APARCH-PET model is more effective than the classical model in measuring the rate of return of financial assets.Based on APARCH-PET model,the VaR formula is given,and the back-test results show that APARCH-PET model is suitable for measuring financial risk.This paper enriches the theory of probability distribution by studying the truncated distribution of positive Edgeworth.The APARCH-PET model is constructed by applying the new distribution to APARCH model,and the financial risk is calculated according to the model,which provides a new way to estimate the financial risk.