Research On Partial Generalized Error-Laplace Distribution And Its Application In Financial Tail Risk

Because financial data often have the characteristics of asymmetry,accompanied by spikes and thick tails,which means that it is no longer appropriate to use the traditional symmetrical distribution to describe such biased data,so it is necessary to find a new probability biased distribution to fit the financial data.On the other hand,with the deepening of economic globalization and the turbulence of domestic and international financial markets,risk management has become more and more important,and the measurement of risk is an indispensable part of risk management,so it is important to choose a suitable method for its accurate portrayal.One of the dominant methods for measuring risk is the value-at-risk(Va R)method,which relies on the distribution of loss random variables to digitize risk,and often yields very different results when different distributions are chosen to portray the loss random variables.Therefore,in order to accurately estimate Va R values,it becomes the research objective of this thesis to construct a model that can adequately describe the new distribution of the data and the financial tail risk metric.The main work of the full paper is broadly divided into three parts as follows.In the first part,based on the idea of biasing the Azzalini distribution,the generalized error distribution and the Laplace distribution are taken as the objects of biasing,and the partial generalized error-Laplace(SGEL)distribution is proposed for the first time,and the mathematical expressions of the probability density function,distribution function,skewness and other numerical characteristics of the SGEL distribution are calculated;the maximum likelihood estimator of the new distribution and the Fisher information matrix;in addition,the maximum likelihood estimates of the parameters are discussed,while random simulation tests of the parameters are considered,and the results show that the parameter estimates of the SGEL distribution have good asymptotic statistical properties in either case.The SGEL distribution is then applied to fit the log-return data of Guizhou Maotai stock price while comparing it with the relevant distribution;the new distribution proposed in this paper is more flexible than the traditional distributions such as normal and skew-normal distributions under the AIC and BIC criteria.In the second part,a risk measure model based on SGEL distribution is constructed and the new model is applied to the calculation of Va R values of Guizhou Maotai data with other classical models;through comparison,it is found that the model based on SGEL distribution yields more reasonable Va R estimates.The third part considers the case of extreme tail risk,and based on the extreme value theory and SGEL distribution,the excess distribution in the POT model is approximated by the SGEL distribution,and the POT-SGEL model is proposed;then the POT-SGEL model is applied to estimate the extreme Va R values of the daily log returns of the S&P 100;through comparison with the POT model,it is found that the POT-SGEL model is able to estimate the extreme Va R values and is to some extent better than the POT model.The study of the new partial generalized error-Laplace distribution in this paper enriches the development of probability distribution theory to a certain extent.Applying the new distribution to measure risk in financial markets and constructing a new extreme risk model based on the new distribution provides further insights into the estimation of financial risk.