Application Of Extreme Value Theory Based On Poisson Process In Risk Measurement

This thesis investigates the application of Extreme Value Theory based on Poisson process in risk measurement.We utilize the Generalized Pareto distribution,Block Maxima method and Poisson process to calculate VaR,expect to describe risk associated with time variable.In today’s financial market,extreme events occur frequently,hence the VaR risk measurement method based on the assumption of normal distribution is problematic to measure market risk.The Extreme Value theory is able to simulate the phenomenon of financial data,i.e."skewed peaks and thick tails".In particular,it would be better to employ the Extreme Value theory to describe tail data.Therefore,this thesis introduces it to measure market risk.However,the Extreme Value theory ignores the influence of time,fortunately the Poisson process can be regarded as the Poisson distribution involving with time variable.As a consequence,this paper introduces the Poisson process,and derives the probability function of Poisson distribution through imitate the derivation process of Binomial distribution under the limit conditions.Finally,we show the probability function of Poisson process related to the variation of return rate.We select the Shanghai Stock Exchange Index return from January 4th,2000 to December 31th,2019,then determine the return threshold via the Excess Mean method.After assuming that the occurrence of threshold-exceeding events is in compliance with the homogeneous Poisson process,and the rate of return beyond threshold is governed by the Generalized Pareto distribution.R language and MATLAB are well used to complete empirical analysis,further verify the model and estimate parameters.To the end,we prove that the VaR calculated by introducing the Extreme Value theory of the Poisson process is more accurate and robust.