The North Carolina Journal of Mathematics and Statistics

Understanding extreme stock trading volume by generalized Pareto distribution

Kumer Pial Das, Shaymal C Halder


The extreme value theory (EVT) is used to assess the risk caused by extreme natural and man made events. These events exhibit clusters of outlying observations that cannot be modeled by a Gaussian distribution. The generalized Pareto distribution (GPD) have proved useful in modeling such events, in particular, it is widely used in modeling the distribution exceeding a high threshold. The GPD has uniform, triangular, exponential, and Pareto distribution as special cases. Estimating parameters of the GPD has become an important task in EVT. There are several methods for estimating parameters of the GPD such as method of moments, method of maximum likelihood, probability weighted moments, maximum Penalized Likelihood, etc. and all estimation techniques have some limitations. Even though EVT is a well-established discipline, no attempt has been made to compare all these estimation techniques together. In particular, studying an appropriate method for modeling GPD in the light of stock trading volume data has not been seen. The aim of the study is manifold: first, to discuss and compare several estimation methods and their limitations; second, to investigate whether GPD can be used to model stock trading volume data; third, to compare the volatility of two stock market indexes in the light of EVT; fourth, to test the efficiency of several estimation methods for different threshold values; and finally, to obtain a required design value with a given return period of exceedance and probability of occurring extreme events. Simulated data and real financial data are considered for our study.


Extreme events, generalized Pareto distribution, peaks over threshold, estimation techniques, return level, Dow Jones Industrial Average, Dhaka Srock Exchange

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