The Distribution Analysis for Extreme Returns of Nikkei 225 Index: Based on the Extreme Value Distribution of GEV and GL

Abstract

This paper focuses on the problem of modelling extreme events in the financial market. The choice of the distribution that adequately models the extreme behavior of the financial time series. Extreme Value Theory outlines the framework for determining the best fit distribution for the data. The generalized extreme value distribution and the generalized Pareto distribution are the traditional distributions that most analysts resort to using. However, recent works have shown that the generalized logistic distribution can also capture the effect of the extreme due to its fat tailed characteristic. In this paper, we determine appropriate distribution for extreme returns of Nikkei225 Index and analyze the importance of the generalized logistic distribution in modelling extreme events in the financial market in order to accurately conduct risk measure analysis.

Keywords: Extreme Value Distribution, Generalized Logistic Distribution, Sub Period Technique, Probability Weighted Moments