Extreme Values Theory and Return Level Analysis
for Catastrophe Prediction

Abstract

As the trade and information flows in the financial markets have grown, they have become increasingly volatile and sensitive to extreme events. Markets are now characterized by more frequent extreme events. Generally, such extreme events in the market are not normally distributed and need to be modeled separately. Extreme value theory (EVT) is highly successful and is dedicated to modeling these catastrophic events. The question now is which extreme values can be better estimated monthly, quarterly, or yearly. Hence, in this study, returns are divided into blocks of various sizes, and minimum return in these blocks is modeled using GEV distribution. Gumbel, Frechet, and Weibull type GEV distribution parameters for blocks of minimum monthly, quarterly, and yearly returns are estimated for NASDAQ returns of the last 30 years. The study also seeks to determine the accuracy of return level estimates obtained using GEV distribution. Return levels can be useful in characterizing bearish and bullish trends and predicting the same.