Extreme Values Theory and Return Level Analysis for Catastrophe Prediction

As the trade and information flow in the financial markets increasing, they are becoming more 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 for modeling these catastrophic events. Now the question is which extreme value can be better estimated monthly, quarterly or yearly. Hence returns are divided in the blocks of various sizes and minimum return in these blocks is modeled using GEV distribution. Gumbel, Frechet and Webuill type GEV distribution parameters for blocks of minimum monthly, quarterly and yearly returns are estimated for Nasdaq returns of last 30 years. Other aim of this paper is to determine accuracy of return level estimates obtained using GEV distribution. Return level can be useful in characterizing bearish and bullish trend and predicting the same