Extreme events and the clustering of extreme values provide fundamental information which can be used for risk assessment in finance. When applying extreme value analysis to financial time series we handle two major issues, bias and serial dependence. The main objective of the study will be to model the extreme values of the NSE all share index using EVT method thus contributing to empirical evidence of the research into the behavior of the extreme returns of financial series in East Africa and specifically Kenya. This study will model the extreme values of the Nairobi Securities Exchange all share index (2008-2015) by applying the Extreme Value Theory to fit a model to the tails of the daily stock returns data. A GARCH-type model will be fitted to the data to correct for the effects of autocorrelation and conditional heteroscedasticity before the EVT method is applied. The Peak-Over-Threshold approach will be employed with the model parameters obtained by means of Maximum Likelihood Estimation. The models goodness of fit will be assessed graphically using Q-Q and density plots.