in Finance

In the last few years, Extreme Value Theory (EVT) has gained increased importance in modeling extreme observations in all social sciences. This is especially true in finance, since EVT is a tool used to consider probabilities associated with extreme and rare events with catastrophic consequences, as happened in the Sub-prime crisis in 2007. To model extreme observations, we use two different statistical distribution families in this thesis: Generalized Extreme Value (GEV) and Generalized Pareto Distribution (GPD). In this thesis, EVT methods were used to investigate and fit the empirical distribution of the monthly maximum and minimum return series of the FTSE 100, NIKKEI 225 and S&P500 indices to the theoretical GEV and GPD distributions. We have applied two approaches of extreme value theory, the Block Maxima and the Peaks Over Threshold (POT) approach, as well as the parametric approach of the Maximum Likelihood Estimate Method (MLE) for the distribution parameter estimation and the non-parametric approach of the Hill estimator. As a result of the application, we have seen that in the GEV distribution application, our data was well represented by the Fréchet and Weibull distributions. On the other hand, in the GPD distribution, using the parametric approach MLE, our data was mostly well represented by the Exponential and Beta distributions. However, applying the GPD using the non-parametric approach of the Hill estimator for the tail index, we have seen that the monthly maximum returns of our indices are well represented by the Pareto distribution