Extreme value approach in analyzing stock returns in Istanbul Stock Exchange

Abstract

The study aims to model the tails of daily returns of securities being traded in ISE via techniques developed by Extreme Value Theory and compute VaR. The performances of classical VaR forecasting methods of Historical Simulation and RiskMetrics are compared with the models estimated using Peaks over Threshold(POT) approach, which is put forward by Extreme Value Theory. POT approach incorporates estimating the tail index of Generalized Pareto distributions (GPD). Aswell as having used nonparametric Hill and Dekkers estimators, also parametric Maximum Likelihood Estimate approach is applied in estimating the tail index ofGPD. VaR has been computed with these various approaches mentioned for sixstocks being traded in ISE, the ISE National 100 index, and an artificial priceweighted index. The models are classified as successful if they satisfy both criteria of unconditional and conditional coverage. Those VaR models that satisfy both criteriaof success have also been tested in terms of a Quantile Loss function. The modelsthat gave lowest loss values are preferred. Among the approaches used in the study, the models that fit Genaralized Pareto distributions to the lower tail are found to outperform the classical Historical Simulation and RiskMetrics approaches.