Extreme Value Modelling for Measuring Financial Risk with Application to Selected Philippine Stocks

Abstract

Extreme value theory (EVT) provides techniques for estimating models that predict events occurring at extremely low probabilities. In this paper, Peaks Over Threshold (POT) method of Extreme Value Theory was utilized. A conditional approach of the EVT was applied with the aid of ARMA-GARCH models to correct for the effects of autocorrelation and conditional heteroscedastic terms. Maximum likelihood estimates of model parameters for the fitted Generalized Pareto Distribution (GPD) were computed. These techniques were applied to the daily returns of Bangko de Oro, Mega World Corporation, Semirara Mining and Power Corporation, SM Investments Corporation, and Universal Robina Corporation. A comparison of value at risk (VaR) estimates showed that as becomes smaller, VaR estimates under normal distribution tend to underestimate VaR while estimates under EVT approaches the empirical results. Backtesting using the Basel Committee three-zone approach to assess the accuracy of VaR models reveal that VaR models under normality are not able to capture extreme returns and therefore underestimate tail risk while VaR models under EVT have high probability of model accuracy.