Value at Risk Estimation using Extreme Value Theory

Abstract

A common assumption in quantitative financial risk modelling is the distributional assumption of normality in the asset's return series, which makes modelling easy but proves to be inefficient if the data exhibit extreme tails. When dealing with extreme financial events like the Global Financial Crisis of 2007-2008 while quantifying extreme market risk, Extreme Value Theory (EVT) proves to be a natural statistical modelling technique of interest. Extreme Value Theory provides well established statistical models for the computation of extreme risk measures like the Return Level, Value at Risk and Expected Shortfall. In this paper we apply Univariate Extreme Value Theory to model extreme market risk for the ASX-All Ordinaries (Australian) index and the S&P-500 (USA) Index. We demonstrate that EVT can be successfully applied to Australian stock market return series for predicting next day VaR by using a GARCH(1,1) based dynamic EVT approach. We also show with backtesting results that EVT based method outperforms GARCH(1,1) and RiskMetrics T M based forecasts.