Garch Models And Evt In Var Estimation

Download or read book GARCH Models and EVT in VaR Estimation written by Stephan Hersperger and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper combines a standard Generalized Autoregressive Conditional Heteroskedasticity [GARCH] model and Extreme Value Theory [EVT] in order to estimate Value-at-Risk [VaR] of 12 different stock market indices. By applying a combined model to historic return series, using a GARCH(1,1) model to estimate volatility and EVT to explicitly model both tails of the innovation distribution separately, this paper aims to gain more information about the accuracy of VaR estimates. VaR measures of 12 stock market indices are estimated for a combined EVT-GARCH(1,1) model as well as a standard GARCH(1,1) model with a Gaussian assumption for the innovation distribution. Backtesting of the VaR forecasts gives out-of-sample evidence about the accuracy of the two different approaches. Looking at the left tail of the return distribution on a 95% confidence level, a standard GARCH(1,1) model with a Gaussian assumption for the innovation distribution performs better than the EVT-GARCH(1,1) model for all stock market indices. Looking at the left tail of the return distribution on a 99% confidence level, the EVT-GARCH(1,1) model outperforms the standard GARCH(1,1) model for all stock market indices. VaR forecasts for the right tail of the return distribution show less clear results. On a 95% confidence level, the GARCH(1,1) model with a Gaussian assumption for the innovation distribution performs better than the EVT-GARCH(1,1) model for most of the indices. On the 99% confidence level, both models perform approximately equally well.