VaR prediction for GARCH (1,1) model with normal and student-t error distribution

Abstract

This study aims at determining the estimated parameters of the GARCH (1.1) model establishing the prediction of the VaR value, and defining the accuracy of the VaR prediction. In this study, the error in the GARCH (1,1) model uses a normal distribution and student-t distribution. The research method focuses on parameter calculation and the prediction of VaR value within two aspects regarding analytic and numeric aspects. Analytically, the prediction of the VaR value and the accuracy of the prediction of VaR value through the VaR coverage opportunity. It isn't easy to estimate the parameters for the GARCH (1.1) model analytically. Thus, the parameters are estimated numerically using the Quansi Newton optimization method. Prediction of VaR value and VaR coverage probability will be simulated numerically by using stock return data of IBM, INDF.JK and GSPC. The results show that the GARCH (1.1) model can model stock returns for IBM, INDF.JK and GSPC. There is no significant difference between the GARCH (1,1) model with a normally distributed error and GARCH (1,1) with a student-t distribution error in determining the prediction of VaR values. The numerical simulation results show that the VaR value prediction using the GARCH (1,1) model with a normally distributed error is more accurate than the student-t-distributed error.