Volatility and Value at Risk modelling using univariate GARCH models

Sammanfattning: Generalised Autoregressive conditional heteroscedasticity (GARCH) models have been very popular for forecasting time varying variance of a time series as a function of lagged variance and lagged square values of the series. This thesis studied performance of GARCH models for forecasting volatility and Value at Risk (VaR) of investment portfolios of Central Bank of Sweden. The thesis used reduced form approach for VaR in which volatility and VaR of the portfolios were modelled directly by fitting GARCH on daily returns series rather than the common practice of using GARCH to model risk factors of a portfolio in the context of the variance-covariance approach of VaR estimation. A comprehensive evaluation framework was employed to test predictive accuracy of volatility forecasts and VaR estimates. To test the accuracy of volatility forecasts, various error statistics and hypothesis testing were employed. To evaluate VaR estimates, Basel back- testing, likelihood ratio tests, non-parametric sign tests and regulatory loss function tests were employed. Out of the all candidate GARCH models, GARCH with student t error term came out to be the best model for all portfolios. GARCH models consistently performed better than constant volatility model in forecasting volatility. However, the results of the VaR evaluation tests were mixed.