Comparison of Value-at-Risk estimates from GARCH models

Fannar Jens Ragnarsson

Student thesis: Master thesis

Abstract

This thesis has the objective to compare Value-at-Risk estimates from selected GARCH models. It will start with a theoretical part which familiarizes the reader with Value-at-Risk and its main concepts. Known models will be explained and applied, time-series analysis with theories and tests for financial time-series are discussed. For evaluating different Value-at- Risk estimates backtests will be described and discussed. The empirical part of this research starts with the selection process for the preferred GARCH (p, q) model, on the time-series of S&P500 Total Return index ranging from 20.07.01- 19.07.11 (10 years of data). The selected model is a restricted GARCH (1, 2) model which is evaluated against the GARCH (1, 1) model and the Riskmetrics model. These models were evaluated at the 5% and 1% Value-at-Risk levels for three sample periods. One being the Full sample, another the Before Crisis sample and lastly the With Crisis sample. The results of the evaluations for the models showed that it is hard to select one of them, as the best model for the time-series. The GARCH (1, 1) performed best on the Full sample, while the Riskmetrics performed best on the Before Crisis sample and the GARCH (1, 2) performed best on the With Crisis sample.

EducationsMSc in Applied Economics and Finance, (Graduate Programme) Final Thesis
LanguageEnglish
Publication date2011
Number of pages83