For many years researchers and also the nancial industry have been trying to replicate nancial data and market movements in order to generate pro ts, for risk management activities or various other reasons. Di erent models have been developed for this purpose, where one of the most famous is the GARCH model. The GARCH model has proven to be a good model for modeling nancial time series. However, due to an often high persistence found in GARCH models, resulting in an overestimation of the conditional variance, the model has also been criticized. For that reason it would make sense to expand the GARCH model in a way that could account for this drawback, but still maintain the qualities of GARCH. The purpose of this master thesis is to expand the GARCH model in order to reduce the drawbacks of GARCH, resulting in a better model for describing the tail distribution of nancial return data. This thesis expands the GARCH model to a regime switching GARCH, switching between two di erent volatility regimes. The regime switching MS-GARCH is expected to reduce the high persistence and long convergence of GARCH, by switching between two regimes when sudden changes in the volatility is observed in the return series. Initially a normal distributed MS-GARCH is introduced. This model is later expanded to include t-distributed innovations. The MS-tGARCH allows for a very exible distribution structure, by modeling di erent t-distributions in each regime. For this reason it was the model, expected to model the return distribution best. The analysis involves a total of four GARCH type models, namely GARCH, tGARCH, MS-GARCH and MS-tGARCH. The data that the models is replicating is daily returns of the Danish OMXC20 index in the period from 01-01-2000 to 31-12-2013. The empirical evidence to test the hypothesis was found through a one-period and a multi-period VaR analysis. The analyses showed that the MS-tGARCH outperformed all other models and was the best model for describing the tail distribution of the OMXC20, when forecasting VaR more than one period head. In the one-period VaR analysis the single regime tGARCH was the best performing model and introduction did not improve the model. The overall conclusion of this study was that using the t-distribution in a regime switching framework, results in the overall best model for modeling the return tail distribution, amongst the models tested.
|Educations||MSc in Mathematics , (Graduate Programme) Final Thesis|
|Number of pages||78|