Parametric estimation of GARCH model using MATLAB

Timely invariant variance is known not to be stylized fact of financial returns data. Motive of this bachelor thesis is to study financial data's typical variability of variance. In theoretical part, assumtions of GARCH models and its extensions, are summarized. GARCH family models' parameters are estimated, using maximum likelihood are estimated in empirical part. These models are estimated and evaluated across five assets, in which stock indicies DAX and SAP 500, FX major EURUSD and commodities natural gas and gold, are represented. In order to make assumptions about robabilistic distribution of data more realistic, not only Gaussian distribution, but also more leptokurtic Student's t-distribution is assumed to be present in data. Estimations are executed using software package MATLAB and EViews environment. For each asset, the best one of estimated GARCH models will be selected. Results suggest, that assumption of leptokurtic distribution generates models that describe volatility of studied assets better. Regarding testing for assymetric effects in volatility and estimation of EGARCH models, leverage effect of financial returns is shown to be present in returns of studied assets