The COVID-19 crisis heavily affected financial stock markets. In March 2020 stock prices dropped immensely and markets became extremely volatile. In this report we model three European stock markets before and during the COVID-19 crisis to determine whether the dynamics of financial markets changed structurally compared to previous periods. Stock markets play a big role in our economy and can cause economic disruption when they crash. Therefore, it can be very useful to understand the dynamics of the stock market. Econometricians are nowadays often asked to model the non-constant volatility (conditional heteroscedasticity) of financial time series. This report uses Generalised AutoRegressive Conditionally Heteroscedastic (GARCH) models that are known for their precise modeling of conditional heteroscedasticity. They are also known for their ability to capture the key stylised facts, the common empirical properties applicable to all types of stock markets. This report includes general definitions and characteristics of the GARCH(p, q) process and covers topics such as autocorrelation of returns, kurtosis, leptokurticity and volatility clustering. For estimating the GARCH models this report uses the statistical program R which estimates the parameters by the Quasi-Maximum Likelihood Estimation (QMLE) method. We modeled different periods before and during COVID-19 and compared the estimated parameters with the corresponding 95% confidence intervals. To test the accuracy of the estimations we performed parametric bootstrapping. Throughout the report, models for the Dutch Amsterdam Exchange (AEX) index, the French Cotation Assistée Continu (CAC 40) index and the German Deutsche Aktien (DAX) index are analysed and compared. It seems that European markets may experience the impact of stock market crashes differently. The DAX index shows significant changes in the dynamics of the stock market due to the COVID-19 crisis whereas the AEX and CAC 40 index do not.