Volatility Transitions in European Stock Markets: A Clustering-Based Approach

This paper investigates the dynamics of stock market volatilities across fifteen European countries using advanced clustering techniques and transition matrix analysis. The study leverages daily data from MSCI national indices covering the period from January 2008 to June 2024. We use a GARCH(1,1) model on daily log-returns to estimate volatilities. The objective is to analyze similar volatility dynamics across national indices. Therefore, we use a set of clustering algorithms that rely on the employment of Dynamic Time Warping (DTW) in combination with k-means, agglomerative clustering, Gaussian mixture and spectral analysis to identify clusters on a monthly basis. The optimal configuration of clusters is decided repetitively each month using metrics such as the Silhouette Score, Davies-Bouldin Index, Calinski-Harabasz Index, and Cluster Size Standard Deviation. Transition matrices are computed to capture the probabilities of transitioning between clusters over time, both for all countries collectively and for each country individually. The analysis includes the computation of stationary distributions and expected times in clusters, providing insights into the stability and long-term behavior of market volatilities. Our findings highlight significant differences in volatility patterns across countries, with implications for investors, policymakers, and financial analysts.