Clustering in Financial Markets : A Network Theory Approach

Abstract: In this thesis we consider graph partition of a particular kind of complex networks referred to as power law graphs. In particular, we focus our analysis on the market graph, constructed from time series of price return on the American stock market. Two different methods originating from clustering analysis in social networks and image segmentation are applied to obtain graph partitions and the results are evaluated in terms of the structure and quality of the partition. Along with the market graph, power law graphs from three different theoretical graph models are considered. This study highlights topological features common in many power law graphs as well as their differences and limitations. Our results show that the market graph possess a clear clustered structure only for higher correlation thresholds. By studying the internal structure of the graph clusters we found that they could serve as an alternative to traditional sector classification of the market. Finally, partitions for different time series was considered to study the dynamics and stability in the partition structure. Even though the results from this part were not conclusive we think this could be an interesting topic for future research.