Network Theory in Finance: Applications to Financial Contagion Analysis and Portfolio Optimization

Network theory is a powerful tool for the analysis of complex systems, and in recent years a growing body of literature highlights its financial applications. This work explores two fields of application of network theory in finance. The first is the modelization of systemic risk and financial contagion in a banking network, the second is portfolio optimization. Systemic risk is studied in three chapters: first we estimate sparse partial correlation networks build from credit default swaps (CDS) spreads using tlasso, a methodology based on the multivariate t-Student distribution, suitable for data with fat tails and outliers. Then we propose an analysis based on network-∆CoVaR, a tail-risk network constructed using quantile graphical models. We study in depth the characteristics of the resulting networks, focusing in particular on the structural properties of the system. Finally, we study a liquidity contagion model in presence of a network with communities. The second field of application is portfolio optimization. In particular, the tlasso model is applied to the estimation of parameters in Markowitz style portfolios. The covariance matrix of a set of assets, and its inverse, the so-called precision matrix, are closely related to graphical models. Here, the previously cited tlasso model is used for the estimation of the precision matrix. Moreover, the interpretation of the precision matrix as a network opens the possibility to implement investment strategies based on network indicators. The main contributions of the thesis are the following: first, we introduce the use of tlasso in the financial literature, extending the results obtained. Then we introduce the network version of ∆CoVaR, and we propose an estimation procedure based on the SCAD penalization framework. Concerning the study of systemic risk, this work is among the first to focus on the presence of a community structure in a banking system, that is particularly relevant in the European setting, where national borders are still relevant divisions.