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

Abstract

Network theory is a powerful tool for the analysis of complex systems, and in re- cent years a growing body of literature highlights the usefulness of this approach in finance. This thesis explores two particular fields of application of network theory in fi- nance. The first is the modelization of systemic risk and financial contagion in a banking network, and is discussed in three chapters: first we estimate sparse par- tial 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 in particular its inverse, the so-called preci- sion matrix, is 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 introduced the use of tlasso in the financial literature, extending the results obtained. Then we in- troduce 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 particular in the Europe setting where national borders are still relevant divisions.

Network theory is a powerful tool for the analysis of complex systems, and in re- cent years a growing body of literature highlights the usefulness of this approach in finance. This thesis explores two particular fields of application of network theory in fi- nance. The first is the modelization of systemic risk and financial contagion in a banking network, and is discussed in three chapters: first we estimate sparse par- tial 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 in particular its inverse, the so-called preci- sion matrix, is 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 introduced the use of tlasso in the financial literature, extending the results obtained. Then we in- troduce 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 particular in the Europe setting where national borders are still relevant divisions.