Hierarchical risk aggregation using aggregation trees and copulasIvanova, Lina (Avtor) Stopar, Nik (Mentor) Milošević, Bojana (Komentor) copulariskhierarchical aggregationaggregation treesrisk measuressample reordering algorithmSeveral historical financial crises have repeatedly demonstrated the importance of accurately modeling dependence structures between different sources of risk. Financial institutions face significant challenges in managing and aggregating risks across portfolios while at the same time assessing possible losses and adhering to ever more demanding regulatory requirements. In particular, traditional risk aggregation techniques based on linear correlation and multivariate normal distribution have proven inadequate, as they fail to capture nonlinear, asymmetric, and tail-dependent behavior that becomes especially pronounced during periods of market stress. This thesis studies portfolio risk aggregation using copula-based methods, with a particular focus on hierarchical risk aggregation. Copulas provide a flexible framework for modeling dependence separately from marginal distributions, allowing for more realistic representations of joint extreme events. However, standard multivariate copulas become restrictive and difficult to interpret in high-dimensional settings. Hierarchical aggregation addresses this limitation by decomposing a high-dimensional portfolio into a tree structure, where dependence is modeled locally between low-dimensional sub-portfolios and aggregated step by step into a total portfolio. Methodologically, the thesis combines parametric modeling of the marginal distributions with copula-based dependence modeling and simulation techniques. Marginal distributions are estimated using heavy-tailed models, including the Student-$t$ and Lévy-stable distributions, while dependence is captured using a combination of different copulas. Estimation is carried out using the inference functions for margins (IFM) approach. The joint distribution of aggregated portfolio return is approximated via the sample reordering algorithm, enabling the computation of risk measures such as Value-at-Risk and Expected Shortfall at the portfolio level. The empirical analysis demonstrates that hierarchical copula-based aggregation provides a substantial improvement over the traditional approaches based on Gaussian distribution, particularly in capturing tail dependence and extreme losses. The results highlight the importance of modeling dependence in a flexible and structured way and show that hierarchical copulas offer a powerful and practical tool for risk aggregation in modern financial risk management.20262026-07-03 08:15:15Magistrsko delo/naloga184289UDK: 519.6VisID: 160564COBISS_ID: 283753219sl