Realistic Modeling of the Underlying Risk Factors of Interest Rates : Leveraging Principal Components, GARCH Processes, and Copulas

Sammanfattning

In the dynamic environment of financial markets, accurate modeling of interest rate curves is critical for investors, risk managers, and policymakers. This thesis aims to develop a realistic model for the underlying risk factors of interest rates, specifically focusing on the Euro market. The derivatives market in the European Union, with a notional value of EUR 314 trillion in 2022, provides a substantial area for this study. The research process is structured into six major steps: data collection, term structure measurement, identification of systematic risk factors, modeling of these factors, simulation, and evaluation. The data collection focuses on Euro Overnight Index Swaps (OIS) spanning from 2005 to 2024. To address the complexity of modeling interest rates over long maturities, this thesis employs Principal Component Analysis (PCA) for dimensionality reduction, capturing the most significant risk factors driving the interest rates. For modeling the marginal distributions of the identified risk factors, Generalized Autoregressive Conditional Heteroskedasticity (GARCH) processes are utilized. Copulas, particularly Gaussian and t copulas, are used to model the co-dependence structure between these risk factors. The combined use of PCA, GARCH, and copulas allows for a comprehensive and realistic representation of the stochastic dynamics of interest rates. The results indicate that modeling the marginals with GJR-GARCH and Student’s t innovations and the co-dependence structure with either Vine or Student’s-t copula in general are the superior models in general. Evalua- tion of the other models indicate that DCC show some promise compared to Gaussian copula and it warrants further research into alternative combinations of univariate and multivariate models. Especially, further research into combining different models during periods of low and high volatility would be of interest.