Predicting the Swap Spread with a Dynamic Nelson-Siegel Model

Abstract

This thesis aims to develop a methodology for predicting the swap spread, which is defined as the difference between the German government bond interest rate and the Euribor swap rate. Thus far, the prediction of interest rates is limited to the prediction of a single interest rate. This thesis introduces the simultaneous prediction of the spread between two correlated interest rate curves. The methodology developed in this thesis considers the dependence between the bond rate and the swap rate. The study utilizes a Dynamic Nelson-Siegel (DNS) model, which is extended to incorporate the correlation between these two rates. The simulation studies reveal that the variants simultaneously predicting both the swap and bond rates using a restricted VAR(1) model for factor dynamics outperform the other variants in predicting the swap spread. Another important aspect considered is the stationarity of the latent factors. The simulation studies demonstrate that the stationarity of the empirical DNS factors accurately represents the stationarity of the true DNS factors. This motivates the reformulation of the DNS model into a new variant where the first-order differences of both the swap and bond rate latent factors are modeled by a restricted VAR(1) model.
A case study validates the developed new variant of the DNS model, demonstrating predictions for the swap and bond curves that have an accuracy comparable to the accuracy of the benchmark model. The key advantage of the DNS model over this benchmark model is that the DNS model predicts the swap curve and bond curve over the whole maturity spectrum. The prediction over the whole maturity spectrum is crucial to compute the spread between the two rates, which emphasizes the relevance of the new model presented in this thesis.