# Shadow Rate Modelling in the Danish Low Yield Environment

Specialeforsvar ved Jacob Bjerre Skov

Titel: Shadow Rate Modelling in the Danish Low Yield Environment

Abstract: Post-crisis government bonds have had their yields drop to zero and even negative values. This has brought an increasing focus on dynamic term structure models being able to cap-ture the change in yield dynamics, as they become constrained by their nominal lower bound. In this thesis we model Danish government bond yields using the Gaussian Arbitrage-Free Nelson-Siegel model and its shadow rate extension, incorporating a lower bound for the short rate. We find that unlike the Gaussian model, the shadow rate model is able to capture the asymmetric distribution of future short rates as well as the decline in short-term yield volatilities present when yields are constrained by their lower bound. Furthermore the shadow rate extension is shown to improve the forecast performance of the model for short to medium term yields during the low yield period. However, we do not find any improvement in forecasting from including the lower bound as a parameter in the model estimation as opposed to fixing it at $-1\%$. Arbitrage-free dynamic term structure models often prove difficult to estimate, which is not made easier by the non-affine yield function of the shadow rate model. Multiple simulation studies are therefore performed to investigate the efficiency of the Extended and Iterated Extended Kalman Filter when estimating shadow rate models in a low yield environment. We find that the real-world mean reversion parameters are subject to a significant upwards finite sample bias, whereas the parameters determining the cross section of yields are estimated close to their true values without bias. Notably the study shows that the lower bound is identifiable when the data reflects yields being in a low rate environment. Comparing the estimates from the two filters shows that the iterated version provides an improved accuracy of the filtered state variables. Also, we find that the estimated parameters are closer to their true values and display less dispersion across all estimates. These improvements are, however, highly dependent on the quality of the observed yields, and mainly present when these show little error

Vejleder: David G. Skovmand

Censor: Bjarne Astrup Jensen (CBS)