Modelling Danish Government Bond Yields & Term Premia in a Shadow Rate Model

Specialeforsvar ved Louise Damgaard

Titel: Modelling Danish Government Bond Yields & Term Premia in a Shadow Rate Model

Abstract: Several years of low and even negative government bond yields have attracted increasing attention to term structure models incorporating a lower bound on yields. We investigate the implications of modelling the Danish government bond yields using a shadow ratemodel where rates are bounded by a constant lower bound. More specifically, we consider a shadow rate extension of the well-known arbitrage-free Nelson-Siegel model. We find that the introduction of a lower bound results in an asymmetric distribution of future yields and a compression of volatility when rates are low.
The estimation of dynamic no-arbitrage term structure models is often problematic and involves large standard errors on the parameter estimates. We conduct a simulation study in order to investigate the small sample behaviour of the commonly-used likelihoodbased parameter estimator. Based on the simulation study, we propose an alternative estimation procedure where parameters related to the real-world dynamics of the interest rate process are estimated using the ordinary least squares estimator. The simulation study indicates a superior behaviour of the OLS estimator in terms of smaller standard errors and unbiasedness.
As the thesis is targeted at the Danish Government Debt Management O_ce (DMO), we investi-gate estimates of the model-implied term premium, which constitutes a central part of the DMO's risk management. Consistent with literature, we find that different models and sample periods produce significantly different estimates of the term premium level.

Vejleder: Rolf Poulsen
Censor:    Elisa Nicolato, Aarhus Universitet