Three essays on the term structure of interest rates

A PhD Dissertation, presented as part of the requirements for the Degree of Doctor of Philosophy from the NOVA - School of Business and Economics

This dissertation comprises of three essays about the term structure of interest rates. The two first chapters are joined works with my PhD thesis advisor, Pedro Santa-Clara. More than being studies on the same underlying asset (bonds), what binds these essays together is the use of simple ideas to bring light to some problems in the literature. In the first essay I show that models proposed in the literature to explain bond excess returns fail to perform out of sample. Instead of regressing returns on a set of explanatory variables, I forecast bond yields and replace them directly in the bond excess return de finition. An investor who used a simple random walk on yields would have predicted bond excess returns with out-of-sample R-squares of up to 15%, while a dynamic Nelson-Siegel approach would have produced out-of-sample R-squares of up to 30%. On the second and third essays I evaluate the performance of a two-factor Cox et al. (1985a,b) model estimation using a state-space framework, while changing the weights in the joint likelihood function. Using EURIBOR zero-coupon yields I show that giving more weight to the likelihood of pricing errors improves the fi tting and forecasting of EURIBOR yields, while giving more weight to the likelihood of short rate factor dynamics improves interest rate derivative pricing at the expense of the fi rst. On the third essay I further explore this idea using Monte Carlo simulations. I show that the bias found in Ball and Torous (1996) and Phillips and Yu (2005) can be minimised by giving more weight to the likelihood of pricing errors. As a consequence, fi tting the yield curve and bond option pricing performance of the model greatly improves. When noise is added to model-implied bond yields, this still holds true for the one-factor model. However, the bond versus bond option pricing tradeo ff is observed for the two-factor model.