Model fitting of a two-factor arbitrage-free model for the term structure of interest rates using markov chain Monte Carlo

Abstract

In this thesis we use Markov chain Monte Carlo (MCMC) simulation to calibrate a two-factor arbitrage-free model for the term structure of interest rates which is proposed by Cairns (2004a) based on the positive-interest framework (Flesaker and Hughston, 1996). The model is a time-homogeneous model driven by latent state variables which follow a two-dimensional Ornstein-Uhlenbeck process. A number of MCMC algorithms are developed and employed for estimating both model parameters and latent variables where simulated data are used in the first place in order to validate the algorithms and ensure that they can result in reasonable and reliable estimates before using UK market data. Once the posterior estimates are obtained, we next investigate goodness of fit of the model and eventually assess the impact of parameter uncertainty on the forecasting of yield curves in which the achieved MCMC output can be used directly. Additionally, the developed algorithm is also applied for estimating the two-factor Vasicek term structure model for comparison. We conclude that our algorithms work reasonably well for estimating the Cairns term structure model. The model is then fitted to UK Strips data, and it found to produce reasonable fits for medium- and long-term yields, but we also conclude that some improvement may be required for the short-end of the yield curves.