Callable Mortgage Bonds

Specialeforsvar ved Kasper Markussen

Titel: Callable Mortgage Bonds

Abstract: This thesis studies callable mortgage bonds. The pricing of callable mortgage bonds basically involves two modelling aspects, that is, modelling the dynamic behaviour of market interest rates and modelling the prepayment behaviour of mortgagors. The latter will be the primary focus and the market short rate is therefore assumed to follow the simple and tractable Vasicek model. The central part of this thesis consists of a comprehensive investigation of the prepayment model proposed by Richard Stanton in 1995 which consistently links prepayment and valuation. This prepayment model is adjusted to be consistent with some aspects of the Danish mortgage legislation. A numerical solution to the model has been implemented which uses finite difference methods in order to approximate the term structure PDEs of callable mortgage bonds. Estimation of the model parameters is performed using the generalised method of moments and based on observed prepayment rates from Danish callable mortgage bonds. The resulting model predicted bond prices are compared to those of a simpler valuation approach in order to get a better idea of what to expect from the model. The model performs very well in capturing and describing observed prepayment behaviour but it performs less well in producing bond prices. We expect that it is the combination of a simple one-factor short rate model and a (simple) prepayment model with constant parameters that causes this. With some extensions and improvements we expect the model to perform better. A natural way to improve the results would be to assume a more realistic and complex short rate model but other possible ways in which one may extend the prepayment model is also discussed.

Vejleder: Rolf Poulsen
Censor:   David Sloth Pedersen, Danske Bank