Valuation of Danish Callable Mortgage Bonds

André Lippert Wijeh

Student thesis: Master thesis


This thesis develops a pricing model for Danish callable mortgage bonds. Pricing a callable mortgage bond is a complicated process since it contains a Bermudan prepayment option. The borrowers do not exercise the option in a strictly rational manner, which affects the price of the bonds as the prepayments alter the cash flows. Initially, a term structure of zero-rates is created from Danish interest rate swaps. This curve is used as input in a Hull-White trinomial tree to describe the future evolution of the rates. The tree’s volatility parameters are then calibrated to the market volatility of several Danish swaptions. The required gain model is used as a prepayment model to estimate the borrowers’ future prepayments and is based on empirical data. The model’s independent variables are the refinance gain, time to maturity and the pool factor while dividing the debtors into five groups depending on the remaining debt. Finally, the interest rate model and the prepayment model are combined and ten callable mortgage bonds are then priced. The prices deviate somewhat from the market prices. This is a consequence of the prepayment model having limited estimation data and generally tends to overshoot the estimated CPR. The model’s prices are expected to become more accurate as the number of bonds in the estimation data is increased along with an extension of the sample period.

EducationsMSc in Finance and Investments, (Graduate Programme) Final Thesis
Publication date2017
Number of pages83