Prisfastsætning af konverterbare realkreditobligationer

Abstract

The purpose of this master's thesis is to establish a model that can estimate pricing of fixed-rate callable mortgage bonds based on market data. A callable mortgage bond can be considered as a noncallable bond, with a built-in US call-option, also called a prepayment option. The prepayment option allows borrowers for each term to repay the loan at par. This means that the price of the callable bond does not follow the normal relationship between price and interest rate. This complicates the pricing of the callable bonds. A term structure model and a prepayment model are essential for the pricing model.

The term structure model describes the development of the short interest rates. In this thesis, the Ho-Lee model is chosen as the term structure model, and it is based on the zero-coupon interest structure and the interest volatility structure. The zero-coupon interest structure is estimated based on swap rates and the interest volatility structure is estimated based on swaptions volatility.

The prepayment model describes borrowers' prepayment behavior as a function of interest rates and other variables. A profit requirement criteria is used in the prepayment model and it is based on three variables, the prepayment profit, the relative remaining maturity, and the pool factor. The three variables are estimated based on historical data.
The pricing is implemented using the binomial model and takes the estimated term structure model and the estimated prepayment model as input. The prepayment model determines the future prepayment rates, and the term structure model is used for discounting back the future cash flows.

Pricing of 15 fixed-rate callable mortgage bonds is estimated using the developed pricing model and US option pricing theory.

The developed models has difficulty pricing bonds with long remaining maturities and low coupon rates but generally produces better estimates than US option pricing theory.