## Abstract

The purpose of this master thesis is to develop a pricing model for Danish callable mortgage bonds. Callable bonds have an embedded prepayment option, where the borrower of the callable mortgage bond has the right to redeem the loan at par. The prepayment option makes callable mortgage bonds complicated to price, because it makes the cash flow of the bond uncertain, since it cannot be known initially when or if the prepayment option will be exercised. There are two main components of a model for pricing callable mortgage bonds. These are a term structure model and a prepayment model. The term structure model determines the possible evolution of the short rate. We use the Ho-Lee model as term structure model, and the model has the zero coupon term structure and the volatility structure as input. The zero coupon term structure is estimated with rates on deposits, forward rate agreements and interest rate swaps. The volatility structure consists of the volatility of swaptions. The prepayment model estimates the size of the prepayments as a function of different explanatory variables. We use a required gain model as prepayment model, which describes the conditional prepayment rate as a function of different variables. As explanatory variables we use the prepayment gain, the pool factor and the relative time to maturity. The variables are based on historical data. We estimate the prepayment model based on observed historical prepayment rates and borrower compositions. The determined term structure and the estimated prepayment model are used in developing the pricing model for callable bonds. The prepayment model is used to determine future prepayment rates. The future prepayment rates are then used to determine the future cash flows. The future cash flows are discounted with the term structure to determine the price of the callable bond. We calculate the price for ten callable bonds. The pricing model has difficulties in pricing bonds with a high coupon rate, but it prices bonds with a low coupon rate good.

Educations | MSc in Mathematics , (Graduate Programme) Final Thesis |
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Language | Danish |

Publication date | 2016 |

Number of pages | 105 |