Pricing of Callable Danish Mortgage Bonds

Specialeforsvar ved Nikolaj Madsen og Kirsten Hell Madsen

Titel: Pricing of callabale Danish Mortgage Bonds

Resume: The main object of this thesis is pricing of callable fixed rate mortgage bonds. Bonds are interest rate derivatives so we need to model the term structure. Here we consider the short rate model given by Vasicek. Pricing is further complicated by the borrower's option to prepay the loan at par value at specific time points during the life of the bond. Therefore, the prepayment behavior needs to be modeled. For this matter, we analyze the prepayment function given by the Minimal Mortgage model, which is used in Danske Bank. We calculate prices by solving partial differential equations numerically by finite difference methods. The maximal prepayment scale in the Minimal Mortgage model is made dynamic and we are able to get a consistent fit to market prices, while maintain an acceptable fit to the realized prepayments. One problem occurred when the Vasicek parameters gave a poor fit to the ZCB yield curve. This is rectified by introducing the Cheyette term structure, which uses today's term structure as initial condition. Based on this we have a model for estimating callable mortgage bond prices and prepayment behavior in the market. 

Vejledere:  Rolf Poulsen, Jacob Nielsen, Danske Bank
Censor:     Bjarne Astrup Jensen, CBS