Prepayment and The Valuation of Danish Mortgage Backed Bonds
In this Ph.D dissertation, Scanrate's co-founder and partner Svend Jakobsen developed and tested
a new pricing model for Danish callable mortgage backed bonds.
Svend Jakobsen, Prepayment and the Valuation of Mortgage Backed Bonds, Ph.D. Thesis. The Aarhus School of Business, 1992.
The purpose of the thesis is to develop and test a pricing model for Danish callable mortgage backed bonds (MBBs). MBBs are issued by mortgage credit institutions and each bond is backed by a pool of several thousands individual mortgages. The borrowers hold a prepayment option allowing them to prepay their loan at par value at any time until maturity. As borrowers tend to prepay when market rates are low relative to the coupon rate of the loan this option has a significant impact on the market value of the MBB.
The pricing model is based on an arbitrage-free Black-Derman-Toy term structure model. The thesis analyses rational prepayment behavior in an after tax setting. To account for heterogeneous borrowers and non-rational prepayment behavior the model is modified to a so-called required gain model, in which the prepayment rate is modelled by a probit-like model. The extension to multiple subpools introduces a path dependent burn-out with no need for time consuming Monte Carlo estimation. The pricing model is estimated on Danish prepayment data for the period 1988 to 1992 and the full pricing model is used to predict risk and return behavior for a subset of 33 mortgage backed bonds.