Closed‐Form Mortgage Valuation Using Reduced‐Form Model

Abstract

Valuing mortgage‐related securities is more complicated than valuing regular defaultable claims due to the borrower's prepayment behavior as well as the possibility of default. Some researchers use a structural‐form model to obtain the closed‐form formulas for the mortgage value. With this method, however, it is difficult to identify the critical region of early exercise. As an alternative, the reduced‐form model developed in this article is able to value the mortgage without setting boundary conditions, and it can thereby accurately handle the multidimensional space of correlated state variables. The purpose of this article is to derive a closed‐form solution of the mortgage valuation equation under a general reduced‐form model that embeds relevant economic variables. This new approach enables portfolio managers to undertake sophisticated portfolio optimization and hedging analyses. An implementation procedure for the model is also provided to demonstrate how the valuation framework can be utilized in practical applications.