TITLE:
A Three-Variable Contingent Claims Residential Mortgage Valuation Model
AUTHORS:
Amitava Chatterjee
KEYWORDS:
Residential Mortgages, Three-Variable Contingent Claims Mortgage Valuation Model, Explicit Finite Difference Method, Default, Prepayment, Adjustable-Rate Options
JOURNAL NAME:
Technology and Investment,
Vol.17 No.1,
January
28,
2026
ABSTRACT: The mortgage valuation literature is saturated with numerous studies using the contingent claims approach to value mortgages. So far, efforts are directed into two alternative model frameworks. First, the pricing of a prepayable mortgage is made possible by using short- and long-term interest rates as relevant variables. Second, a defaultable mortgage is valued with short-term interest rate and building value as explanatory variables. However, the comprehensive valuation of a defaultable and prepayable residential mortgage requires three variables. This study proposes a three-variable model, in which the pricing of a defaultable and prepayable residential mortgage is explained by short- and long-term interest rates, as well as the building value. The model incorporates both fixed-rate and adjustable-rate mortgages. Loan-level residential mortgage data is used for empirical analysis. Valuation results indicate a positive pricing spread between the primary market and the theoretically estimated value. Mean, median, and variance-based statistical studies suggest that the three-variable model is generally efficient in predicting primary mortgage prices, with efficiency being more pronounced for longer-term mortgages. Nonparametric Kernel Density regression analysis reveals that model efficiency increases with longer-term and larger mortgages.