The Option Value of Mortgage Interest Tax Deductibility

Abstract

We offer a continuous-time contingent claims valuation framework to quantify the tax shield value of US mortgage interest deduction (MID) under uncertainty. We identify non-linear forms (both convex and concave regions) in the pay-off of MID, and discuss the implications for optimal mortgage purchase decisions. The model provides insights regarding the relationship between the effective MID and a set of underlying variables, including income level, house price, mortgage size, and state and local tax rates. In particular, we show how the tax shield value of a mortgage loan changes with key variables such as the life of the loan and the volatility of underlying processes. We apply the model to the case of optimal choice of adjustable versus fixed rate mortgages and prove that under a mean-preserving interest rate, an adjustable mortgage always offers a bigger tax saving. Our work demonstrates a novel aspect of dynamic analysis in the mortgage market.

Keywords: Mortgage Interest, Tax Shield, Option Value, Housing Policies, Dynamic Valuation

JEL Classification: G21, R31