Valuation of mortgage interest deductibility under uncertainty: An option pricing approach

We propose a dynamic option pricing model 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 the valuation of MID. 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. We also show how the tax shield value of mortgage loans changes with the volatility of underlying processes. We apply the model to the case of the 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. We use the framework to study how the tax reforms of 2017 have affected the MID benefits of different households, and find that no household is expected to receive a larger mortgage deduction under the new law. Finally, we find that, by putting a cap on deductible state and local taxes, the 2017 reform has significantly reduced the quantitative impact of income and house price volatility on the expected MID value.