A Steady State Solution to a Mortgage Pricing Problem
Dejun Xie
TL;DR
This paper derives an analytical steady-state solution for a mortgage pricing model with prepayment options, assuming CIR interest rate dynamics, using variational methods to solve a free boundary problem.
Contribution
It provides the first analytical solution to a mortgage pricing problem with prepayment under CIR interest rate dynamics using variational methods.
Findings
Analytical solution to the free boundary problem is obtained.
The free boundary is characterized by a transcendental algebraic equation.
The model captures the impact of CIR interest rates on mortgage prepayment pricing.
Abstract
This paper considers a mortgage contract where the borrower pays a fixed mortgage rate and has the choice of making prepayment. Assume the market interest follows the CIR model, a free boundary problem is formulated. Here we focus on the infinite horizon problem. Using variational method, we obtain an analytical solution to the problem, where the free boundary is implicitly given by a transcendental algebraic equation.
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Taxonomy
TopicsStochastic processes and financial applications · Mathematical and Theoretical Analysis · Economic theories and models