A Three-Factor Mortgage Default Option Pricing Model with Applications to the Loan Modifications

Abstract

The classic contingent-claims pricing model views the borrower’s right to default on a mortgage as a put option. By defaulting on a mortgage the borrower effectively sells the property to the lender with the current value of the mortgage. The primary goal of this dissertation is to develop a three-factor structural default option pricing model to explain and evaluate the default options in the residential mortgage contracts. Home price, interest rate and net transaction cost are the three underlying factors of this model. Because a borrower can default at any time when a mortgage payment is due, the mortgage default option is by nature a path dependent Bermudan-American type option. Similar to the American type equity options, there is no analytical solution to the mortgage default option price. By applying the least-squares Monte Carlo (LSM) method to numerically evaluate the mortgage default option prices under different economic scenarios, this dissertation attempts to explain the borrowers’ behaviors of strategic defaulting on their mortgages. In addition, this dissertation applies the mortgage default pricing model to an important mortgage research area - loan modifications. The effectiveness of the strategic default prevention of the payment reduction modification method and the equity sharing modification method are quantitatively compared. This dissertation also proposes a flexible parametrized loan modification framework by generalizing and extending the existing modification methods.