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

The classic contingent-claims pricing model views the borrower’s right to default ona mortgage as a put option. By defaulting on a mortgage the borrower effectivelysells the property to the lender with the current value of the mortgage. The primarygoal of this dissertation is to develop a three-factor structural default option pricingmodel to explain and evaluate the default options in the residential mortgagecontracts. Home price, interest rate and net transaction cost are the three underlyingfactors of this model. Because a borrower can default at any time when amortgage payment is due, the mortgage default option is by nature a path dependentBermudan-American type option. Similar to the American type equity options,there is no analytical solution to the mortgage default option price. By applyingthe least-squares Monte Carlo (LSM) method to numerically evaluate the mortgagedefault option prices under different economic scenarios, this dissertation attemptsto explain the borrowers’ behaviors of strategic defaulting on their mortgages.In addition, this dissertation applies the mortgage default pricing model to an importantmortgage research area - loan modifications. The effectiveness of the strategicdefault prevention of the payment reduction modification method and the equitysharing modification method are quantitatively compared. This dissertationalso proposes a flexible parametrized loan modification framework by generalizingand extending the existing modification methods.