Three essays on the mortgage market

The first paper reviews the existing theoretical work on the option-theoretic mortgage valuation. The mortgage market has become an increasingly important segment of the financial market. There are two strands in the mortgage valuation literature; reduced-form (econometric) and structural-form (option-theoretic) valuation model. The option theoretic model provides clear endogenous explanations as to why the mortgage termination occurs. This approach shows that the mortgage value is determined by the interaction between the contractual features of mortgages and the uncertain future economic environment.;In the second paper, we construct a continuous time version of an option pricing model for mortgage valuation to examine the effects of a prepayment penalty on the default and the prepayment decision of subprime borrowers. We show that the options embedded in mortgage contract have significant positive values for the mortgage borrower. In particular, the value of prepayment option for the subprime mortgage borrower is significant. One of the defining features of subprime mortgages relative to prime mortgages is the prevalence of a prepayment penalty. The prepayment penalty reduces the value of the prepayment option on subprime mortgages and increases the likelihood of default by subprime borrowers. The major finding from the study is that the prepayment penalty affects not only the prepayment decision but also the default decision of subprime borrowers by reducing the value of options; The higher the prepayment penalty is, the higher the default rate on subprime mortgage contracts becomes. We show this by constructing a parsimonious mortgage valuation model. With high periodic payments and prepayment penalties, subprime mortgage lending that is based on equity extraction is not viable when the price of the underlying asset, the house, falls dramatically.;In the third paper, we develop an equilibrium valuation model that incorporates optimal default to show how mortgage yields and lender recovery rates on defaulted mortgages depend on initial loan-to-value (LTV) ratios. The analysis treats both the frictionless case and the case in which borrowers and lenders incur deadweight costs upon default. The model is calibrated using data on California mortgages. Given reasonable parameter values, the model does a surprisingly good job fitting the risk premium in the data for high LTV mortgages. Thus, from an ex ante perspective, we do not find strong evidence of systematic underpricing of default risk in the run-up to the housing market crisis.