ALBERT

Notes: The same option-based methodology now commonly used to value mortgages and their termination features also can be applied to calculate the probabilities that mortgage default will occur. This paper pursues that idea, and furthermore, enriches the idealized option-based approach by introducing both transaction costs and “suboptimal” termination. These latter features capture the individual considerations that cause a mortgage holder's actions to differ from what rationality would indicate based solely on the market value of the mortgage. These features are of considerable importance if the results of options-based models are to be made comparable to those calculations of default probabilities occurring in the empirical literature.

Notes: This paper examines the valuation of fixed-rate mortgages and the pricing of insurance against default on such mortgages. Both the mortgage and the insurance are treated as compound European put options. A put is the right, but not the obligation, to turn over an asset to another party for a specified payment, and being a European put indicates that this can only occur at a specified expiration date. The mortgage contract, and hence the insurance on it, fit into a European option framework because no rational borrower would ever choose to default until a payment is due. Mortgages are compound options in nature because at each payment data prior to the last one, the borrower either defaults or purchases a new option to default at the next payment date by making the scheduled payment.Since the current value of the mortgage is affected by options to default in the future, the problem is solved working backwards in time with the value of later options feeding into the earlier ones, so that the process builds on itself in a recursive fashion. Using familiar arguments from option-pricing theory, the value of any of the assets in the model is expressed as the solution to a partial differential equation, where the terms of the contract yield the appropriate terminal conditions. Standard numerical procedures are then used to produce the value of the mortgage and the insurance under various economic conditions.The simulations indicate that the prime determinants of the value of the assets considered are the volatility of the house price and the volatility of the spot interest rate. Sensitivity tests show that changing either of these parameters affects the results substantially more than any of the other parameters examined.The paper completely analyzes the default option and insurance against default on the mortgage. It is one part of a complete model of fixed-rate mortgages that would allow for both prepayment and default and treat the interaction of the two options. The general approach outlined in this paper can be used to develop such a model as well as to value any mortgage-related security. In light of the increasing variety and the complexity of such instruments in the market today, the presentation of our approach to these valuation problems is perhaps the most important contribution of the paper.

Notes: In this paper we develop a general method for valuing adjustable rate mortgages and by producing a set of simulation results, we show that our approach can be implemented. While the simulations are of interest in their own right, we view the approach itself as the major contribution of the paper.

Notes: This paper analyzes the opportunity for early termination of a mortgage contract. We consider the possibility of defaulting on the property and explore the rules that are used by a value-maximizing borrower in exercising this option to default. The discussion centers on the value of waiting to make such a decision and the consequences of this rational inertia. We show that the observed delay in default usually attributed to transaction costs can instead be explained as entirely rational choice in a dynamic environment.

Notes: This paper addresses the issue of why discount points exist in the mortgage market. In the process of resolving these questions, a number of insights into the mortgage market are achieved. An important principle is that changes in loan structure due to points, prepayments or other deviations in the typical mortgage have no impact on the competitive rate of return. Thus, the essential role of points is not to raise the effective rate of return nor are they the purchase price a risk-averter desires for an option to prepay. Instead it is taxes that play the critical role.