James B. Kau

A Generalized Valuation Model for Fixed-Rate Residential Mortgages

This paper uses option pricing techniques to rationally price mortgage instruments subject to both default and prepayment risk. Attention is given to terminations due to purely financial consideration of the mortgage contract itself, as well as to personally induced terminations. Explicit inclusion of default in the mortgage valuation procedure also permits the valuation of insurance against such default. Qualitatively, it is found that default differs significantly in the behavior from either prepayment or nonfinancial termination. Quantitatively, however, there is significant substitution between prepayment and default, so that the addition of a default feature to the contract has only a modest impact on mortgage values, unless there is substantial price volatility in the housing market or a high loan-to-value ratio. Copyright 1992 by Ohio State University Press.

A General Equilibrium Model of Congressional Voting

In this paper we specify a model in which Congressmen, constituents, and campaign contributors simultaneously decide on behavior. Constituents and contributors desire to influence the voting behavior of Congressmen; Congressmen, on the other hand, want to be elected and vote accordingly. We empirically test this model using roll call voting on eight bills dealing with economic regulation and find support for the model. Our results indicate that part of the voting behavior of Congressmen may be explained by noneconomic factors. We also find that unions and businesses as campaign contributors are sometimes influential; unions are more often influential than is business. Ideological factors are also important in explaining voting.

The Valuation at Origination of Fixed Rate Mortgages with Default and Prepayment

This paper develops a model to rationally price fixed-rate mortgages, using the arbitrage principles of option pricing theory. The paper incorporates amortization, prepayment and default in valuing the mortgage. Having completely specified the model, numerical procedures value the different features of the mortgage contract under a variety of economic conditions. The necessity of having both the interest rate and the house price as explanatory variables, due to the interaction of default and prepayment, is demonstrated. The numerical solutions presented center around mortgage pricing at origination. Thus, variations in the equilibrium contract rate are examined for differing economic conditions and changes in the contract. Finally, by presenting a complete model, the paper yields insights for the existence of common institutional practices.

The size of government

Most research on the causes of growth in government expenditure has focused on the demand for government services. In this paper, we argue that in fact this growth may have occurred because of changes in supply. Changes in technology leading to increased specialization and thus increased opportunity costs of self-production have led to increased market production and increased record keeping. Also, female labor force participation has increased. Both of these factors serve to reduce the (efficiency) cost of collecting taxes; if the demand for government spending has not changed, this increase in supply would lead to a larger public sector. We estimate a system of simultaneous equations for the period 1929–1970 incorporating this hypothesis, and the results are consistent with the theory. We are able to explain virtually all of the growth of government; increases in female labor force participation seems to be a very important variable in this explanation.

Pricing Default Risk in Mortgages

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. Copyright American Real Estate and Urban Economics Association.

Pricing Commercial Mortgages and Their Mortgage-Backed Securities

This article has taken considerable effort to accurately model the complexity of a commercial mortgage and its mortgage-backed security. In fact, it is the first example in the general literature on mortgage pricing to present a comprehensive set of numerical results in which the valuation of a mortgage-backed security is explicitly tied to that of the underlying mortgage. The conclusion we reach is that option pricing provides an accurate and flexible approach to valuing the complex mortgage instruments now being developed in the financial community.

Option Theory and Floating-Rate Securities with a Comparison of Adjustable- and Fixed-Rate Mortgages

This article demonstrates how to value floating-rate securities, in particular adjustable-rate mortgages, in the presence of default. The problem is not a straightforward one since endogenous termination (default and prepayment) necessitates solution by backward procedures, but caps on the floating rate then create path dependencies. The solution is to introduce an artificial state variable, the past contract rate, in addition to the natural stochastic variables, the interest and the house price process. With this technique, a numerical investigation of the properties of defaultable adjustable-rate mortgages is provided. In all cases, a comparison is made with standard fixed-rate mortgages. Coauthors are Donald C. Keenan, Walter J. Muller III, and James F. Epperson. Copyright 1993 by University of Chicago Press.

Urban land value functions and the price elasticity of demand for housing

The structural characteristics of an urban area are determined to a great extent by the spatial pattern of land values. It is thus important to develop urban land value functions which accurately describe the spatial structure of cities. This paper provides evidence on the functional form of the relationship between land values and distance from the city center. Using historical data for Chicago, the Box and Cox transformation technique is employed to examine the land value function. The functional form parameter can be used to determine the price elasticity of demand for housing.

Waiting to Default: The Value of Delay

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.

Valuing Prepayment and Default in a Fixed‐Rate Mortgage: A Bivariate Binomial Options Pricing Technique

This paper uses a bivariate binomial options pricing technique to value the prepayment and default options in a fixed-rate mortgage. The American style options are dependent on two stochastic variables: (1) house price, (2) one year spot rate. The paper uses the standard lognormal process for house price and the CIR square-root process for interest rates. By forcing the two underlying state variables to undergo transformations, two new uncorrelated variables with constant volatilities are established. With constant volatilities, a computationally simple bivariate binomial tree is formed which greatly reduces the complexity of working with two state variables and is pedagogicallyuseful. Using this procedure, the price of any real estate contingent claim whose value is dependent on the one year spot rate and house price can be determined. Results are compared with those from a finite difference model.