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.     

MATCHING SUBSIDIES AND VOLUNTARY CONTRIBUTIONS: A REVIEW

This paper provides a synthesis of the experimental literature on matching subsidies in the context of charitable giving. We classify results according to four different outcome variables frequently considered in the literature and address (i) short‐term effects of linear matching, (ii) the role of the matching rate, (iii) context‐dependence of behavioural responses, (iv) the relevance of the price of giving, (v) long‐term effects and (vi) nonlinear matching schemes. Based on this comprehensive review, we highlight several avenues for future research, such as putting stronger emphasis on competition in fundraising, long‐term effects or heterogeneity in responses.     

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.     

Program planning with Tobit analysis—the United States food stamp case

The purpose of this paper is to illustrate the usefulness of the Tobit model in program planning. The avenue of display is the U.S. Food Stamp Program. Special analytical problems are encountered when the number of eligible nonparticipants of government programs is substantial. Under such circumstances difficulties arise with the use of ordinary regression techniques. The Tobit model is designed to reliably estimate relations from data encumbered with obstacles of this kind. Applications shown herein include program participation prediction and elasticities and probability changes associated with isolated exogenous variable changes.     

A decomposition approach to analysing racial and gender biases in Farm Service Agency's lending decisions

This study provides a different perspective in revisiting the racial and gender discrimination issue at the Farm Service Agency (FSA). Employing the Oaxaca–Blinder decomposition method, this study analyses disparities in approved loan amounts among racial and gender classes of borrowers. This study's results indicate substantial differentials in approved loan amount gaps between racial and gender classes, favouring white and female borrowers, respectively. Further scrutiny of the borrowers’ comparative financial conditions presented to FSA to support their loan applications, however, indicate that these borrower groups significantly dominate their peers in a number of measures that indicate their financial strengths and relatively greater capability to repay their future lending obligations. Hence, this study's results can hardly be construed as evidence of biased lending decisions as these borrower groups should rightfully be offered more favourable loan terms, such as larger loan amounts, by the FSA.     

Rational Pricing of Adjustable Rate Mortgages

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.     

Bridging the leadership divide

The study of generational leadership differences has now broadened and intensified to an impressive body of literature and discussion. The problem is that the conversation continues to be framed as a demographic challenge of difference, which only furthers the division, rather than a relationship challenge that calls for new ways to connect the generations. This article discusses the nature of the relationships needed to ensure vital connections between generations of leaders. It uses the authors' own cross‐generational leadership relationship as a case study in what we believe exemplifies the kind of relationship our research suggests is both needed, and desired, by leaders in both incumbent and emerging leadership generations.     

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.     

Subsidizing unit donations: matches,rebates, and discounts compared

Experimental Economics - An influential result in the literature on charitable giving is that matching subsidies dominate rebate subsidies in raising funds. We investigate whether this result...