Commercial Mortgage Pricing with Unobservable Borrower Default Costs

This paper develops a pricing model for commercial real estate mortgage debt that recognizes the influence of default transaction costs on the borrower's default decision. These costs are heterogeneous across borrowers and largely un-observable to the lender/investor at the time of origination or loan purchase. A recognition of these unobservable costs can explain why borrower default decisions may differ from those predicted by "ruthless" mortgage-default pricing models. We address the determinants of default choice and timing by replacing sharp default boundaries found in the ruthless models with "fuzzy" boundaries that account for investor uncertainty with respect to evaluating borrower default decisions. To implement our model, we estimate probabilities of default as a junction of time and net equity in the property. Then, given that default occurs, loss severities are modeled based on expected property value recovery net of foreclosure costs and time until the asset is actually sold. Under reasonable parameter value choices, resulting Monte Carlo simulations produce numerical mortgage price estimates as well as component default frequency and severity levels that realistically reflect default premiums and loss levels observed in the marketplace.     

Mortgage Default Risks and the 1971 San Fernando Earthquake

The paper is based on a study of mortgage default risks associated with natural disasters. These risks are faced by holders of mortgages when forced by default to acquire damaged properties. A sample of residential mortgage properties damaged in the 1971 San Fernando, California earthquake is studied. Some of the mortgagors defaulted while others did not. The paper identifies and analyzes those variables associated with default using discriminant and probit regression analysis. The study concentrates on earthquake exposures in California, but has implications for all major disasters.     

Regional Economic Stability and Mortgage Default Risk in the Netherlands

This paper investigates the relationship between regional economic diversification and stability, and residential mortgage default risk in the Netherlands. To describe and measure regional economic diversity and stability, methods from both the regional economics and the industrial economics literature are used. All measures are based on regional employment characteristics. Mortgage default rates were obtained from a database of the population of insured mortgage defaults in the Netherlands from 1983 through 1990. To test the relationship between the measures and mortgage default risk, cross sectional Seemingly Unrelated Regression was used. The paper concludes that the employed measures explain regional mortgage default rates to a significant extent, and that stability measures outperform diversity measures.     

Mortgage Prepayment and Default Decisions: A Poisson Regression Approach

This paper uses an extensive and geographically dispersed sample of single-family fixed rate mortgages to assess the prepayment and default behavior of individual homeowners. We make use of Poisson regression to efficiently estimate the parameters of a proportional hazards model for prepayment and default decisions. Poisson regression for grouped survival data has several advantages over partial likelihood methods. First, when dealing with time-dependent covar-iates, it is considerably more efficient in terms of computations. Second, it is possible to estimate full-hazard models which include, for example, functions of time as well as multiple time scales (i.e., age of the loan and calendar time), in a much more straightforward manner than partial likelihood methods for un-grouped data. Third, Poisson regression can be used to estimate non-proportional hazards models such as additive excess risk specifications. Taken together, our data and estimation methodology allow us to obtain a better understanding of the economic factors underlying prepayment and default decisions.     

A Note on Mortgage Risk: Default vs. Loss Rates

This note reexamines the role of the loan-to-value ratio on mortgage risk. Whereas previous studies have focused on the default rate as a function of this term, this study considers the additional effect on the loss rate of defaulted loans. Because the dollar loss per amount originated is the product of the default rate and the loss rate on defaulted loans, the impact of the loan-to-value ratio on both the default and loss rates is crucial to explaining the impact of the loan-to-value ratio on mortgage risk. I find that both rates are significantly positively related to loan-to-value ratio and that the loss rate accounts for between 13% and 20% of total loan-to-value impact.     

Handing Over the Keys: A Perspective on Mortgage Default Research

This paper is the text of the 1992 Presidential Address for the American Real Estate and Urban Economics Association. A comparative evaluation of mortgage default research finds that both the residential and commercial markets evolved from informal underwriting rules, to formalized (though unvalidated) ratios and rules of thumb, to early risk ratings based upon empirical evidence, to gener-alizable econometric models of default, to option-based pricing models. The commercial market lagged the residential market by about 10 to 20 years at first but is now only about five years behind. The survey finds that research and progress in understanding mortgage credit risk has been precipitated by a public policy need or mandate, data availability, and adequate technology. The absence of any one of these factors has hindered progress in the past. Finally, six emerging issues in default research are identified and discussed: (1) the degree of "ruth-lessness" with which default is exercised, (2) loan recourse, (3) the magnitude and timing of revenues and losses associated with default, (4) loan modification, (5) default in a portfolio context, and (6) leasehold default. Progress in these areas will enhance the efficiency of both the residential and commercial markets.     

Privatized Default Risk and Real Estate Recessions: The U.K. Mortgage Market

A mortgage pricing model is developed when a borrower goes through a series of distress states, including delinquency, long-term nonpayment and ultimate default. These steps are sequential, and depend on prices and alternatives faced by the borrower. The multistate default model is applied to the mortgage market in the United Kingdom. As a byproduct, a pricing structure for the U.K. endowment mortgage, which combines a good and a life insurance policy, is developed. Income and liquidity constraints are shown to affect the decision to keep a mortgage current in different states of distress. Solvent borrowers may thus keep their mortgages current, even when equity is negative.     

Industrial Real Estate Mortgage Default Experience of the New York State Job Development Authority Second Loan Program: A Preliminary Investigation

This paper explores the loan loss experience of a public industrial lending authority, employing contemporaneous borrower net equity as a link to mortgage loan default. The relationship between default, net equity and bankruptcy is tested on a small longitudinal data set of loans using nonparametric statistics and a proportional hazard model. Results show that negative net equity and firm bankruptcy are strongly associated with default among the study population. Further, the borrowers studied did not exercise the put option promptly, suggesting potential benefits from monitoring net equity one year or more prior to default.     

The Demand and Supply of Mortgage Funds and Mortgage Loan Terms

The supply of and demand for residential mortgages has been the subject of much discussion in the literature. Many of these studies have used single equation, partial adjustment models with the price specified as the contract rate. In this study, two of the assumptions that underlie these previous studies are tested empirically. First, the proper specification of the price of mortgage funds is tested by using both the contract rate alone and all of the terms of the mortgage as the price. Second, the speed of adjustment in the mortgage market is examined by estimating the model in both the instantaneous adjustment and partial adjustment forms. Both of these tests are carried out using a simultaneous equation rather than a single equation model. The empirical results indicate that the contract rate along with the loan initiation fees, the loan-to-value ratio and the maturity is the better specification of price and that the partial adjustment model performs better than the instantaneous model in the mortgage market.     

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.     

Mortgage Choice†

Mortgage choice refers to a set of problems faced by a homeowner that includes the choice of a loan-to-value ratio, the refinancing and default decisions, and the choice of mortgage instrument. This paper reviews much of the literature that has been written on the topic. It begins with a listing of the major stylized facts the literature seeks to explain. Models used to explain mortgage choice are categorized and discussed. It is argued that the relatively simple certainty model that incorporates liquidity constraints seems capable of explaining some of the stylized facts, but is unable to explain some others. The paper concludes with a discussion of three policy questions that require a better understanding of mortgage choice before they can be answered. The paper is based upon the author's Presidential Address to the American Real Estate and Urban Economics Association, which was delivered in Atlanta, Georgia on December 29, 1989.     

Elective Mortgage Prepayment: Termination and Curtailment

Mortgage-prepayment risk underlies the structuring of mortgage-backed derivative securities, such as tranched real estate mortgage investment conduits. This prepayment comes either from mortgage termination or from curtailment, where the borrower retains the existing mortgage and prepays a portion. There are differences in cash flows from the two types of prepayment. In termination, the loan disappears from a pool, and the scheduled payment to investors in the pool is reduced. In curtailment, the loan survives, and the scheduled payment is unchanged but the term is reduced. There are implications for structuring mortgages and derivative securities. The prepayment decision is embedded in an in-tertemporal household utility maximization framework where choices are made between refinancing, making the regular payment, default or curtailment. Empirical results are presented for Government National Mortgage Association (GNMA) pools, and an algorithm is presented that separates the termination and curtailment components, facilitating the development of derivative securities.     

Risk and the Home Equity Conversion Mortgage

This article analyzes the risks involved with reverse mortgage insurance and explains the pricing model developed for the Home Equity Conversion Mortgage (HECM) demonstration. The paper demonstrates how borrower longevity, interest rates and property value changes all affect pricing, and why the HECM model focuses on property value as the primary source of uncertainty. It goes on to explain why a random walk specification was chosen to forecast property values, and how the principal limit factors, which determine cash payments to borrowers in the HECM program, are calculated.     

房地产抵押的风险及防范

根据抵押的概念，介绍了房地产抵押的风险及应对措施。     

Predicting Commercial Mortgage Foreclosure Experience

This study has two objectives: (1) it directly evaluates the relationship between commercial mortgage default incidence and characteristics of the mortgage, borrower, property, market, and general economic conditions, and (2) it uses this relationship to predict the exposure of life insurers to future mortgage defaults and to examine the relative importance of various causes of current and past credit quality problems. A theoretical model of the default decision predicts that the decision would be expected to be driven primarily by the borrower's current equity stake in the property, or the ratio of the market value of the loan to property value (M_t/V_t), but that the presence and magnitude of transaction costs associated with default would be expected to result in underexercise of the default option. Empirical estimation making use of American Council of Life Insurance (ACLI) and National Council of Real Estate Investment Fiduciaries (NCREIF) data confirms both expectations. A high proportion of the longitudinal variation in foreclosure incidence is explained by variations in M_t/V_t, but even at high ratios M_t/V_t in excess of 1.1. only 5% to 8% of mortgagors default, although this magnitude of underexercise is probably overstated because of problems in measuring M^t and for other reasons. Simulations using the model provide a pessimistic outlook for future defaults. Default rates are predicted to double in the five-year period 1988–93. Other simulations examine the relative importance of interest rate fluctuations, property value declines, and geographic or temporal correlations in lending during the 1976–88 period on current default experience.     

Mortgage Borrower Repayment Behavior: A Microeconomic Analysis with Canadian Adjustable Rate Mortgage Data

In this paper we estimate a model of mortgage borrower behavior using micro-level data on Canadian borrowers with rollover mortgages—a form of adjustable-rate mortgage. Our results suggest that the probability of default rises with a decrease in housing equity and an increase in the mortgage contract rate; however the size of these changes is relatively small. They also show that partial prepayment is sensitive to fluctuations in the rates of return from investing in housing versus other assets. For the United States experience, our results suggest that, relative to fixed-rate mortgage borrowers, adjustable-rate mortgage borrowers are more likely to default and less likely to prepay.     

Mortgage Refinancing with Asymmetric Information

Information asymmetry exists between the lender and the borrower regarding the holding period of the mortgaged real estate; the lender does not know how long the borrower plans to own the house. This information asymmetry allows the cost of obtaining a mortgage to deviate from its value to the borrower. As a result, the exercise price of the option to refinance becomes the cost to the borrower of obtaining a new mortgage instead of the outstanding balance of the existing mortgage as used in previous models. The option to refinance is a sequential option; after the borrower refinances, a new option is obtained to refinance again in the future. A mortgage refinancing model is developed taking information asymmetry and sequential refinancing into account. The model is used to solve for (1) the value to the borrower of a callable mortgage and (2) the minimum interest rate differential between the contract rate of the existing mortgage and the market interest rate needed to justify refinancing.     

贸易成本、本地关联与产业集群迁移

本文着重分析在劳动力成本上升和人民币升值的背景下,沿海产业集群迁移的影响因素、可能的迁移倾向和应对策略。由于产业集群的本地关联性和对国际市场的依赖程度不同,生产和贸易成本上升对这些集群区位再选择的影响也不同。由跨国公司主导的一些高技术产业加工贸易集群向沿海中小城市或低成本国家迁移的倾向会越来越明显;而数量众多的传统产业集群,随着出口增长率的下降和内需的提升,向中西部地区扩散或迁移的速度将会加快。东部沿海地区应积极扩散一些已丧失优势的劳动密集型产业,同时抓住世界服务业转移的机会实现产业升级;中西部地区要着力创造有利于承接沿海产业转移的软硬环境,尤其是降低物流成本和交易成本。开展区域合作,减少企业迁移的不确定性,是促进产业理性转移和区域协调发展不可忽视的环节。