Yongheng Deng

Mortgage Terminations, Heterogeneity and the Exercise of Mortgage Options

As applied to the behavior of homeowners with mortgages, option theory predicts that mortgage prepayment or default will be exercised if the call or put option in in the money by some specific amount. Our analysis: tests the extent to which the option approach can explain default and prepayment behavior; evaluates the practical importance of modeling both options simultaneously; and models the unobserved herterogeneity of borrowers in the home mortgage market. The paper presents a unified model of the competing risks of mortgage termination by prepayment and default, considering the two hazards as dependent competing risks which are estimated jointly. It also accounts for the unobserved heterogeneity among borrowers, and estimates the unobserved heterogeneity simultaneously with the parameters and baseline hazards associated with prepayment and default functions. Our results show that the option model, in its most straightforward version, does a good job of explaining default and prepayment; but it is not enough by itself. The simultaneity of the options is very important empirically in explaining behavior. The results also show that there exists significant heterogeneity among mortgage borrowers. Ignoring this heterogeneity results in serious errors in estimating the prepayment behavior of homeowners.

Mortgage default and low downpayment loans: The costs of public subsidy

Abstract This paper presents a unified model of the default and prepayment behavior of homeowners in a proportional hazard framework. The model uses the option-based approach to analyze default and prepayment, and considers these two interdependent hazards as competing risks. The results indicate the sensitivity of default to the initial loan-to-value ratio of the loan and the course of housing equity. The latter is a measure of the extent to which the default option is in the money. The results also indicate the importance of trigger events, namely unemployment and divorce, in affecting prepayment and default behavior. The empirical results are used to analyze the costs of a current policy proposal-stimulating homeownership by offering low downpayment loans. We simulate default probabilities and costs on zero-downpayment loans and compare them with conventional loans with conventional underwriting standards. The results indicate that if zero-downpayment loans were priced as if they were mortgages with 10% downpayments, then the additional program costs would be 2–4% of funds made available-when housing prices increase steadily. If housing prices remained constant, the costs of the program would be much larger indeed. Our estimates suggest that additional program costs could be between

Economic Returns to Energy-Efficient Investments in the Housing Market: Evidence from Singapore

74,000 and

Racial Differences in Homeownership: The Effect of Residential Location

87,000 per million dollars of lending. If the expected losses from such a program were not priced at all, the losses from default alone could exceed 10% of the funds made available for loans.

Unobserved heterogeneity in Models of Competing Mortgage Termination Risks

Since January of 2005, 250 building projects in the City of Singapore have been awarded the Green Mark for energy efficiency and sustainability. This paper analyzes the private returns to these investments, evaluating the premium in asset values they command in the market. We analyse almost 37,000 transactions in the Singapore housing market to estimate the economic impact of the Green Mark program on Singapores residential sector. We adopt a two-stage research design; in the first stage, a hedonic pricing model is estimated based on transactions involving green and non-green residential units in 697 individual projects or estates. In the second stage, the fixed effects estimated for each project are regressed on the location attributes of the projects, as well as control variables for a Green Mark rating. Our results suggest that the economic returns to green building are substantial. This is one of the first analyses of the economics of green building in the residential sector, and the only one analysing property markets in Asia. Our results provide insight about the operation of the housing market in one country, but the policy implications about the economic returns to sustainable investments in the property market may have broader applications for emerging markets in Asia.

A Dynamic Analysis of Fixed- and Adjustable-Rate Mortgage Terminations*

The rate of homeownership among African-American households is considerably lower than white households in American urban areas. This paper examines whether racial differneces in residential location outcomes are among the factors that contribute to the large racial differences in homeownership rates in major US metropolitan areas. Based on the 1985 metropolitan sample of the American Housing Survey for Philadelphia, the paper does not find any evidence that existing racial differences in residential location in Philadelphia decrease the homeownership rate among African Americans. Rather, the empirical evidence suggests that African-American residential location outcomes are associated with lower than expected racial differences in homeownership. Therefore, after controlling for neighborhood, racial differences in homeownership are larger than originally believed, and the ability of racial differences in endowments to explain hoeownership differences is more limited.

Risk-Based Pricing and the Enhancement of Mortgage Credit Availability among Underserved and Higher Credit-Risk Populations

This article extends unobserved heterogeneity to the multinomial logit (MNL) model framework in the context of mortgages terminated by refinance, move or default. It tests for the importance of unobserved heterogeneity when borrower characteristics such as income, age and credit score are included to capture lender-observed heterogeneity. It does this by comparing the proportional hazard model to MNL with and without mass-point estimates of unobserved heterogeneous groups of borrowers. The mass-point mixed hazard (MMH) model yields larger and more significant coefficients for several important variables in the move model, whereas the MNL model without unobserved heterogeneity performs well with the refinance estimates. The MMH clearly dominates the alternative models in sample and out of sample. However, it is sometimes difficult to obtain convergence for the models estimated jointly with mass points.

A Proportional Hazards Model of Commercial Mortgage Default with Originator Bias

This paper provides a side-by-side comparison of loan-level statistical models for fixed- and adjustable-rate mortgages. Multinomial logit models for quarterly conditional probabilities of default and prepayment are estimated. We find that the estimated impacts of embedded option values for prepayment and default are generally quite similar across both FRM and ARM loans, providing additional empirical support for the basic predictions of the options theory. We also find that differences in estimates of conditional probabilities of prepayment and default associated with mortgage age, origination period, original LTV, and relative loan size, indicate the continued significance of these other economic and demographic factors for empirical models of mortgage terminations.

Asymmetric Information, Adverse Selection, and the Pricing of CMBS

While prior analyses have provided substantial evidence of elevated default probabilities among mortgages originated to lower income, less credit worthy and minority borrowers, those risks may be offset by the reduced prepayment probabilities of those loans. To the investor in FHA-insured mortgages, such offsets could serve to appreciably reduce total loan termination risk and in so doing boost investment returns. To assess those effects, this paper employs micro-data from the FHA to estimate an option-based hazard model of the competing risks of mortgage termination. The empirical model derives from option theory and includes controls for mortgage put and call options, borrower credit worthiness, and a large number of other contemporaneous and time-invariant indicators of borrower, loan, and locational risk. Results of the analysis indicate that the elevated default probabilities of loans originated to lower credit quality and minority borrowers are more than offset by their reduced prepayment risks. The estimated cumulative probability of mortgage termination among lower credit-quality and African-American borrowers is only about three-fourths that of higher credit-quality and white borrowers, respectively. Recognition of this mortgage performance advantage should enhance the willingness of lenders and investors to originate and acquire such loans and at more competitive pricing. Findings suggest that the extension of mortgage credit to less credit-worthy and underserved borrowers, in a manner consistent with their lower termination risks, would serve to advance both their homeownership opportunities and related federal housing policy objectives.

Optimal Put Exercise: An Empirical Examination of Conditions for Mortgage Foreclosure

A proportional hazards model with competing risks is specified and is extended to correct for the possibility of originator bias. The model is used to examine the ability of option-theoretic models of mortgage pricing to forecast commercial mortgage defaults. Among the findings, those especially of interest include the influence of contemporaneous loan-to-value and debt-service-coverage ratios on commercial mortgage default probabilities. The paper also finds that option-theoretic models of mortgage pricing are quite capable of producing default estimates that fit the actual default rates well, especially when the model is corrected for originator bias.