Frictions, Heterogeneity and Optimality in Mortgage Modeling

The purpose of this article is to provide a unified framework for incorporating frictions into a theoretical options-pricing model (OPM) for mortgages. This article presents formulation for a frictions-adjustable mortgage model that integrates borrower heterogeneity while simultaneously preserving prepayment and default financial decisions. Our model demonstrates the flexibility of the OPM by simulating separate and concurrent effects of three categories of frictions on the mortgage and mortgage components. Researchers can use our example formulation to determine the effects of specific borrower characteristics on mortgage values without destroying the options theoretic framework.     

The pricing of adjustable rate mortgage contracts

This article analyzes the structure of ARM contracts and the pricing of their component features, based on the view of ARMs as a complex bundle. Unlike previous studies, which have generally relied on option-based simulation techniques, our analysis specifies a microeconomic model of the lender as a profit-maximizer which is then tested using firm-specific data. The empirical results, which are consistent with the microeconomic model, indicate that the lender acts as a profit-maximizing firm in pricing the features of the ARM contract. Furthermore, the results suggest that while the interest-rate cap parameters dominate in the pricing of ARMs, other features are also important. Thus, theoretical and empirical ARM pricing models should embrace other features of the contract besides the cap parameters.     

Termination of distressed residential mortgages: An empirical analysis

A sample of 209 distressed mortgages is used to analyze the terminations of distressed mortgages. An option-based model is compared to a traditional default model. Results show that the traditional model is statistically superior. However, the model's ability to identify a default is similar to that of the simpler option-based model. Alternative measures of borrower's equity are compared. Measuring borrower's equity using total debt more accurately explains default than using either the mortgage balance or the mortgage value.     

Subprime Lenders and Mortgage Market Completion

Without a subprime market, some borrowers by virtue of poor credit history, unstable income, and other characteristics are unable to qualify for a mortgage. With a subprime market, there is a more complete credit supply schedule with the market pricing for poorer credit quality in the mortgage rate. By completing the capital market, subprime lenders reduce borrowing constraints. The result is a social welfare gain. Low-credit applicants otherwise denied funding are able to qualify by paying higher interest rates in exchange for offering more equity or lower loan-to-value ratios. This prediction is consistent with the subprime applicants financing or refinancing their mortgages at relatively low loan-to-value ratios.     

The Subprime Panic*

Understanding the ongoing credit crisis or panic requires understanding the designs of a number of interlinked securities, special purpose vehicles, and derivatives, all related to subprime mortgages. I describe the relevant securities, derivatives, and vehicles to show: (1) how the chain of interlinked securities was sensitive to house prices; (2) how asymmetric information was created via complexity; (3) how the risk was spread in an opaque way; and (4) how trade in the ABX indices (linked to subprime bonds) allowed information to be aggregated and revealed. These details are at the heart of the origin of the Panic of 2007. The events of the panic are described.     

A Reconsideration of the Jumbo/Non-Jumbo Mortgage Rate Differential

Consistent with a series of recent papers, the interest-rate differential between mortgages eligible for purchase based on loan size by Fannie Mae and Freddie Mac and larger loans is estimated to be 22 basis points over the 1986–2000 period. This differential averaged 19 basis points for the 1996–2000 period. Other significant effects include: loans slightly above the conforming loan limit and originated late in a calendar year often have a lower rate that nearly fully anticipates their likely characterization as a non-jumbo loan after the conforming loan limit is indexed effective each January; loan-to-value ratios affect jumbo loan rates much more than they affect non-jumbo loan rates; loans located in non-metropolitan areas have a 3 basis point differential versus loans in metropolitan areas that is surprisingly small given the likely higher cost to service non-metropolitan loans and the higher degree of uncertainty about non-metropolitan collateral values; and estimated regional mortgage rate differentials have narrowed through time.     

Legal Restrictions in Personal Loan Markets

This study examines the pricing of personal loans in the form of second mortgages to determine whether state-specific default laws have an effect on the availability and cost of that debt. We examine the pricing of loans to higher risk borrowers and whether borrowers in states that limit lender ability to seek default remedies pay higher credit costs. Our results indicate that, for the most part, lenders rationally price loans to higher risk borrowers. However, when we focus on borrowers with low credit scores, the results indicate that mean actual loan rates are higher than those predicted by our model. The results also indicate that state-specific default laws have an effect on the price of credit. Finally, the results show that there is a greater degree of error in the pricing of second mortgage loans to borrowers with low credit scores than to borrowers with high credit scores.     

An Improved Fixed-Rate Mortgage Valuation Methodology with Interacting Prepayment and Default Options

This paper considers in detail a realistic mortgage valuation model (including the potential for early prepayment and the risk of default), based on stochastic house-price and interest-rate models. As well as the development of a highly accurate numerical scheme to tackle the resulting partial differential equations, this paper also exploits singular perturbation theory (a mathematically rigorous procedure, based on the idea of the smallness of the volatilities), whereby mortgage valuation can be accurately approximated by very simple closed-form solutions. Determination of equilibrium contract rates, previously requiring many computational hours is reduced to just a few seconds, rendering this a highly useful portfolio management tool; these approximations compare favorably with the full numerical solutions. The method is of wide applicability in US or other mortgage markets and is demonstrated for UK fixed-rate mortgages, including insurance and coinsurance.     

House arrest: the effects of underwater and low-equity mortgages on small business failure and mobility

This paper studies the effects of the recent housing crash on small business survival and household geographic mobility. Although a number of other works have studied these issues, our analysis differs from these because we do not focus only on underwater mortgages (less than 0% home equity), but also those slightly above water (0-10% equity). Homeowners with little or no equity face considerable constraints regarding moving, starting a business or keeping a current business open. They are more like underwater homeowners, but they differ enough to deserve a separate categorization in comparative studies, rather than being conflated with all other homeowners that have positive equity. We use the Federal Reserve’s Survey of Consumer Finances panel data for 2007 and 2009, which allows us to track the exact same households during this critical time in the housing crisis.     

住房抵押贷款的违约风险分析

本文运用期权数值方法分析住房抵押贷款借款者的违约行为,主要是分析抵押贷款违约期权的最优实施边界。这使得我们能够解释哪些房价和利率组合会引发借款者违约以及未来的违约概率。我们发现导致违约的房产价格高度依赖于同期市场利率,而且违约与贷款类型高度相关。我们考察了次优出售和再融资的情形,还考察了借款者面临违约声誉损失的情形,结果表明期权数值方法是稳健可靠的。本文的分析还使我们对美国次贷危机有更为客观理性的认识。