Commercial Mortgage-Backed Securities: Prepayment and Default

One of the major developments in real estate finance during the 1990s was the emergence of a viable market for commercial mortgage backed securities. The growth in this market has spurred greater interest in empirical and theoretical research on commercial mortgage default and prepayment. We employ a competing risks model to examine the default and prepayment behavior of commercial loans underlying CMBS deals. We find that changes in the yield curve have a direct impact on the probability of mortgage termination. Furthermore, we do not find any statistical relationship between LTV and prepayment or default.     

An Analysis of Mortgage Contracting: Prepayment Penalties and the Due-on-Sale Clause

The due-on-sale clause contained in most conventional home mortgage contracts is equivalent to a prepayment penalty equal to the difference between the face value and market value of the loan. We analyze a bilateral game with asymmetric information and show that the bank demands the full penalty unless the market value of the loan is sufficiently low. In that case, the bank demands a prepayment penalty which is independent of the market value of the loan in order to induce additional prepayments. We also demonstrate, by a risk-sharing argument, that the due-on-sale clause is optimal in some settings, even though it eliminates some beneficial home sales.     

Housing-Price Cycles and Prepayment Rates of U.S. Mortgage Pools

Empirical mortgage prepayment models generally have trouble explaining differences in mortgage-prepayment speeds among pools with similar interest rates on the underlying mortgages. In this article, we model some of the sources of termination heterogeneity across mortgage pools, particularly the role of regional variations in housing prices in generating atypical prepayment speeds. Using a sample of Freddie Mac mortgage pools from 1991 to 1998, we compare two classes of empirical models: a rational option-pricing model using a backward-solving pricing algorithm and an empirical hazard model. In both empirical estimation strategies, we find evidence that differences in house-price dynamics across regions are an important source of between-pool heterogeneity. This finding is then shown to be robust to alternative ways of parameterizing pool heterogeneity in mortgage termination models.     

Analyses of Mortgage-Backed Securities Based on Unobservable Prepayment Cost Processes

We propose a prepayment model of mortgage based on a structural approach in order to analyze prepayment risk of mortgage-backed securities (MBS). We introduce a continuous process named prepayment cost process. Specifically, each mortgager's prepayment time is defined by the first time when her or his prepayment cost process falls below zero, but prepayment cost processes are supposed to be unobservable in the market. We also introduce a risk unique to each loan pool of mortgages, called a loan pool risk (LPR), and we regard LPR as a systematic risk other than interest rate. Using the model, we discuss the conditional distribution of prepayment times and a risk-neutral valuation of pass-through MBS. It is shown that each mortgager's conditional non-prepayment probability and the posterior distribution of LPR play quite important roles in our study.This research is partially supported by Grant-in-Aid for Young Scientists (B) No. 16710108 from the Ministry of Education, Culture, Sports, Science and Technology.     

浮动利率房贷提前还款的损失度量

住房抵押贷款是银行一项重要业务和资产.随着利率的波动和其他因素的影响,借款人有可能提前还款从而影响银行的收益.准确地度量提前还款给银行带来的损失有助于商业银行更好地管理这类经营风险.在具有均值回复特性的随机市场利率和服从纯跳跃过程的浮动住房贷款利率条件下,以最常见的每月等本金还款方式为基础,根据对利率的预测,使用求期望的办法估算出银行房贷总收益的预期值,然后将该预期值折现到提前还款发生时刻,从而构造出借款人在合同期间提前偿还房贷给银行造成的利息损失度量模型.     

A Prepayment Model for the Japanese Mortgage Loan Market: Prepayment-Type-Specific Parametric Model Approach

This paper proposes a framework for construction of a prepayment model suitedto the Japanese mortgage loan market and assesses the validity of thisframework based on an empirical analysis using data from Japan. In thisframework, a model is constructed for each of three prepayment types, namely,`full prepayment', `partial prepayment', and `subrogation', using a parametricproportional hazards model, which was also employed by Schwartz and Torous(1989). Combining these three types of models allows one to take into accountthe effects of partial prepayments, which are frequently used in the Japanesemortgage market, and to simultaneously construct a model for both prepaymentand default. Time-dependent (path-dependent) covariates are introduced intothe model, which are estimated by the maximum likelihood method based on thefull likelihood that takes into account the time-dependence of the covariates.Results of the empirical analysis indicate that the hazard functions differsubstantially depending on the prepayment type. In addition, results indicatethat the fit of the model can be improved by the distinction of prepaymenttypes and the introduction of the market interest rates as path-dependentcovariates.     

A Closed Form Formula for Valuing Mortgages

We develop a closed form formula for the value of a fixed-rate residential mortgage that includes the provision that the borrower can prepay at any time with no penalty. The value of the mortgage equals the expectation, under the risk neutral probability measure, of the future cash flows. We model future cash flows by estimating an empirical model of prepayment behavior. A second change of measure leads to a closed form expression for the expectation. The closed form values explain most of the time series variation in MBS prices. The closed form formula significantly shortens the time to calculate mortgage values and durations and can be a useful tool for portfolio management and hedging.     

Valuation of Mortgage-Backed Securities Based upon a Structural Approach

This paper studies the valuation of mortgage-backed securities (MBS) based upon a structural approach of several risks involving the prepayment and/or default behavior of mortgagors. For the Kariya and Kobayashi (1999) model using a time-consuming Monte-Carlosimulation, we provide an alternative semi-analytic valuation methodology closely related to solving the (Volterra type) integral equation with respectto the first hitting time density for a curved/flat boundary; consequently that enables us to calculate the MBS price faster and more precisely. Next, to capture the path-dependent prepayment behavior of the interest ratemovements we give some prepayment models based upon a two-dimensional Markov process of the interest rate and its long-run average rate. Third, we study the simultaneous assessment issue of prepayment and defaultrisks, encountered in practice.Finally we discuss the calculation of the joint probability density ofmultiple first hitting times.     

Predicting Prepayment and Default Risks of Unsecured Consumer Loans in Online Lending

Online lending provides a means of fast financing for borrowers based on their creditworthiness. However, borrowers may undermine this agreement due to early repayment or default, which are two major concerns for the platform and lenders, since both affect the profitability of a loan. While default risk is frequently focused on credit scoring literature, prepayment has received much less attention, despite a higher prepayment rate being observed in online lending when compared with default. This article uses multivariate logistic regression to predict the probability of both the underlying prepayment and default risks. Real consumer lending data of 140,605 unsecured loans provides evidence that these two events have their own distinct patterns. We consider systemic risk by incorporating macroeconomic factors in modeling and address the influence of economic conditions, which are lessons learnt from the last financial crisis. The out-of-sample validation has shown that both prepayment and default can be accurately predicted. This article highlights the necessity of regulations on prepayment given the fast growing online lending market.     

Mortgage prepayment with an uncertain holding period

A discrete-time-option pricing model is developed to value a mortgage and its embedded prepayment option when the effective life of the mortgage is a random variable with a probability distribution of known parameters. The model can be applied when the borrower's ex ante expectation of his tenure follows any probability distribution bounded to the left at zero. The Gamma distribution is used to illustrate the model.The pricing model is further applied to determine the conditions under which financially motivated prepayment is optimal. The results show that the certainty model understates the Interest Rate Differential needed to justify prepayment (IRD) for short Expected Holding Period (EHP) borrowers and overstates the IRD for long EHP borrowers. When the EHP is relatively long, the certainty model provides relatively good estimates of IRD during the beginning years of the mortgage life. Under most other conditions, the estimates of the certainty holding period model are biased.     

Valuation of Mortgage Servicing Rights with Foreclosure Delay and Forbearance Allowed

We develop a bivariate binomial model to price Mortgage Servicing Rights (MSRs). Our model is an improvement over previous MSR pricing models by explicitly incorporating the realistic assumptions that there are additional costs involved in servicing delinquent loans. In addition to the Hilliard et al. mortgage-pricing tree, we extend additional sub-branches to model the borrower's decision of prepayment, cure, and foreclosure after a loan becomes delinquent. We then investigate how the value of the Mortgage Servicing Right varies with interest rate volatility, house price volatility, delinquency options, deficiency judgments, default penalties, forbearance periods, and speed of adjustments factors. JEL Classification: C15, G21     

Household Income, Termination Risk and Mortgage Pricing

The premium embedded in home mortgage loans to compensate investors for their exposure to prepayment risk is a significant component of the cost of home mortgage lending. Moreover, there is some reason to believe that prepayment risk may be lower for loans to lower-income housing borrowers, especially those that are first-time home owners. If so, investor recognition of this advantage should facilitate greater willingness to acquire portfolios of lower-income housing loans, and encourage more competitive pricing in this segment of the market. This study investigates the possibility of differential mortgage prepayment behavior between lower-income home owners and non-low income home owners. The investigation relies on samples of the American Housing Survey spanning ten years of experience from 1985 to 1995. We find no significant difference between the termination or refinancing behavior of non-low income and low-income households. This result is robust to a number of alternative specifications such as restricting the low-income test group to non-moving households and to first-time owners. The same conclusions are derived from both aggregate prepayment rates and from analysis of individual household prepayment behavior.     

美国次级住房抵押贷款危机的原因及影响

需求大于供给导致美国次级住房抵押贷款快速增长,"贷款—分散"模式链条上各主体的收益激励结构和次级贷款品种设计导致的次级债市场扭曲繁荣,进而导致次级债危机。次级债危机将在较长的时间里困扰美国经济,但是从次级贷款支持证券及其衍生产品的分档设计可以预测该市场的绝大部分投资者不会因次级债危机而受到损失。     

商业银行住房抵押贷款证券化可行性研究

住房抵押贷款证券化是1970年代在美国开始兴起的一种新兴金融工具,其意义不仅在于使更多的居民买得起住房而推动房地产业的发展,同时能降低金融风险,为资本市场提供一种新型的金融工具而推动金融市场的稳健发展.在我国现行资本条件下,住房抵押贷款证券化亦具有可行性.     

Valuing Mortgage Insurance Contracts in Emerging Market Economies

We develop a new option-based method for the valuation of mortgage insurance contracts in closed form in an economy where agents are risk neutral. While the proposed valuation method is general and can be used in any market, it may be particularly useful in emerging market economies where other existing methods may be either inappropriate or are too difficult to implement because of the lack of relevant data. As an application, we price a typical Serbian government-backed mortgage insurance contract.     

An Early Assessment of Residential Mortgage Performance in China

The residential mortgage market becomes a financial engine for the booming residential housing development and sustained economic growth in China. Our study provides the first rigorous empirical analysis on the earlier performance of residential mortgage market in China based on a unique micro dataset of mortgage loan history collected from a major residential mortgage lender in China. We found that while the option theory fails to explain prepayment and default behavior in the residential mortgage market in China, other non-option theory related financial economic factors play major roles in determining the prepayment and default risks in China. We also found that borrower’s characteristics are significant in determining prepayment behavior, hence may be used as an effective tool for screening potential high risk borrowers in the loan origination process. Adopting a risk-based pricing in residential mortgage lending in China can improve the efficiency of the market, and enhance the credit availability to the most needed households, i.e., the younger households, blue-collar workers, lower income households, and help them become homeowners.     

Mortgage Refinancing Activity: An Explanation [1990–2001]

Mortgage refinancing activity reached unprecedented high levels during 1990–2001. Using GARCH to control for heteroskedasticity and separating the data into regimes to control for potential structural changes over time, we estimate a model explaining changes in mortgage refinancing activity over the period studied. We find changes in refinancing activity to be negatively related to current as well as past changes in the 30-year mortgage rate with a declining significant lag over time. Similarly, there is a significant lagged dependent variable with a declining lag. Moreover, mortgage refinancing activity is a substitute for other investments during certain regimes. These results offer evidence that home owners cash out the mortgage for other investments. The lags suggest that the process is delayed for a variety of reasons. The declining lag signals a faster response by consumers. The reasons for a faster response include a consumer perception that interest rates have “bottomed out,” the presence of an increase in consumer sophistication, and improvements in technology and market coordination that facilitate and reduce the cost of the refinancing process.     

个人住房抵押贷款违约风险跃迁概率研究

巴塞尔新资本协议提出针对个人住房抵押贷款可采用内部评级高级法评估其风险,在满足某些最低条件和披露要求的前提下,商业银行可根据自己对个人住房抵押贷款违约概率、违约损失率、违约风险暴露和期限等要素的估计值确定相应的资本要求。本文提出将风险跃迁概率引入到对个人住房抵押贷款提前还款-违约概率的定量估计中。借助逻辑斯特模型,本文将这一概念实际运用到对个人住房抵押贷款微观数据的分析当中,得到的实证研究结论包括借款人历史还款状态可以作为表征其未来还款状态的重要指标,贷龄与借款人还款状态的跃迁概率显著相关等。     

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.     

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

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.