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.     

Competing Risks of Mortgage Termination: Who Refinances,Who Moves,and Who Defaults?

The Journal of Real Estate Finance and Economics - Why, when, and who terminates their mortgages? The primary reasons for mortgage termination are refinancing, selling of the property, and default....     

Modeling conventional residential mortgage refinancings

This article models fixed-rate mortgage refinancings and offers an empirical test of the model. The model relates the probability that a household prepays its residential mortgage to both financial and economic variables. The financial variables included in the model measure the value of the embedded call option present in conventional fixed-rate mortgage loans. The economic variables measure the household's propensity to prepay for housing consumption adjustment reasons. Our main empirical finding is that increased interst-rate volatility significantly decreases prepayment probability. In addition, we find some statistical evidence to support the hypothesis that prepayment rates increase with increases in household income, increases in household size, and vary by age of household head and regionally.     

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.     

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     

Anatomy of an ARM: The Interest-Rate Risk of Adjustable-Rate Mortgages

This article analyzes the dynamics of the commonly used indices for adjustable rate mortgages and systematically compares the effects of their time-series properties on the interest-rate sensitivity of adjustable-rate mortgages. Our ARM valuation methodology allows us simultaneously to capture the effects of index dynamics, discrete coupon adjustment, mortgage prepayment, and both lifetime and periodic caps and floors. We can, moreover, either calculate an optimal prepayment strategy for mortgage holders or use an empirical prepayment function. We find that the different dynamics of the major ARM indices lead to significant variation in the interest-rate sensitivities of loans based on different indices. We also find that changing assumptions about contract features, such as loan caps and coupon reset frequency, has a significant, and in some cases unexpected, impact on our results.     

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.     

Applied Nonparametric Regression Techniques: Estimating Prepayments on Fixed-Rate Mortgage-Backed Securities

We assess nonparametric kernel-density regression as a technique for estimating mortgage loan prepayments—one of the key components in pricing highly volatile mortgage-backed securities and their derivatives. The highly nonlinear and so-called irrational behavior of the prepayment function lends itself well to an estimator that is free of both functional and distributional assumptions. The technique is shown to exhibit superior out-of-sample predictive ability compared to both proportional-hazards and proprietary-practitioner models. Moreover, the best kernel model provides this improved predictive power utilizing a more parsimonious specification in terms of both data and covariates. We conclude that the technique may prove useful in other financial modeling applications, such as default modeling, and other derivative pricing problems where highly nonlinear relationships and optionality exist.     

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 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.     

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.     

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.     

Valuation of Residential Mortgage-Backed Securities with Default Risk Using an Intensity-Based Approach

This paper develops a valuation model for fixed-rate mortgages, mortgage pools, and residential mortgage-backed securities (RMBS's) using an intensity-based approach. This model incorporates full prepayment, partial prepayment, and default in valuing a mortgage. Full prepayment is further classified into “refinancing” and “sale of a house” depending on the reason. The time of occurrence of each of these three types of prepayment and default is modeled as the first jump time of a Cox process. Under these conditions, the valuation formula for a mortgage as well as a partial differential equation (PDE) that the mortgage value satisfies is provided. As for implementation of the model, the short-term riskless interest rate and the house price are adopted as state variables. Each intensity process is specified in a manner that allows a jump in intensity depending on the state variables and the borrower's incentive for prepayment or default. Through such specifications, it is shown that our model has characteristics similar to some structural models in previous literature. As for the numerical method for valuation, we propose a simple backward induction technique on a tree instead of the commonly used Monte Carlo method. Additionally, the method for estimating the model is discussed, and the results of numerical simulations are reported.This paper represents the view of the author and does note necessarily the views of the Mitsubishi UFJ Securities Co., Ltd. or members of its staff.     

The timing of prepayment: A theoretical analysis

This article develops the analytical methods necessary to determine the prepayment patterns of a mortgage contract. The most obvious measure of how many years a mortgage is likely to last is the expected time to termination. It is this measure that we most fully explore. However, since the method employed is able to characterize the probability of prepayment in any given time period, the means is provided to determine any measure of the time to termination.     

How Much Are Car Purchases Driven by Home Equity Withdrawal?

Previous research indicates that changes in housing wealth affect consumer spending on cars. We find that home equity extraction plays only a small role in this relationship. Consumers rarely use funds from equity extraction to purchase a car directly, even during the mid‐2000s’ housing boom; this finding holds across three nationally representative household surveys. We find in credit bureau data that equity extraction does lead to a statistically significant increase in auto loan originations, consistent with equity extraction easing borrowing constraints in the auto loan market. This channel, though, accounts for only a tiny share of overall car purchases.     

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.     

Mortgage Refinancing,Adverse Selection,and FHA's Streamline Program

When interest rates decline, borrowers whose houses have appreciated significantly refinance out of FHA, while those whose houses have not do not. We provide evidence of the negative impact of regular (nonstreamline) refinancing in the mid-1980s on the average quality of FHA's surviving business. We demonstrate this adverse selection both informally and econometrically. We also argue that the sharp reduction in the cost of streamline refinancing (limited documentation, no required appraisal, and so on) in FHA's streamline refinance program in 1992 likely reduced the level of adverse selection in the FHA portfolio during the 1993 to 1994 refinancing boom, and we provide quantitative estimates of the resultant reduction in claim rates. While this reduction in cost almost certainly increased the financial viability of FHA during the middle 1990s, it may not in the long run.