The probability of prepayment

Prepayment is a risk of holding a mortgage or derivative security. Incorrect pricing of prepayment risk leads to increased volatility and uncertainty in mortgage security markets. This article prices prepayment risk within an underlying callable bonds model. To price mortgages accurately, a probability of prepayment is required. A mortgage is a callable bond with a package of an option to prepay currently and a sequence of options to prepay up to the date of maturity. This sequence is summarized by a compound option. The probability of prepayment is determined by the prices of the current call and this compound option. These option prices depend on market interest rates and age, and on the contract terms of the originated mortgage.     

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.     

The prepayment option on mortgage securities: A random coefficient approach

Using the Swamy (1970) model for pooled data and a Hildreth and Houck (1968) model for individual securities, this article investigates whether the parameters describing the prepayment behavior of the fixed-rate debt underlying mortgage-backed securities are better estimated as a stochastic behavior. Empirical results indicate that differences between securities are random. The Hildreth and Houck model yields additional information on randomness over time. The use of the aggregate data to estimate prepayment of individual securities, as opposed to use of the prepayment history of the individual security, may yield more reliable results.     

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.     

A note on refinancing costs,prepayment assumptions,and the value of mortgage-backed securities

This article analyzes the effect and timing of the FHA's streamline refinance program on the value of GNMA 15s. The program announced in March 1989 reduced the refinancing costs for those mortgages of 15 percent and above. The program is expected to reduce the value of GNMA's. The authors find a reduction of .47 to 3.40 points in the value of GNMA 15s during the 3-week to 13-week period following the announcement of the plan. The drop in value translates into a wealth loss for GNMA 15 holders of about $20 million over this time.     

住房贷款二级市场的经验教训与政策建议

本文结合主要国家实践,分析了一国住房贷款二级市场的驱动因素、成功要素及其主要的经济金融功能;在总结次贷危机带来的市场发展启示的基础上,探讨了未来房贷二级市场的主流模式。鉴于房贷二级市场对中国经济金融长期稳定发展具有一定的重要意义,文章进一步探讨了我国建立证券化房贷二级市场的模式选择与发展对策。     

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.     

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.     

Interest-only and principal-only mortgage strips as interest-rate contingent claims

Interest-only (IO) and principal-only (PO) mortgage strips are valued in a stochastic interest-rate environment. The prepayment rate of the underlying mortgages is affected by two considerations not present in the pure financially rational model: (1) The property owner's holding period is assumed to follow a Gamma distribution, resulting in the possibility of prepayment due to the sale of the property (i.e., prepayment that is too early based on market interest rates); and (2) borrowers are assumed to face heterogeneous transaction costs related to refinancing the existing mortgage, and delay refinancing when market conditions make it optimal to do so (refinancing too late). Properties of IO/PO strips are identified by the finite difference method.     

Valuing Fixed-Income Options and Mortgage-Backed Securities with Alternative Term Structure Models

To value mortgage-backed securities and options on fixed-income securities, it is necessary to make assumptions regarding the term structure of interest rates. We assume that the multi-factor fixed parameter term structure model accurately represents the actual term structure of interest rates, and that the values of mortgage-backed securities and discount bond options derived from such a term structure model are correct. Differences in the prices of interest rate derivative securities based on single-factor term structure models are therefore due to pricing bias resulting from the term structure model. The price biases that result from the use of single-factor models are compared and attributed to differences in the underlying models and implications for the selection of alternative term structure models are considered.     

Explicit tests of contingent claims models of mortgage default

This paper provides explicit and powerful tests of contingent claims approaches to modeling mortgage default. We investigate a model of frictionless default (i.e., one in which transactions costs, reputation costs, and moving costs play no role) and analyze its implications-the relationship between equity and default, the timing of default, its dependence upon initial conditions, and the severity of losses. Absent transactions costs and other market imperfections, economic theory makes well-defined predictions about these various outcomes.The empirical analysis is based upon two particularly rich bodies of micro data: one indicating the default and loss experience of all mortgages purchased by the Federal Home Mortgage Corporation (Freddie Mac), and a large sample of all repeat sales of single family houses whose mortgages were purchased by Freddie Mac since 1976.     

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.     

Optimal mortgage contracts with time-inconsistent preferences

This paper integrates a time-inconsistent preference into the mortgage design problem and studies the corresponding effects on the optimal contract. By assuming exogenous time inconsistency in borrower's preference, we find that the time-inconsistent preference increases the loss in the lender's value and the compensation boundary. We implement the optimal contract using standard securities and option adjustable-rate mortgages (ARMs). The findings show that the time-inconsistent preference increases the default rate, and relative to standard securities, option ARMs increase the total debt capacity, but the borrower's time inconsistency can lead to sudden jumps in the total debt capacity. We also consider the endogenous time inconsistency in the borrower's preference and derive the corresponding mortgage contract; we find that a lender can perfectly offset the effect of a borrower's time inconsistency on the value function and compensation strategy. The liquidation boundary at the low interest rate varies with the degree of time inconsistency, explaining the heterogeneity in mortgage default behaviors observed in practice.     

美国资产支持证券市场结构与次按危机解析

美国次按危机不仅给世界多家金融巨擎造成巨大损失,甚至险些在世界范围内酿成了一场全面的流动性危机。文章从信贷资产证券化发起机构、CDO发起流程、信用评级的制定及下调原理,流动性危机的成因这一逻辑顺序全面回顾了美国资产支持证券市场的运作机制以及次贷危机产生的根源,以期为深入研究次级债问题提供参考。     

美国次级抵押贷款危机对银行业改进的启示

美国次贷危机促使银行业积极应对房地产周期性调整,改进风险管理框架,进一步加强表外关联机构管理,优化区域布局.美国次贷危机对于中国银行业的警示作用大于直接影响.中国商业银行应当认识到房价快速上涨会掩盖大量的风险,应当重视房地产周期性调整风险,尤其是房地产信贷业务的信用风险、操作风险、政策性风险以及突发性事件引发的系统性风险,谨慎推进金融工具创新,专注于核心业务增长,优化区域布局,提高中国银行业的整体经营水平及抵御国内经济周期的实力,完善金融监管协调机制.     

Home mortgage debt financing of nonhousing investments

Home mortgage debt is decomposed into a component that represents debt demand, derived from housing demand and a residual excess demand. This excess demand derives principally from the demand for nonhousing assets. An empirical model of the determinants of the demand for excess debt is specified and estimated using databases from the 1983 and 1986 Surveys of Consumer Finance. The estimations focus on evidence of linkages between debt demand and household preferences for illiquid risky assets, and on the substitutability of personal debt for mortgage debt. Positive linkages are found between household choices of investments in vacation homes, investment real estate, and closely held business and the demand for excess debt. However, personal debt and mortgage debt appear to have largely separate financing roles.     

Subprime mortgage funding and liquidity risk

In this article, we use actuarial methods to solve a nonlinear stochastic optimal liquidity risk management problem for subprime originators with deposit inflow rates and marketable securities allocation as controls. The main objective is to minimize liquidity risk in the form of funding and credit crunch risk in an incomplete market. In order to accomplish this, we construct a stochastic model that incorporates originator mortgage and deposit reference processes. Finally, numerical examples that illustrate the main modeling and optimization features of the article are provided.     

The role of prepayment penalties in mortgage loans

We study the effect of mortgage prepayment penalties on borrowers’ prepayments and delinquencies by exploiting a 2007 reform in Italy that reduced penalties on outstanding mortgages and banned penalties on newly-issued mortgages. Using a unique dataset of mortgages issued by a large Italian lender, we provide evidence that: 1) before the reform, mortgages issued to riskier borrowers included larger penalties; 2) higher prepayment penalties decreased borrowers’ prepayments; and 3) higher prepayment penalties did not affect borrowers’ delinquencies. Moreover, we find suggestive evidence that prepayment penalties affected mortgage pricing, as well as prepayments and delinquencies through borrowers’ mortgage selection at origination, most notably for riskier borrowers.