Microfoundations of a mortgage prepayment function

This article focuses on the following question: how much of an interest rate decline is needed to justify refinancing a typical home mortgage? Modern option pricing theory is used to answer the question; this theory indicates that the answer depends upon several factors, which include the volatility of interest rates and the expected holding period of the borrower. The analysis suggests that the commonly espoused “rule of thumb” refinance if the interest rate declines by 200 basis points — is a fair approximation to the more precisely derived differential for many households. We also construct the prepayment behavior of a pool of mortgages in which the expected holding periods of the borrowers in the pool vary. The prepayment behavior of this simulated pool is used to generate a series of empirically testable hypotheses regarding the likely shape of an actual prepayment function and its determinants. Finally, actual prepayment data are used to estimate a hazard function that explains prepayment behavior. We find that the estimated model understates prepayment behavior relative to that predicted by the simulation model, which suggests that the simple option pricing model is not adequate to explain aggregate prepayment behavior.     

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.     

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.     

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.     

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.     

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....     

Housing and the mortgage securities markets: Review,outlook, and policy recommendations

During the 1980s, strong demographic demand for housing created a bulging need for mortgage credit. The mortgage market has creatively accommodated this need through extensive securitization of residential mortgages. This process greatly facilitated the financing of housing demand. During this decade, however, the scheme of funding long-term mortgages with short-term deposits bankrupted savings institutions. A gigantic federal bailout for thrifts was finally required. In the 1990s, the weakening demographics and the resulting reduction in the demand for mortgage credit afford the federal government opportunities to reformulate its housing policies in terms of limiting federal insurance on consumer deposits, phasing out income tax deductibility of mortgage interest, and ensuring capital adequacy at federally sponsored credit agencies.     

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.     

Returns to scale at large banks in the US: A random coefficient stochastic frontier approach

This paper investigates the returns to scale of large banks in the US over the period 1997–2010. This investigation is performed by estimating a random coefficient stochastic distance frontier model in the spirit of Tsionas (2002) and Greene (2005, 2008). The primary advantage of this model is that its coefficients can vary across banks, thereby allowing for unobserved technology heterogeneity among large banks in the US We find that failure to consider unobserved technology heterogeneity results in a misleading ranking of banks and mismeasured returns to scale. Our results show that the majority of large banks in the US exhibit constant returns to scale. In addition, our results suggest that banks of the same size can have different levels of returns to scale and there is no clear pattern among large banks in the US concerning the relationship between asset size and returns to scale, due to the presence of technology heterogeneity.     

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.     

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.     

Binomial option pricing with stochastic parameters: A beta distribution approach

This research extends the binomial option-pricing model of Cox, Ross, and Rubinstein (1979) and Rendleman and Barter (1979) to the case where the up and down percentage changes of stock prices are stochastic. Assuming stochastic parameters in the discrete-time binomial option pricing is analogous to assuming stochastic volatility in the continuous-time option pricing. By assuming that the up and down parameters are independent random variables following beta distributions, we are able to derive a closed-form solution to this stochastic discrete-time option pricing. We also derive an upper and a lower bounds of the option price.     

The effect of large investors on asset quality: Evidence from subprime mortgage securities

Fannie Mae and Freddie Mac (the GSEs), the dominant investors in subprime mortgage-backed securities before the 2008 crisis, substantively affected collateral composition in this market. Mortgages included in securities designed for the GSEs performed better than those backing other securities in the same deals, holding observable risk constant. Consistent with the transmission of private information, these effects are concentrated in low-documentation loans and for issuers that were highly dependent on the GSEs and were corporate affiliates of the mortgage originators. Additional analysis of yield spreads shows that these performance differences were not reflected in prices.     

The information content of three credit ratings: the case of European residential mortgage-backed securities

We assess the information content of three credit ratings for tranches of newly issued European residential mortgage-backed securities. We find that tranches rated by three credit rating agencies where the rating by Standard & Poor's (S&P's) Ratings Service or Fitch is inferior to Moody's lead to higher funding costs and reflects what we refer to as rating risk. Our results suggest that market participants do not view credit ratings by Fitch and S&P's as redundant despite the fact that both employ the same rating approach.     

Putting the squeeze on a market for lemons: Government-sponsored mortgage securitization

Lenders either sell or obtain insurance for many of the mortgages they originate to reduce credit risk and enhance liquidity. An overwhelming majority of the mortgages sold are purchased by government-sponsored enterprises. The prevailing view is that government-sponsorship of mortgage securitization causes mortgage rates to be lower than they would otherwise be. Using a model that incorporates asymmetric information and adverse selection, we provide an example in which government-sponsored mortgage securitization raises the mortgage rate.The analysis and conclusions set forth are our own and do not indicate concurrence by members of the Federal Reserve Research stafls, by the Board of Governors, or by the Federal Reserve Banks. We wish to thank Mark Fisher for his Mathematica expertise. All errors are ours exclusively.     

The impact of option introduction on the conditional return distribution of underlying securities

This paper combines several interesting econometric techniques to examine changes in the conditional return distribution of security returns following option introduction. An EGARCH model is used to characterize the return generating process. An intervention analysis is performed to determine whether the parameters of the EGARCH model shift following initial options listing. This paper finds that the conditional distribution of security returns is unaffected by option introduction. Estimation of a transfer function-noise model also shows that option introduction has no effect on conditional volatility.     

The effect of mortgage form on borrower interest rate risk: A portfolio theory approach

The problems faced by U.S. regulatory authorities in controlling residential housing cycles have resulted in a continuing search for methods of reducing the volatility of housing construction. One of the most widely discussed methods of decreasing volatility in mortgage credit is the variable rate mortgage (VRM) whose interest rate is linked to some interest rate index. In this paper we employ a portfolio theory approach to examine the relative riskiness of the VRM and fixed rate mortgage (FRM) for borrower and lender. As expected, we find that relative riskiness depends on the composition of the borrower/lender portfolio of assets and liabilities.     

Loss coverage and stress testing mortgage portfolios: A non-parametric approach

This paper outlines the development of a practical approach to simulating a credit loss distribution function and to implementing a stress test exercise focusing on the entire Spanish mortgage portfolio. Specifically, we determine, via regression model, the main factors that explain why households fail to meet their mortgage payment commitments. This allows us to assign individual borrowers’ PDs and to estimate a rating system for the mortgage portfolio. Then, we simulate the empirical distribution function of mortgage loss rates using a Monte-Carlo resampling method, and compare the loss rates from this function with those provided by the Basel II IRB formulas. Finally, we assess, by running a stress exercise, the ability of banks to withstand certain adverse situations. The main result from this exercise is that, in general terms, Basel II IRB regulatory loss coverage offers fairly adequate protection for banks.     

Economic volatility and financial markets: The case of mortgage‐backed securities

The volatility of aggregate economic activity in the United States decreased markedly in the mid‐eighties. The decrease involved several components of GDP and has been linked to a more stable economic environment, identified by smaller shocks, more effective policy, and a diverse set of innovations in technology as well as financial markets. We study one such financial innovation, and document a negative relation between the rapid growth of mortgage‐backed securities and the volatility of GDP and some of its components from the mid‐1970s to the late 1990s. We also document that this relation changed sign, from negative to positive, in the early 2000s.