Prepayment Model Research Articles

An ARMs Prepayment Model

This research provides evidence that a parsimonious prepayment speed model, using publicly available resources, can reasonably project prepayment speeds for single-family one-year Fannie Mae ARMs. Two incentives to refinance appear to be the two strongest predictors of projected prepayment speeds for the 1997–2001 period. A 100 basis point increase in the ARM-to-ARM incentive to refinance variable increased prepayment rates by 2.8%, holding other model variables constant. A 100 bp increase in the incentive to refinance from an adjustable-rate mortgage to a fixed-rate mortgage increased the prepayment rate of Fannie Mae-issued single-family ARMs by 2.3%. A limited approach to modeling adjustable-rate mortgages may thus be a cost-effective alternative to costlier and more sophisticated models.

Implied Mortgage Refinancing Thresholds

The optimal prepayment model asserts that rational homeowners would refinance if they can reduce the current value of their liabilities by an amount greater than the refinancing threshold, defined as the cost of carrying the transaction plus the time value of the embedded call option. To compute the notional value of the refinancing threshold, researchs have traditionally relied on a discrete option-pricing model. Using a unique loan level dataset that links homeowner attributes with property and loan characteristics, this study proposes an alternative approach of estimating the implied value of the refinancing threshold. This empirical method enables us to measure the minimum interest rate differential needed to justify refinancing conditional on the borrower's creditworthiness, remaining maturity, and other observable characteristics.

Prepayment Behavior of Dutch Mortgagors: An Empirical Analysis

The suboptimal exercise of the prepayment option in a mortgage is relevant for mortgage pricing and the management of a mortgage portfolio. Construction of an accurate prepayment model requires quantification of driving factors such as seasoning, seasonality, refinance incentive and burnout. We focus on Dutch mortgages but also discuss the Dutch market in a European setting. Within the euro‐denominated MBS market, the Dutch market is often referred to as the benchmark market. In our application we include typical Dutch market and contract characteristics such as the annual penalty‐free prepayment of 10 to 20% of the original loan amount. We use loan‐level historical data on mortgages originated between January 1989 and June 1999 to estimate separate models for two popular redemption types: savings mortgages and interest‐only mortgages. In both models we allow for suboptimal prepayment behavior. The results clearly indicate that prepayment rates depend on interest rates and the age of the mortgage contract. Moreover, we find that burnout is an important element in describing the prepayment behavior of Dutch mortgagors.

Prepayment Modeling and Valuation of Dutch Mortgages

The Dutch mortgage-backed securities (MBS) market is the benchmark euro-denominated MBS market. It is also one of the few European markets where mortgage coupons are fixed for extended periods of time, so prepayment risk is an important factor. A general prepayment modeling framework is used to develop a model for Dutch MBS, using historical speeds on Dutch mortgage deals. A key issue for the refinancing component is reconciliation of the fast speeds observed in periods of low rates, such as in 1999, with the presence of severe prepayment penalties, which in theory should discourage refinancings. An innovative approach models the refinancing incentive not just in terms of the current level of rates, but also taking into account the relationship of rates to the past. An option-adjusted spread analysis of the fixed-rate A2 class of the Match 2002–1 MBS deal provides an illustration.

Universal Asymptotic Behavior of Mortgage Prepayments

Mortgage prepayments play a crucial role in the pricing and hedging of mortgage backed securities. An important feature of mortgage prepayment modeling is burnout; as time goes on those borrowers who have the greatest tendency to refinance are removed from the pool leaving only those that are less likely to refinance. In this paper we examine the implications of burnout on the late time prepayment rate using rather general assumptions. Analytic formulas are derived for the average prepayment rate in the N'th month, P_N, and the fraction of borrowers remaining in the pool in the N'th month, y_N. In the case where the incentive to refinance, and other relevant economic factors, are constant these results are particularly simple. For example, P_N=p+(1-p)/N+..., where p is a constant and the ellipses denote terms suppressed by more powers of 1/N or exponentially suppressed. The term of order 1/N indicates that burnout causes the probability of prepayment to decrease as a very simple function of N.

Improving Parametric Mortgage Prepayment Models with Non-parametric Kernel Regression

Developing a good prepayment model is a central task in the valuation of mortgages and mortgage-backed securities but conventional parametric models often have bad out-of-sample predictive ability. A likely explanation is the highly non-linear nature of the prepayment function. Non-parametric techniques are much better at detecting non-linearity and multivariate interaction. This article discusses how non-parametric kernel regression may be applied to loan level event histories to produce a better parametric model. By utilizing a parsimonious specification, a model can be produced that practitioners can use in valuation routines based on Monte Carlo interest rate simulation.

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.

Movers and Shuckers: Interdependent Prepayment Decisions

We model competing risks of mortgage termination where the borrower faces a repeated choice to continue to pay, refinance the loan, move or default. Most previous empirical work on mortgage prepayment has ignored the distinction between prepayments triggered by refinancing and moving, combining them into a single prepayment rate. We show that financial considerations are the primary drivers of the refinance choice while homeowner characteristics have more influence on the move decision. We demonstrate that these differences are statistically significant and that combining these two distinct choices into a single measure of prepayment shifts coefficients toward zero and produces inaccurate predictions of aggregate termination rates. For example, a combined model underestimates the effect of the market price of the loan on refinancing; it misses entirely the opposite effects of borrower income on moving and refinancing. Our results suggest that existing prepayment models are inconsistent predictors of mobility‐driven prepayment and underestimate the effect of market conditions and borrower characteristics on refinancing and housing decisions. Our findings have great significance to mortgage investors because mobility‐driven prepayments are likely to be a more significant source of prepayments in thenext decade.

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.

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.

Controlling for Burnout in Estimating Mortgage Prepayment Models

Burnout is a consequence of unobservable predictive variables. This paper describes a methodology for estimating mortgage prepayment models which corrects for burnout. The paper generalizes the approach of Deng, Quigley, and Van Order (Econometrica, 68, 275–307, 1998) and Stanton (Rev. Finan. Stud.8, 677–708, 1995) in modeling the impact of unobservable variables as a probability distribution. The estimator is applied to a sample of loan histories and the results compared to a conventional logit analysis of the data. Predictions and simulations from both models are compared to illustrate the properties of the new estimator.

Implied Mortgage Refinancing Thresholds

The optimal prepayment model asserts that rational homeowners will refinance if they can reduce the current value of their liabilities by an amount greater than the refinancing threshold, defined as the cost of carrying the transaction plus the time value of the embedded call option. To compute the notional value of the refinancing threshold, researchers have traditionally relied on discrete- or continuous-time option-pricing models. Using a unique loan level database that links homeowner attributes with property and loan characteristics, this study proposes an alternative approach for estimating the implied value of the refinancing threshold. This empirical method enables us to measure the minimum interest-rate differential needed to justify refinancing conditional on the borrower's creditworthiness, loan-to-value ratio and other observable characteristics.

A Non-Parametric Prepayment Model and Valuation of Mortgage-Backed Securities

A non-parametric technique called generalized additive model (GAM) estimation is particularly useful in high-dimension non-parametric estimations and in situations that involved mixed parametric and non-parametric specifications. The relationship between prepayment rates, and variables such as the age of the mortgage, the ratio of the mortgage coupon rate and prevailing interest rates, and expected and unexpected burnouts is highly non-linear, and it is difficult to capture these relations with parametric functions. Decomposition of pool burnouts into expected and unexpected components improves the model fit and has important pricing implications. The prepayment model estimated here fits the data significantly better than other models in use, and illustrates the factors that affect prepayments and the prices of mortgage-backed securities.

Anatomy of Prepayments

Prepayment models have come to be widely used in the mortgage market. Effective models are based on fundamental relationships that are likely to persist over time, but allow time-varying values of key inputs in order to capture environmental changes over time. The authors explain the major causes of prepayments, and describe how the modeling framework deals with them through turnover, refinancing, default, and curtailment sub-models. They applied the model to five applications covering a range of borrower demographics and mortgage terms, including home equity loans, hybrid ARMs, and prepayment penalty mortgages. A “user9s guide” cautions readers about the conditional nature of projections and prepayment model error.

On the Origin and Interpretation of OAS

OAS, or “option-adjusted spread,” a commonly quoted statistic in the mortgage-backed securities market, is a mathematical construct used to ensure that a mortgage9s estimated equivalent martingale mode price is equal to is quoted market price. Absent any OAS adjustment, common risk-neutral mortgage pricing models fail to accurately predict mortgage market prices. As such. OAS is a particular approach to error correction. Pitfalls arise in the interpretation and use of OAS in portfolio management. A common but flawed interpretation holds that OAS measures the expected risk premium compensation for bearing prepayment risk. Our interpretation suggests that the existence of OAS is symptomatic of a misspecified prepayment model; OAS is not an estimate of an expected risk premium. The analysis shows that prepayment model error - a mean zero random innovation in prepayments - is also not a source of OAS, nor is OAS an estimate of the expected compensation for bearing the risk of prepayment model error.

Hong Kong Residential Mortgage Prepayment Analysis and Modeling

Prepayment analysis has play a crucial role in the development of the U.S. mortgage-backed securities market. Fortunes have been made and lost on right or wrong prepayment forecasts. The mortgage-backed securities market is expected to develop significantly in Hong Kong. To help investors and issuers understand prepayment behavior and analyze different mortgage-backed instruments, this report describes one of the first prepayments analyses and models for Hong Kong residential mortgages. The article discusses the economic variables and mortgage characteristics that influence prepayment behavior.

A Simple Prepayment Model of Commercial Mortgages

Prepayment behavior of single family mortgages has been intensively researched over the past 10 years. This knowledge is essential for valuing the uncertain cash flows of publicly traded mortgage-based securities. A similar need in the much smaller commercial mortgage market remains unfilled. Commercial data to support empirical research are generally unavailable, while results from the single family market are not readily transferable since commercial contracts are different, often including a lockout or yield maintenance provision, and commercial borrowers are believed to behave more “ruthlessly” than single family borrowers. This paper reports prepayment data and presents the results from a simple prepayment model, using a sample of 7,800 multifamily mortgages owned by Freddie Mac and originated over the period 1984 to 1990. The empirically estimated model follows the current literature in relying primarily on the spread between the book value and the market value of the mortgage to measure the prepayment incentive. The Wall Street characterization of commercial mortgages being “fast prepays” is assessed by comparing these model results with a Foster and Van Order single family specification.

An Arbitrage‐Free Estimate of Prepayment Option Prices in Fixed‐Rate GNMA Mortgage‐Backed Securities

In an efficient market, the no‐arbitrage condition implies that the price difference between any two assets must be the market value of all differences in their cash flows. We use this logic to deduce the price of the prepayment option embedded in fixed‐rate Government National Mortgage Association (GNMA) mortgage‐backed securities. The option price equals the difference between an observed GNMA price and the cost of a synthetic, nonprepayable GNMA constructed from the least expensive portfolio of Treasury securities that exactly replicates the promised GNMA cash flow stream, assuming prepayment is precluded. We regress the option prices on variables found significant in previous prepayment studies, finding that five key regressors explain more than 90% of the prepayment option value in pooled time‐series cross‐sectional analysis. We also show that the time value of the prepayment option calculated by our method displays a pattern similar to that produced by the Black‐Scholes (1973) option pricing model. An additional empirical result is the existence of negative option prices and negative time value of the option prices. We attribute these to the fact that homeowners sometimes exercise their prepayment options when they are out‐of‐the‐money, and to refinancing transaction costs. Our method is independent of assumptions regarding interest rate processes and the homeowner's prepayment behavior, and it provides a benchmark for testing theoretical prepayment models.

Improved Prepayment Modeling for OAS Analysis

SAM CHOI is a consultant in the fixed income research department at BARR4 in Berkeley, California. n early 1992, prepayments on mortgage-backed securities (MBS) began their climb to historic levels and caught many investors by surprise. Many long-term prepayment models, which are built using many years of historical data, severely underestimated prepayments of MBS during this past period. The simple explanation for this inaccuracy is that there is no historical precedent for the recent prepayment wave. The new generation of prepayment models must now be built to allow for constantly changing and unprecedented market conditions, and at the same time work within the framework of tradtional option-adjusted spread (OAS) analysis. One way to approach this problem is to develop a model with two components: a short-term component that incorporates only recent data; and a long-term component that incorporates all available historical data, and maintains the traditional, robust behavioral model properties that are necessary for OAS analysis. From an investor’s perspective, short-term accuracy in prepayment predictions is extremely important. Many of the bonds IOs, POs, Jump Zs, TAG, and so on are extremely sensitive to prepayments. Average lives, durations, and fitted prices fluctuate dramatically with even moderately different prepayment assumptions for these tranches. As a good example, let’s look at an FNMA PAC-PO (series 1993-19 Class K) with a PSA band of 140-225 under the different prepayment scenarios in Exhibit 1. Clearly, accurate prepayment projections are imperative for accurate valuation and risk characterization of mortgage-backed bonds.

Mortgage Prepayments and an Analysis of the Wharton Prepayment Model

Predicting the behavior of homeowners in paying or prepaying their mortgages is a key feature of both pricing and portfolio management models. All major players in the market of mortgage-backed securities have to deal with the idiosyncracies of mortgage owners. A variety of prepayment models are currently in routine use by Wall Street firms, insurance and pension fund companies, investment advisory firms, and mortgage agencies. However, most of these models are proprietary, and the analytics underlying them are carefully guarded. We evaluate empirically a model developed at the Wharton School, intending to validate a model developed in academia—whose details are available in the open literature [Kang and Zenios 1992]—by using standard industrial tests.