Journal of Real Estate Finance and Economics, 23:2, 139±160, 2001
# 2001 Kluwer Academic Publishers. Manufactured in The Netherlands.
Applied Nonparametric Regression Techniques:
Estimating Prepayments on Fixed-Rate
CLARK L. MAXAM
New York Life Investment Management and Montana State University College of Business,
51 Madison Avenue, Room 201, New York, NY 10010
Wells Fargo Home Mortgage, 7911 Forsyth Blvd, Suite 600, Clayton, MO 63105
We assess nonparametric kernel-density regression as a technique for estimating mortgage loan prepaymentsÐ
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 speci®cation in terms of
both data and covariates. We conclude that the technique may prove useful in other ®nancial modeling
applications, such as default modeling, and other derivative pricing problems where highly nonlinear
relationships and optionality exist.
Key Words: mortgage, prepayment, nonparametric, kernel regression
This article presents nonparametric kernel-density regression as a technique for modeling
and predicting highly nonlinear functional relationships. We apply kernel regression to the
problem of estimating mortgage prepayments. The primary advantage of nonparametric
modeling is that it does not require restrictive assumptions such as prespeci®ed functional
forms or distributions.
In this case, we ®nd that the nonparametric kernel-density
regression either demonstrates notable strengths or outperforms both proportional-hazards
and other nonlinear models in terms of out-of-sample predictive ability and thus exhibits
promise in uncovering implicit optionality in prepayment.
Valuation of mortgages and mortgage-backed securities (MBS) requires both a term
structure and a prepayment model. We focus here on use of kernel-regression techniques to
model only prepayments; the problem of evaluating a joint model of MBS pricing is
beyond our scope. Speci®cally, we show how kernel-density estimation may be applied in