Improving parametric mortgage prepayment models with non-parametric kernel regression

Journal of Real Estate Research, The, Nov/Dec 2002 by LaCour-Little, Michael, Marschoun, Michael, Maxam, Clark L

Abstract

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.

Introduction

The importance of mortgage loan prepayments has been the topic of much academic and practitioner research. Many highly publicized losses by investors in mortgage-related derivative securities have been attributed to unexpected changes in prepayments. Understanding prepayment risk is important in assessing the risk, capital, solvency and insurance of financial institutions that originate and hold fixed-rate mortgages. Prepayment risk also affects the government and government-sponsored enterprises (GSEs) such as Fannie Mae, Ginnie Mae and Freddie Mac, which guarantee securities backed by mortgage loans.1 In addition, much of the S&L crisis during the 1980s can be attributed to the poor management of interest rate risk (duration mismatch) in mortgage portfolios brought on by rapid, unforecasted and unhedged prepayment changes. At present, approximately $6.0 trillion of home mortgage debt is outstanding. With $4.0 trillion now securitized in the form of mortgage-backed securities (MBS) guaranteed by the GSEs, holdings of these securities have spread beyond traditional banking institutions to all types of financial institutions, money funds and investment groups. These securities have, in turn, been re-packaged into derivatives such as CMO's, IO's, PO's and inverse floaters, all of which can exhibit even greater prepayment sensitivity. As a result, the analysis and forecasting of mortgage loan prepayments has become increasingly crucial to a growing group of investors as well as regulatory bodies.

This article discusses how non-parametric techniques can be used to improve parametric modeling resulting in better out of sample estimation. Maxam and LaCour-Little (2001) previously applied these techniques to mortgage pool data with promising results; however, purely non-parametric approaches are of little practical value given the necessity of off-the-support predictions in the Monte Carlo interest rate simulations used to actually value mortgages. This article extends the kernel regression estimation approach in Maxam and LaCour-Little to individual loan event histories. Prepayment probability is estimated as a function of the "moneyness" of the prepayment option, the age of the mortgage and the previous path of interest rates. The patterns produced by the kernel then guide development of a parametric alternative, which is shown to be a "second best" solution in terms of model fit.

A mortgage is frequently modeled as consisting of two components: a straight bond, which fluctuates with interest rates in the usual manner and an option component reflecting the borrower's right to prepay the mortgage and refinance at any time.' Thus, a mortgage or MBS investor is implicitly writing a call on the underlying fixed-rate bond. The household decision to prepay is based, of course, on a variety of factors, some directly related to interest rates while others reflect broader demographic factors. In contrast to option theory predictions, it is well documented that mortgage prepayment option exercise appears to be sub-optimal (Green and LaCour-Little, 1999). Mortgages are prepaid even when prevailing mortgage rates are higher than loan rates (when the option is out-of-the-money) and mortgages are not prepaid even when the loan rate exceeds the prevailing mortgage rate (when the option is deep in-the-money). This apparent irrationality on the part of borrowers is part of the problem in predicting prepayments. Among the earliest to examine the topic of prepayment were Dunn and McConnell (1981), Brennan and Schwartz (1985), Green and Shoven (1986), and Quigley (1988), all of whom identified the role of interest rates as well as borrower mobility on rates of mortgage prepayment. In two often-cited articles, Schwartz and Torous (1989, 1993) use variations on the proportional hazard approach together with a Poisson regression to integrate prepayment into an overall valuation framework. Academic interest in the topic accelerated during the early 1990s with theoretical papers by Brueckner (1992, 1994), Follain, Scott and Yang (1992), Kau, Keenan, Muller and Epperson (1992) and Stanton (1995). These articles dealt with optimal exercise of the borrower's call option given stochastic interest rates and the implications for mortgage contract design and pricing, both of mortgages and mortgage-backed securities. Concurrently, Wall Street firms were developing proprietary prepayment models for use in valuation routines that supported their trading strategies (Richard and Roll, 1989; Patruno, 1994; Hayre and Rajan, 1995: Hayre, Chaudhary and Young, 2000). The refinancing wave of 1993 followed by the sharp increase in rates during 1994 produced large losses for many market participants, reinforcing the business imperative to develop better models.3