Mortgage terminations: The role of conditional volatility

Journal of Real Estate Research, The, Jan-Apr 2002 by Harrison, David M, Noordewier, Thomas G, Ramagopal, K

Abstract

This article is the winner of the Real Estate Finance manuscript prize (sponsored by Fannie Mae Foundation) presented at the 2001 American Real Estate Society Annual Meeting.

Studies of mortgage termination decisions typically rely on a competing risks framework comparing defaults and prepayments. While useful tools have been developed to approximate the values of these competing default and prepayment options, the available metrics do not adequately account for the role of the conditional volatility of interest rates and housing prices in option valuation. Using a sample of 1,428 mortgage loan payment histories, this study finds that exponential GARCH estimates of the conditional volatility of housing prices and interest rates influence mortgage termination decisions in a predictable manner. Specifically, increased housing price volatility is shown to enhance default option values, while increased interest rate volatility is shown to enhance prepayment option values. Therefore, it would appear that conditional volatility represents a more refined input into the competing risks option framework.

Introduction

The competing options framework offers powerful insights into mortgage default and prepayment decisions. In this framework, the borrower must ultimately choose between continuing to make timely payments of principal and interest, prepaying the loan in full, or defaulting on the obligation. If the market value of a property drops below the outstanding balance of the loan, the borrower may rationally choose to ruthlessly exercise the default (i.e., put) option.1 This action would preclude the potentially profitable future exercise of the prepayment option. Conversely, if the value of the property rises, the borrower captures the entire gain in the underlying value of the asset.2 With respect to prepayments, if market wide interest rates fall, the borrower may choose to exercise the prepayment (i.e., call) option and refinance at a lower rate. Again, such action precludes a future default option exercise on the (now) prepaid obligation. On the other hand, if rates rise, the borrower retains the loan at its (now) below-market interest rate.

The competing risks conceptualization of mortgage contracts has resulted in the increasingly accurate pricing of mortgages and management of risks associated with these securities. Both default and prepayment represent termination alternatives that are potentially valuable to borrowers and costly to lenders. Thus, a borrower's true equity position within a property is most accurately viewed as the equity position in the underlying real estate plus two competing options (Hilliard, Kau and Slawson, 1998).

Since Foster and Van Order's (1984) path breaking application of option theory to the mortgage terminations literature, Deng, Quigley and Van Order (1996) and Ambrose and Capone (1998, 2000) have introduced a pair of measures designed to capture the extent to which the default and prepayment options are in the money. These measures, originally labeled PNEQ and PREPAY, are regarded as state-of-the-art with respect to capturing the relative degree of default and prepayment option moneyness, respectively.3 Despite their usefulness, these measures do not fully account for the role and importance of conditional volatility as indicated by the empirical options literature.4 Specifically, the PNEQ measure of default option moneyness incorporates a time-varying volatility metric by using the standard error of the housing price index. However, this volatility input is limited insofar as it does not address the fact that housing price volatility changes more rapidly when there are decreases in market values than when there are increases. The PREPAY measure of prepayment option moneyness does not incorporate any volatility metric.

The main contribution of this study is to develop and test more refined volatility inputs into the default and prepayment competing risks framework. Specifically, exponential Garch techniques are employed to model the conditional volatility of housing prices and interest rates. These volatility estimates are then used as inputs, along with other control variables, to model default and prepayment termination decisions. These conditional volatility estimates exhibit a statistically significant relationship to mortgage termination decisions.

The remainder of the study is structured as follows. The next section considers different approaches to obtaining estimates of conditional volatility for both housing prices and interest rates, presents the rationale for the choice of a particular specification and formally articulates the hypotheses. Following this, the data available for analysis and descriptive statistics are presented. Next, the hypotheses are tested by estimating Cox regression models for the timing of defaults and prepayments, and performing a logistic regression to formally model the competing risks aspect of default and prepayment terminations. The findings from the logistic regression are also utilized to conduct a simulation in which the marginal effects and economic significance of the findings are estimated. The final section offers a summary of the current investigation, and suggests future research possibilities.