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

6 The Vega of the default (prepayment) option is the change in the price of the option relative to the change in the volatility of housing prices (interest rates).

7 See Kim and Kim (1994). Two additional critical features are skewness and kurtosis.

8 Conditional volatility estimates for interest rates are derived in an analogous fashion.

9 The data are first-differenced to ensure stationarity.

10 In order to ensure stationarity, the restriction on the parameters in the GARCH (1,1) is alpha^sub 1^ beta^sub 1^

11 In order to accommodate the probability sampling design employed, all analyses reported below were conducted using the software program SUDAAN, which offers Taylor series linearization to produce correct standard errors.

12 Traditional lender cut-offs for acceptable borrower credit risk include an LTV of 80% for non-insured loans, a total debt ratio of 31%-33%, and a FICO score of approximately 620.

13 Closing costs and financing charges associated with refinancing the loan are also frequently rolled into the new mortgage. The underwriting lender for all the loans in the dataset defined non-cashout refinance loans as loans for which the value of the ratio of the loan amount to the outstanding lien is less than or equal to 1.06.

14 Multiple "default" definitions are possible and have been employed throughout the literature. Consistent with the general consensus of both industry practitioners and the academic community (Ambrose and Capone 1998, 2000), delinquency is viewed as superior to foreclosure as a default metric, since delinquency status is not subject to the differential application of loss mitigation strategies across borrower characteristics or property attributes. Similarly, foreclosure as a measure of default is potentially troublesome due to differential bankruptcy provisions and other jurisdictional variances across geographic regions. For a further discussion of the appropriate definition of bad loans, see Avery, Bostic, Calem and Canner (1996) or Jaske (1997).

15 The correlation between PREPAY and INTEREST - EGARCH is 0.21. Estimating the prepayment model and excluding the call option variable PREPAY produces a coefficient estimate that is consistent in sign and stronger in both magnitude and significance for the corresponding conditional volatility input parameter INTEREST - EGARCH. The conditional volatility of interest rates in the prepayment decision appears robust to the inclusion or exclusion of the PREPAY optionality parameter.

16 Theoretically, the multinomial logit framework is one approach that could be used for estimation purposes, since the dataset includes loans with three distinct, mutually exclusive and exhaustive outcomes (i.e., 889 defaults, 446 prepayments and 93 current loans). However, the distribution of mortgage outcomes across these three classifications leads to convergence and singularity problems when applying the framework to the data, as less than 7% of the sample loans remained current as of July 1997. Therefore, this study employs a two-stage approach to modeling mortgage termination decisions. For a complete discussion of appropriate operationalizations of competing risks models, see Allison (1995).