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

Looking first at the volatility estimates, a high degree of variability surrounding both of these option characteristics is observed. Specifically, the EGARCH measure of housing price volatility (HPI - EGARCH) reveals that average prices varied by over 2% per quarter, while analogous interest rate volatility (INTEREST - EGARCH) averaged 20 basis points per month. Given the importance of volatility as demonstrated by the empirical options literature, these estimates suggest that volatility may play a significant role in explaining mortgage termination decisions.

Consistent with the view that default and prepayment are competing options, the models incorporate two variables designed to measure the degree to which each option is in-the-money. Following Deng, Quigley and Van Order (1996) and Ambrose and Capone (1998, 2000), the probability that a mortgaged property investment is in a negative equity situation (i.e., the probability that the option to default is in-the-money, or that the option to "put" the loan back to the lender is profitable) is estimated as:

where mbal is the current market value of the property estimated using the Office of Federal Housing Enterprise Oversight (OFHEO) state level weighted repeat sales index to capture changes in single-family house prices, outbal is the present value of all remaining mortgage payments discounted at the contract interest rate, s is the standard error of the OFHEO index number estimate and phi is the cumulative standard normal distribution function. The positive average value of PNEQ in Exhibit 2 indicates that the default option is frequently in-the-money at termination for the loans in this dataset. Ex ante, increases in the probability of negative equity (PNEQ) are expected to be associated with enhanced default probabilities.

Similarly, as modeled by Deng et al. and Ambrose and Capone, the prepayment option is in-the-money when the discounted value of the remaining mortgage payments at the current market rate is greater than the outstanding mortgage balance. Thus, the degree to which the prepayment option is in-the-money may be calculated as:

where pbal is the discounted value of the remaining mortgage payments at the current market rate, and outbal is the discounted value of the remaining mortgage payments at the contract interest rate (i.e., the unpaid mortgage balance). Positive values of PREPAY indicate that the market interest rate is higher than the contract rate and prepayment option exercise is not profitable (i.e., the option is out-ofthe-money). Conversely, negative values of PREPAY indicate that the market interest rate is lower than the contract rate and option exercise is profitable (i.e., the option is in-the-money). In Exhibit 2, the negative average value of PREPAY indicates that the prepayment option is typically in-the-money at termination.

Borrower Heterogeneity

Deng, Quigley and Van Order (2000) advocate the options framework as a useful tool for analyzing and explaining the behavior of mortgage termination options. However, they qualify this by stating "there exists significant heterogeneity among mortgage borrowers, particularly regarding prepayment." They continue, "ignoring heterogeneity among mortgage borrowers leads to serious errors in estimating the prepayment risk."