The value of mortgage prepayment and default options

Abstract

We use an implicit alternating direction numerical procedure to estimate the value of a fixed-rate mortgage (FRM) with embedded default and prepayment options. The value of FRMs depends on interest rates, the house value, and mortgage maturity. Our numerical results suggest that the joint option value of prepayment and default is considerably high, even at loan origination. We extend the model to include prepayment penalties in FRM valuation.

Lessons from Over 30 Years of Buy versus Rent Decisions: Is the American Dream Always Wise?

“…The probability that renting will be preferred to buying for each period is estimated by running a Monte Carlo simulation with 1,000 21 iterations to compare the expected renter's portfolio value to the expected home selling proceeds. To compensate homebuyers for the value of the prepayment and default option embedded in the mortgage, the present value of the mortgage is reduced by 2.9%, which is consistent with the estimated value of these options by Chen et al . (2009) 22 .…”

“…20 The probability that renting will be preferred to buying for each period is estimated by running a Monte Carlo simulation with 1,000 21 iterations to compare the expected renter's portfolio value to the expected home selling proceeds. To compensate homebuyers for the value of the prepayment and default option embedded in the mortgage, the present value of the mortgage is reduced by 2.9%, which is consistent with the estimated value of these options by Chen et al (2009). 22 Additionally, because rent growth, price appreciation and opportunity cost are correlated and not independent, each of the 1,000 iterations generates values for these three stochastic variables that are highly correlated to actual observations during the 1978-2009 time period.…”

“…22 22 The value of 2.9% is derived by averaging Chen et al's (2009) results for a fixed‐rate mortgage with 0.04 and 0.07 standard deviations in spot rate and 2% refinancing fee. This figure is also in line with the observed value of these options during the period 1978–2009, which is calculated to be 2.7% and 3.7%, on average, with and without tax consideration, respectively. …”

Valuation of the Prepayment Option of a Perpetual Corporate Loan

“…Literature. There exist few articles (e.g., works by Cossin and Lu [1]) on the loan prepayment option but a close subject, the prepayment option in a fixed-rate mortgage loan, has been widely covered in several papers by Hilliard et al [4] and more recent works by Chen et al [5]. To approximate the PDE satisfied by the prepayment option, they define two state variables (interest rate and house price).…”

Fixed Come Hell or High Water? Selection and Prepayment of Fixed‐Rate Mortgages Outside the United States

“…We consider two possible break fees here. The first break fee is simply a flat portion of the principal outstanding, as considered by Azevedo‐Pereira, Newton and Paxson (2002) and Chen et al (2009). where is a constant.…”