Commercial mortgage prepayments under heterogeneous prepayment penalty structures

Journal of Real Estate Research, The, Jul-Sep 2003 by Fu, Qiang, LaCour-Little, Michael, Vandell, Kerry D

Follain, Huang and Ondrich (1999) examine default and prepayment risk in FHA-insured multifamily loans, using a competing risks-proportional hazards method. They find evidence consistent with the option pricing theory of prepayments but very low rates of prepayment during the initial twenty years of a thirty-year mortgage. This pattern is even more pronounced for those loans in their data that were secured by Section 8 properties, possibly because public subsidy utilization produces a substantial disincentive for prepayment.

Kelly and Slawson (K&S) (2001) use simulation to address the value of delay in the case of commercial mortgages containing prepayment penalties. Their approach extends the line of research showing a value to delay for both default and prepayment options in the single-family market (Kau and Kim, 1994). Intuitively, an additional cost to exercising an option today is the loss of the right to exercise that same option in the future. K&S consider a full range of possible prepayment penalties, including permanent, fixed, step-down, yield maintenance and lockouts, but adopt an admittedly simplistic view of default, in which cash flows are proportional to property values and asset values follow a standard diffusion process. K&S find that time-varying prepayment penalties significantly affect optimal prepayment decisions, since the value of delay differs between static and declining prepayment penalty structures. Among their conclusions, K& S state that "it is crucial that empirical researchers consider the effect of time-varying prepayment penalties."2 The empirical effort here follows this prescription.

In summary, both single-family and multifamily research has been hampered by the lack of detailed data that would allow researchers to separate call option exercise from borrower mobility effects (in the single-family area) and detailed information on the nature and extent of prepayment penalties (in the multifamily area). The current research remedies these problems through use of micro-level data on 1,165 multifamily mortgage loans, with heterogeneous prepayment penalties, originated during the period 1991-1996 and observed through April 2000.

Expectations from Option Theory: Simulation Results

A binomial option-pricing model is solved first, which has been extended to include alternative prepayment penalties. Default risk is excluded for the purposes of the simulation and to focus on prepayments.3 The analysis borrows from Tian (1992) and Deng (1997) the method of interest rate simulation. Tian proposes a simplified binomial process to mimic the interest rate processes. This method is later adopted by Deng to replicate the Cox-Ingersoll-Ross (CIR) (1985) interest rate process and then used to evaluate mortgage prepayment and default option values.4 Under the CIR assumption, the spot interest rate follows:

where r is the spot interest rate, [lambda] is the speed of mean reversion, [theta] is the long-term interest rate, [sigma] is volatility and dz is a standard Wiener process.