Universal Asymptotic Behavior of Mortgage Prepayments

Mortgage prepayments play a crucial role in the pricing and hedging of mortgage backed securities. An important feature of mortgage prepayment modeling is burnout; as time goes on those borrowers who have the greatest tendency to refinance are removed from the pool leaving only those that are less likely to refinance. In this paper we examine the implications of burnout on the late time prepayment rate using rather general assumptions. Analytic formulas are derived for the average prepayment rate in the N'th month, P_N, and the fraction of borrowers left in the pool in the N'th month, y_N. In the case where the incentive to refinance, and other relevent economic factors, are constant these results are particularly simple. For example, P_N=p+(1-p)/N+... , where p is a constant and the ellipses denote terms suppressed by more powers of 1/N or exponentially suppressed. The term of order 1/N indicates that burnout causes the probability of prepayment to decrease as a very simple function of N.