  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.
