Endogenous Mortgage Current Coupons

We consider the problem of identifying current coupons for agency-backed To-Be-Announced pools of residential mortgage loans. In a doubly stochastic model which allows for prepayment intensities to depend upon current and origination mortgage rates, as well as underlying investment factors, we identify the current coupon with solutions to a degenerate elliptic, non-linear fixed point problem. Using Schaefer’s theorem we prove existence of current coupons. We also provide an explicit approximation to the fixed point, valid for compact perturbations off a baseline model where intensities only depend on the underlying factors. Numerical examples are provided which show that the approximation performs well in estimating the current coupon.