Endogenous Current Coupons

TL;DR

This paper develops a mathematical model to identify current coupons for TBA mortgage-backed securities, incorporating complex factors like prepayment rates and market variables, and provides an explicit approximation method validated by numerical tests.

Contribution

It introduces a new fixed point approach for determining current coupons in a stochastic, factor-based model with prepayment dependencies, and offers an explicit approximation method.

Findings

The fixed point problem has a proven existence of solutions.

The explicit approximation performs well in numerical tests.

The model captures key market factors affecting current coupons.

Abstract

We consider the problem of identifying current coupons for Agency backed To-be-Announced (TBA) Mortgage Backed Securities. In a doubly stochastic factor based 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 factor-based intensity model. Numerical examples are provided which show the approximation performs remarkably well in estimating the current coupon.