On convergence of MOATS Mortgage Rate Model

A number of mortgage prepayment models require a specification of the mortgage rate process. In 2006, Citigroup published its MOATS model where the prepayment model was based on the endogenously defined mortgage rate process. MOATS was based on the “End of Finance” (EOF) assumption, which stated that the term for a new mortgage is 30 years or the rest of time until EOF (assumed to be in sixty years ”from now”), whatever is less. This article shows that MOATS gives a sufficient approximation to the “real” endogenous mortgage rate (i.e., without the EOF assumption). Next, we show a number of techniques to significantly reduce the high computational price of MOATS (which is very high even for one stochastic factor). Some of these techniques require practically no coding effort if the original MOATS is already implemented. The result is based on our simple and transparent generalized formulation of the MOATS model which is not tied to a specific numerical method. In particular, in our model set-up Monte Carlo methods can be used as well.