An innovative form of credit enhancement for securitized reverse mortgages: Finding paths of cross‐over points isolated from changes in interest and inflation rates

One of the main risks to investors in securitized reverse mortgages is that the value of the reverse mortgage exceeds that of the property. The purpose of this paper is to develop a model that determines paths of constant cross‐over points across any pairs of interest and inflation rate.

To study the behavior of hyper‐surfaces, multivariate calculus was used.

Knowing that the value of a reverse mortgage increases above that of the property value once it goes beyond the cross‐over point t*, it is possible to construct a pool of reverse mortgages, such that for any pairs of inflation rate and interest rate (x, r), these reverse mortgages move along lines of constant cross‐over points t*.

The paper develops a model that determines paths of constant cross‐over points across any pairs of interest and inflation rate, which can be used when structuring pools of reverse mortgage‐backed securities, to credit‐enhance investors.