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

Carlos E. Ortiz (Department of Mathematics and Computer Science, Arcadia University, Philadelphia, Pennsylvania, USA)
Charles A. Stone (Department of Finance, Brooklyn College, University of New York, Brooklyn, New York, USA)
Anne Zissu (Department of Business, CityTech, City University of New York, Brooklyn, New York, USA)

Journal of Risk Finance

ISSN: 1526-5943

Article publication date: 9 August 2013

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Abstract

Purpose

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.

Design/methodology/approach

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

Findings

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*.

Originality/value

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.

Keywords

Citation

Ortiz, C.E., Stone, C.A. and Zissu, A. (2013), "An innovative form of credit enhancement for securitized reverse mortgages: Finding paths of cross‐over points isolated from changes in interest and inflation rates", Journal of Risk Finance, Vol. 14 No. 4, pp. 414-431. https://doi.org/10.1108/JRF-03-2013-0015

Publisher

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Emerald Group Publishing Limited

Copyright © 2013, Emerald Group Publishing Limited