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Optimal surrender policy for reverse mortgage loans

Published online by Cambridge University Press:  24 September 2024

Carole Bernard ,
Adam Kolkiewicz  and
Junsen Tang Open the ORCID record for Junsen Tang [Opens in a new window]
Carole Bernard
Affiliation:
Department of Accounting, Law and Finance, Grenoble Ecole de Management, Grenoble, France Faculty of Economics, Vrije Universiteit Brussel, Ixelles, Belgium
Adam Kolkiewicz
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada
Junsen Tang*
Affiliation:
Department of Mathematics, University of Saint Thomas, Saint Paul, MN 55105, USA
*
Corresponding author: Junsen Tang; Email: junsen.tang@stthomas.edu
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Abstract

This study conducts an optimal surrender analysis of reverse mortgage (RM) loans offered to elderly homeowners as a financing option. Recent market evidence on borrower early surrenders has raised concerns about the marketability of RM products and their impact on the program viability. In this article, we derive the borrower optimal surrender strategy as a function of the underlying value of the home used as collateral for RM contracts with tenure payment option. Using a probabilistic approach to American option pricing, we present a decomposition result for the value of the contract as the sum of its European counterpart without the surrendering provision and an early exercise premium. The methodology allows policymakers to assess the financial incentive of their policy design, from which we explain the existing market evidence about borrower rational lapse by means of the resulting surrender boundary and reference probabilities.

Keywords

Reverse mortgageoption pricingoptimal surrenderpolicy design

Information

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 54 , Issue 3 , September 2024 , pp. 600 - 625
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The International Actuarial Association

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