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A Semi-Markov Multiple State Model for Reverse Mortgage Terminations

Published online by Cambridge University Press:  15 May 2012

Min Ji ,
Mary Hardy  and
Johnny Siu-Hang Li
Min Ji*
Affiliation:
Department of Mathematics, Towson University, USA
Mary Hardy
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Canada
Johnny Siu-Hang Li
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Canada
*
*Correspondence to: Min Ji, Department of Mathematics, Towson University, USA. E-mail: mji@towson.edu
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Abstract

Reverse mortgages provide a mechanism for seniors to release the equity that has been built up in their home. At termination, the mortgagors are usually guaranteed to owe no more than the value of their property. The value of the reverse mortgage guarantee is heavily dependent on the maturity or termination date, which is uncertain. In this paper, we model reverse mortgage terminations using a semi-Markov multiple state model which incorporates three different modes of exit: death, entrance into a long-term care facility, and voluntary prepayment. We apply the proposed model specifically to develop the valuation formulas for roll-up mortgages in the UK and Home Equity Conversion Mortgages (HECMs) in the USA. We examine the significance of each mode of termination by valuing the contracts allowing progressively for each mode. On the basis of our model and assumptions, we find that both health related terminations and voluntary (non-health related) terminations significantly impact the contract value. In addition we analyze the premium structure for US reverse mortgage insurance, and demonstrate that premiums appear to be too high for some borrowers, and substantial cross-subsidies may result.

Keywords

Equity release productsReverse mortgagesGuaranteeTermination ratesDependenceSemi-Markov modelJoint lives
Type
Papers
Information
Annals of Actuarial Science , Volume 6 , Issue 2 , 23 August 2012 , pp. 235 - 257
Copyright
Copyright © Institute and Faculty of Actuaries 2012

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