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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: [email protected]
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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
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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References

Alai, D.H., Chen, H., Cho, D., Hanewald, K. and Sherris, M. (2014) Developing equity release markets: Risk analysis for reverse mortgages and home reversions. North American Actuarial Journal, 18, 217–241.CrossRefGoogle Scholar
Bacinello, A.R., Millossovich, P., Olivieri, A. and Pitacco, E. (2011) Variable annuities: A unifying valuation approach, Insurance: Mathematics and Economics, 49, 285–297.Google Scholar
Bardhan, A., Karapandža, R. and Urošević, B. (2006) Valuing mortgage insurance contracts in emerging market economies. Journal of Real Estate Finance and Economics, 32, 9–20.CrossRefGoogle Scholar
Bauer, D., Kling, A. and Russ, J. (2008) A universal pricing framework for guaranteed minimum benefits in variable annuities. ASTIN Bulletin: The Journal of the IAA, 38, 621–651.CrossRefGoogle Scholar
Bernard, C., Hardy, M. and MacKay, A. (2014a) State-dependent fees for variable annuity guarantees. ASTIN Bulletin: The Journal of the IAA, 44, 559–585.CrossRefGoogle Scholar
Bernard, C., MacKay, A. and Muehlbeyer, M. (2014b) Optimal surrender policy for variable annuity guarantees. Insurance: Mathematics and Economics, 55, 116–128.Google Scholar
Blevins, J.R., Shi, W., Haurin, D.R. and Moulton, S. (2020) A dynamic discrete choice model of reverse mortgage borrower behavior. International Economic Review, 61, 1437–1477.CrossRefGoogle Scholar
Carr, P., Jarrow, R. and Myneni, R. (1992) Alternative characterizations of American put options. Mathematical Finance, 2, 87–106.CrossRefGoogle Scholar
Chiang, S.L. and Tsai, M.S. (2019) A microeconomic model for the decision of reverse mortgage borrowers to sell their house early and its application on the estimation of termination rates. Journal of Real Estate Finance and Economics, 61, 1–25.Google Scholar
Choi, H.-S. (2019) A Numerical analysis to study whether the early termination of reverse mortgages is rational. Sustainability, 11, 6820.CrossRefGoogle Scholar
Davidoff, T. (2015) Can “high costs” justify weak demand for the Home Equity Conversion Mortgage?. Review of Financial Studies, 28, 2364–2398.CrossRefGoogle Scholar
Davidoff, T. and Welke, G.M. (2017) The role of appreciation and borrower characteristics in reverse mortgage terminations. Journal of Real Estate Research, 39, 99–126.CrossRefGoogle Scholar
Grosen, A. and Jørgensen, P.L. (2000) Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options, and bonus policies. Insurance: Mathematics and Economics, 26, 37–57.Google Scholar
Han, W., Wang, P., Xu, H. and Choi, J.-S. (2017) Evaluation of the reverse mortgage option in Hong Kong. Asian Economic Journal, 31, 187–210.CrossRefGoogle Scholar
Haurin, D., Ma, C., Moulton, S., Schmeiser, M., Seligman, J. and Shi, W. (2016) Spatial variation in reverse mortgages usage: House price dynamics and consumer selection. Journal of Real Estate Finance and Economics, 53, 392–417.CrossRefGoogle Scholar
Ji, M., Hardy, M. and Li, J.S.-H. (2012) A semi-Markov multiple state model for reverse mortgage terminations. Annals of Actuarial Science, 6, 235–257.CrossRefGoogle Scholar
Jiang, S. and Miller, C.L. (2019) Termination risk of reverse mortgages. International Real Estate Review, 22, 169–196.CrossRefGoogle Scholar
Kau, J.B., Keenan, D.C., Muller, W.J. and Epperson, J.F. (1992) A generalized valuation model for fixed-rate residential mortgages. Journal of Money, Credit and Banking, 24, 279–299.CrossRefGoogle Scholar
Kim, I.J. and Yu, G.G. (1996) An alternative approach to the valuation of American options and applications. Review of Derivatives Research, 1, 61–85.CrossRefGoogle Scholar
Lee, Y.-T. and Shi, T. (2021) Valuation of reverse mortgages with surrender: A utility approach. The Journal of Real Estate Finance and Economics, 65, 593–621.CrossRefGoogle Scholar
Lee, Y.-T., Wang, C.-W. and Huang, H.-C. (2012) On the valuation of reverse mortgages with regular tenure payments. Insurance: Mathematics and Economics, 51, 430–441.Google Scholar
McKean, H.P. (1965) A free boundary problem for the heat equation arising from a problem of mathermatical economics. Industrial Management Review, 6, 32–39.Google Scholar
Milevsky, M.A. and Salisbury, T.S. (2006) Financial valuation of guaranteed minimum withdrawal benefits. Insurance: Mathematics and Economics, 38, 21–38.Google Scholar
Moulton, S., Haurin, D.R. and Shi, W. (2015) An analysis of default risk in the Home Equity Conversion Mortgage (HECM) program. Journal of Urban Economics, 90, 17–34.CrossRefGoogle Scholar
Myneni, R. (1992) The pricing of the American option. The Annals of Applied Probability, 2, 1–23.CrossRefGoogle Scholar
Nakajima, M. and Telyukova, I.A. (2017) Reverse mortgage loans: A quantitative analysis. Journal of Finance, 72, 911–950.CrossRefGoogle Scholar
Poterba, J.M., Venti, S.F. and Wise, D.A. (2010) Demographic trends, housing equity, and the financial security of future retirees. In Demography and the Economy, pp. 227–287. University of Chicago Press.CrossRefGoogle Scholar
Pu, M., Fan, G.-Z. and Deng, Y. (2014) Breakeven determination of loan limits for reverse mortgages under information asymmetry. Journal of Real Estate Finance and Economics, 48, 492–521.CrossRefGoogle Scholar
Shan, H. (2011) Reversing the trend: The recent expansion of the reverse mortgage market. Real Estate Economics, 39, 743–768.CrossRefGoogle Scholar
Shao, A.W., Hanewald, K. and Sherris, M. (2015) Reverse mortgage pricing and risk analysis allowing for idiosyncratic house price risk and longevity risk. Insurance: Mathematics and Economics, 63, 76–90.Google Scholar
Shi, T. and Lee, Y.-T. (2021) Prepayment risk in reverse mortgages: An intensity-governed surrender model. Insurance: Mathematics and Economics, 98, 68–82.Google Scholar
Szymanoski, E.J., Enriquez, J.C. and DiVenti, T.R. (2007) Home equity conversion mortgage terminations: Information to enhance the developing secondary market. Cityscape, 9, 5–45.Google Scholar
Thomas, R.G. (2021) Valuation of no-negative-equity guarantees with a lower reflecting barrier. Annals of Actuarial Science, 15, 115–143.CrossRefGoogle Scholar
United States Government Accountability Office (2019) Reverse mortgages: FHA needs to improve monitoring and oversight of loan outcomes and servicing.Google Scholar
Van Bragt, D., Francke, M.K., Singor, S.N. and Pelsser, A. (2015) Risk-neutral valuation of real estate derivatives. Journal of Derivatives, 23, 89.CrossRefGoogle Scholar
Venti, S.F. and Wise, D.A. (1991) Aging and the income value of housing wealth. Journal of Public Economics, 44, 371–397.CrossRefGoogle Scholar