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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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References

Chen, H., Cox, S., Wang, S. (2010). Is the Home Equity Conversion Mortgage in the United States sustainable? Evidence from pricing mortgage insurance premiums and non-recourse provisions using the conditional Esscher transform. Insurance: Mathematics and Economics, 46, 371–384.Google Scholar
Chow, M.H., Szymanoski, E.J., DiVenti, T.R. (2000). Applying survival analysis techniques to loan terminations for HUD's reverse mortgage insurance program-HECM. Proceedings of the 13th Northeast SAS Users Group Conference, available at http://www.nesug.org/proceedings/nesug00/st/st9003.pdf.Google Scholar
Cox, P.R., Ford, J.R. (1964). The mortality of widows shortly after widowhood. Lancet, 1, 163–164.Google Scholar
Dickson, D.C.M., Hardy, M.R., Waters, H.R. (2009). Actuarial Mathematics for Life Contingent Risk. Cambridge University Press.CrossRefGoogle Scholar
Frees, E.W., Carriere, J., Valdez, E. (1996). Annuity valuation with dependent mortality. Journal of Risk and Insurance, 63, 229–261.CrossRefGoogle Scholar
Hosty, G.M., Groves, S.J., Murray, C.A., Shah, M. (2007). Pricing and risk capital in the equity release market. British Actuarial Journal, 14(1), 41–109.CrossRefGoogle Scholar
IBM Global Business Services (2010). An Actuarial Analysis of FHA Home Equity Conversion Mortgage Loans In the Mutual Mortgage Insurance Fund Fiscal Year 2010. Available at: http://www.hud.gov/offices/hsg/rmra/oe/rpts/actr/2010actr_hecm.pdf.Google Scholar
Institute of Actuaries (2005a). Equity release report 2005. Volume 1: Main Report. Available at http://www.actuaries.org.uk/research-and-resources/documents/equity-release-report-2005-volume-1-main-report.Google Scholar
Institute of Actuaries (2005b). Equity release report 2005. Volume 2: Technical supplement: pricing considerations. Available at http://www.actuaries.org.uk/research-and-resources/documents/equity-release-report-2005-volume-2-technical-supplement-pricing-co.Google Scholar
Jagger, C., Sutton, C.J. (1991). Death after marital bereavement – is the risk increased? Statistics in Medicine, 10, 395–404.CrossRefGoogle ScholarPubMed
Ji, M., Hardy, M.R., Li, J.S.-H. (2011). Markovian approaches to joint-life mortality. North American Actuarial Journal, 15(3), 357–376.CrossRefGoogle Scholar
Lee, R., Carter, L. (1992). Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87, 659–671.Google Scholar
Li, J.S.-H., Hardy, M.R., Tan, K.S. (2010). On pricing and hedging the no-negative-equity-guarantee in equity release mechanisms. Journal of Risk and Insurance, 77, 499–522.Google Scholar
Miles, W. (2010). Clustering in U.K. Home Price Volatility. Journal of Housing Research, 20(1).Google Scholar
Rickayzen, B.D., Walsh, D.E.P. (2002). A multi-state model of disability for the United Kingdom: implications for future need for long-term care for the elderly. British Actuarial Journal, 8, 341–393.CrossRefGoogle Scholar
Rodda, D.T., Lam, K., Youn, A. (2004). Stochastic modeling of Federal Housing Administration Home Equity Conversion Mortgages with low-cost refinancing. Real Estate Economics, 32, 589–617.CrossRefGoogle Scholar
US Department of Housing and Urban Development (2003). Refinancing premium, national loan limit, and long-term care premium waiver for FHA's HECM Program, available at http://www.huduser.org/portal/publications/HSGFIN/Refining_Premium.html.Google Scholar
US Department of Housing and Urban Development (2008). A turning point in the history of HUD's Home Equity Conversion Mortgage program, available at http://reversemortgagemedia.com/ch1.pdf.Google Scholar
Youn, H., Shemyakin, A. (1999). Pricing practices for joint last survivor insurance. Proceedings of American Statistical Association, 34–38.Google Scholar
Young, M., Benjamin, B., Wallis, C. (1963). The mortality of widowers. Lancet, 2, 454–456.CrossRefGoogle ScholarPubMed
Zhai, D.H. (2000). Reverse mortgage securitizations: understanding and gauging the risks. New York: Moody's Investors Service.Google Scholar