Developing equity release markets: risk analysis for reverse mortgages and home reversions. (English) Zbl 1412.91028

Summary: Equity release products are sorely needed in an aging population with high levels of home ownership. There has been a growing literature analyzing risk components and capital adequacy of reverse mortgages in recent years. However, little research has been done on the risk analysis of other equity release products, such as home reversion contracts. This is partly due to the dominance of reverse mortgage products in equity release markets worldwide. In this article we compare cash flows and risk profiles from the provider’s perspective for reverse mortgage and home reversion contracts. An at-home/in long-term care split termination model is employed to calculate termination rates, and a vector autoregressive (VAR) model is used to depict the joint dynamics of economic variables including interest rates, house prices, and rental yields. We derive stochastic discount factors from the no arbitrage condition and price the no negative equity guarantee in reverse mortgages and the lease for life agreement in the home reversion plan accordingly. We compare expected payoffs and assess riskiness of these two equity release products via commonly used risk measures: value-at-risk (VaR) and conditional value-at-risk (CVaR).


91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
Full Text: DOI


[1] Abraham, J.; Hendershott, P., Bubbles in Metropolitan Housing Markets, Journal of Housing Research, 7, 191-208, (1994)
[2] Ang, A.; Piazzesi, M., A No-Arbitrage Vector Autoregression of Term Structure Dynamics with Macroeconomic and Latent Variables, Journal of Monetary Economics, 50, 745-787, (2003)
[3] Ang, A.; Piazzesi, M.; Wei, M., What Does the Yield Curve Tell Us about GDP Growth?, Journal of Econometrics, 131, 359-403, (2006) · Zbl 1337.91058
[4] Equity Release Product, (2005)
[5] Boehm, T. P.; Ehrhardt, M. C., Reverse Mortgage and Interest Rate Risk, Journal of the American Real Estate and Urban Economics Association, 22, 387-408, (1994)
[6] Bridge, C.; Adams, T.; Phibbs, P.; Mathews, M.; Kendig, H., Reverse Mortgages and Older People: Growth Factors and Implications for Retirement Decisions, (2010)
[7] Brownfield, C., An Actuarial Approach to Home Equity Release, Actuaries Magazine, (2012)
[8] Chang, C.; Wang, C.; Yang, C., The Effects of Macroeconomic Factors on Pricing Mortgage Insurance Contracts, Journal of Risk and Insurance, 79, 867-895, (2012)
[9] Chen, H.; Cox, S. H.; Wang, S. S., Is the Home Equity Conversion Program 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, (2010) · Zbl 1231.91154
[10] Chinloy, P.; Megbolugbe, I. F., Reverse Mortgages: Contracting and Crossover Risk, Real Estate Economics, 22, 367-386, (1994)
[11] Cho, D., Risk Management and Payout Design of Reverse Mortgage. Honor thesis, (2012), University of New South Wales
[12] Chow, M. H.; Szymanoski, E. J.; Diventi, T. R., Applying Survival Analysis Techniques to Loan Terminations for HUD’s Reverse Mortgage Insurance Program. Proceedings of the 13th Northeast SAS Users Group Conference
[13] Cochrane, J. H.; Piazzesi, M., Bond Risk Premia, American Economic Review, 95, 138-160, (2005)
[14] Cunningham, D. F.; Hendershott, P. F., Pricing FHA Mortgage Default Insurance, 1382, (1986)
[15] Daykin, C. D.; Pentikainen, T.; Pesonen, M., Practical Risk Theory for Actuaries, (1994), London: Chapman and Hall, London · Zbl 1140.62345
[16] Media Release: Australia’s Reverse Mortgage Market Reaches \(3bn at 31 December 2010. SEQUAL Deloitte Research Report, May 27, (2011\)
[17] Response to Productivity Commission Draft Report: Caring for Older Australians. Deloitte report prepared for Homesafe Solutions Pty Ltd, March 17, (2011)
[18] Media Release: Australia’s Reverse Mortgage Market Reaches \(3.3bn at 31 December 2011. SEQUAL Deloitte Research Report, June 4, (2012\)
[19] Hoevenaars, R., Strategic Asset Allocation and Asset Liability Management. Ph.D. dissertation, (2008), Maastricht University
[20] Huang, H.-C.; Wang, C.-W.; Miao, Y.-C, Securitization of Crossover Risk in Reverse Mortgages, Geneva Papers on Risk and Insurance–Issues and Practice, 36, 622-647, (2011)
[21] An Actuarial Analysis of FHA Home Equity Conversion Mortgage Loans in the Mutual Mortgage Insurance Fund Fiscal Year 2010, (2010)
[22] Equity release report 2005. Volume 2: Technical Supplement: Pricing Considerations, (2005), LondonUK: Institute of Actuaries, LondonUK
[23] Ivanov, V.; Kilian, L., A Practitioner’s Guide to Lag Order Selection for VAR Impulse Response Analysis, Studies in Nonlinear Dynamics and Econometrics, 9, 1-34, (2005) · Zbl 1081.91575
[24] Ji, M.; Hardy, M. R.; Li, J. S.-H., A Semi-Markov Multiple State Model for Reverse Mortgage Terminations, Annals of Actuarial Science, 6, 235-257, (2012)
[25] Kau, J.; Keenan, D. C.; Muller, W. J. III; Epperson, J. F., A Generalized Valuation Model for Fixed-Rate Residential Mortgages, Journal of Money, Credit and Banking, 24, 279-299, (1992)
[26] Kilian, L., Impulse Response Analysis in Vector Autoregressions with Unknown Lag Order, Journal of Forecasting, 20, 161-179, (2001)
[27] Lee, P., A General Framework for Stochastic Investigations of Mortality and Investment Risks. Paper presented at Wilkiefest, Heriot-Watt University
[28] Li, J. S.-H.; Hardy, M. R.; Tan, K. S., On Pricing and Hedging the No-Negative-Equity-Guarantee in Equity Release Mechanisms, Journal of Risk and Insurance, 77, 499-522, (2010)
[29] Lin, X. S.; Tan, K. S., Valuation of Equity-Indexed Annuities under Stochastic Interest Rates, North American Actuarial Journal, 7, 72-91, (2003) · Zbl 1084.60530
[30] Loeys, J.; Panigirtzoglou, P.; Ribeiro, R. M., Longevity: A Market in the Making. J. P, (2007), London: Morgan Research Publication, London
[31] Lütkepohl, H.; Ma, S.; Deng, Y., New Introduction to Multiple Time Series Analysis, (2005), Cambridge: Cambridge University Press, Cambridge
[32] Ma, S.; Kim, G.; Lew, K., Estimating Reverse Mortgage Insurer’s Risk Using Stochastic Models
[33] Muellbauer, J.; Murphy, A., Booms and Busts in the UK Housing Market, Economic Journal, 107, 1701-1727, (1997)
[34] Move Beyond the HECM in Equity Release Markets? Oliver Wyman Financial Services technique report, (2005)
[35] Reifner, U.; Clerc-Renaud, S.; Pérez-Carrillo, E. F.; Tiffe, A.; Knobloch, M., Study on Equity Release Schemes in the EU, Part I: Country Reports. Institut für Finanzdienstleistungen e.V., Hamburg, (2009)
[36] Rodda, D. T.; Lam, K.; Youn, A., Stochastic Modeling of Federal Housing Administration Home Equity Conversion Mortgages with Low-Cost Refinancing, Real Estate Economics, 32, 589-617, (2004)
[37] Shao, A.; Sherris, M.; Hanewald, K., Equity Release Products allowing for Individual House Price Risk. Working paper, University of New South Wales
[38] Sherris, M.; Sun, D., Risk Based Capital and Pricing for Reverse Mortgages Revisited. Working paper, University of New South Wales
[39] Sims, C. A., Macroeconomics and Reality, Econometrica, 48, 1-48, (1980)
[40] Sims, C. A.; Stock, J. H.; Watson, M. W., Inference in Linear Time Series Models with Some Unit Roots, Econometrica, 58, 113-144, (1990) · Zbl 0724.62087
[41] Sixsmith, A.; Sixsmith, J., Ageing in Place in the United Kingdom, Ageing International, 32, 219-235, (2008)
[42] Szymanoski, E. J. Jr, Risk and the Home Equity Conversion Mortgage, Journal of the American Real Estate and Urban Economics Association, 22, 347-366, (1994)
[43] Szymanoski, E.; Enriquez, J. C.; DiVenti, T. R., Home Equity Conversion Mortgage Terminations: Information to Enhance the Developing Secondary Market, Cityscape: A Journal of Policy Development and Research, 9, 5-45, (2007)
[44] Tatsiramos, K., Residential Mobility and Housing Adjustment of Older Households in Europe, 2435, (2006)
[45] Tilse, C.; Setterlund, D.; Wilson, J.; Rosenman, L., Minding the Money: A Growing Responsibility for Informal Carers, Ageing and Society, 25, 215-227, (2005)
[46] Tsai, C.; Kuo, W.; Chen, W.-K., Early Surrender and the Distribution of Policy Reserves, Insurance: Mathematics and Economics, 31, 429-445, (2001) · Zbl 1031.62092
[47] Valadez, R. M., The Housing Bubble and the GDP: A Correlation Perspective, Journal of Case Research in Business & Economics, 3, 1-18, (2010)
[48] Wang, L.; Valdez, E. A.; Piggott, J., Securitization of Longevity Risk in Reverse Mortgages, North American Actuarial Journal, 12, 345-371, (2008)
[49] Yang, S., Securitisation and Tranching Longevity and House Price Risk for Reverse Mortgage Products, Geneva Papers on Risk and Insurance-Issues and Practice, 36, 648-674, (2011)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.