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On the valuation of reverse mortgages with regular tenure payments. (English) Zbl 1284.91550

Summary: For the valuation of reverse mortgages with tenure payments, this article proposes a specific analytic valuation framework with mortality risk, interest rate risk, and housing price risk that helps determine fair premiums when the present value of premiums equals the present value of contingent losses. The analytic valuation of reverse mortgages with tenure payments is more complex than the valuation with a lump sum payment. This study therefore proposes a dimension reduction technique to achieve a closed-form solution for reverse annuity mortgage insurance, conditional on the evolution of interest rates. The technique provides strong accuracy, offering important implications for lenders and insurers.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91B30 Risk theory, insurance (MSC2010)
91G40 Credit risk
91D20 Mathematical geography and demography
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[1] Bardhan, A.; Karapandza, R.; Urosevic, B., Valuing mortgage insurance contracts in emerging market economics, Journal of real estate finance and economics, 32, 1, 9-20, (2006)
[2] Bollerslev, T., Generalized autoregressive conditional heteroskedasticity, Journal of econometrics, 31, 307-327, (1986) · Zbl 0616.62119
[3] Brouhns, N.; Denuit, M.; Vermunt, J., A Poisson log-bilinear approach to the construction of projected lifetables, Insurance: mathematics and economics, 31, 3, 373-393, (2002) · Zbl 1074.62524
[4] Bühlmann, H.; Delbaen, F.; Embrechts, P.; Shiryaev, A.N., No-arbitrage, change of measure and conditional esscher transforms, CWI quarterly, 9, 291-317, (1996) · Zbl 0943.91037
[5] Cairns, A.J.G., Blake, D., Dowd, K., 2004, Pricing frameworks for securitization of mortality risk, in: Proceedings of the 14th International AFIR Colloquium, pp. 509-540. · Zbl 1162.91403
[6] Cairns, A.J.G.; Blake, D.; Dowd, K.; Coughlan, G.D.; Epstein, D.; Ong, A.; Balevich, I., A quantitative comparison of stochastic mortality models using data from england and wales and the united states, North American actuarial journal, 13, 1, 1-35, (2009)
[7] Case, K.E.; Shiller, R.J., The efficiency of the market for single-family homes, American economic review, 79, 1, 125-137, (1989)
[8] Chen, M.C.; Chang, C.C.; Lin, S.K.; Shyu, S.D., Estimation of housing price jump risks and their impact on the valuation of mortgage insurance contacts, Journal of risk and insurance, 77, 2, 399-422, (2010)
[9] Chen, H.; Cox, S.H.; Wang, S.S., 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, 2, 371-384, (2010) · Zbl 1231.91154
[10] Chinloy, P.; Cho, M.; Megbolugbe, I.F., Appraisals, transaction incentives, and smoothing, Journal of real estate finance and economics, 14, 1, 89-112, (1997)
[11] Chinloy, P.; Megbolugbe, I.F., Reverse mortgages: contracting and crossover risk, Journal of the American real estate and urban economics association, 22, 2, 367-386, (1994)
[12] Cox, J.C.; Ingersoll, J.E.; Ross, S.A., A theory of the term structure of interest rate, Econometrica, 53, 385-407, (1985) · Zbl 1274.91447
[13] Dahl, M., Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts, Insurance: mathematics and economics, 35, 1, 113-136, (2004) · Zbl 1075.62095
[14] Denuit, M.; Devolder, P.; Goderniaux, A.C., Securitization of longevity risk: pricing survivor bonds with Wang transform in the lee – carter framework, Journal of risk and insurance, 74, 1, 87-113, (2007)
[15] Hancock, R., Can housing wealth alleviate poverty among britain’s older population?, Fiscal studies, 19, 3, 249-272, (1998)
[16] Hilliard, J.E.; Reis, J., Valuation of commodity futures and options under stochastic convenience yields, interest rates, and jump diffusions in the spot, Journal of financial and quantitative analysis, 33, 1, 61-86, (1998)
[17] Hosios, A.J.; Pesando, J.E., Measuring prices in resale housing markets in Canada: evidence and implications, Journal of housing economics, 1, 4, 303-317, (1991)
[18] 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, 4, 622-647, (2011)
[19] Ito, T.; Hirono, K.N., Efficiency of the Tokyo housing market, Bank of Japan monetary and economic studies, 11, 1, 1-32, (1993)
[20] Kau, J.B.; Keenan, D.C., An overview of the option-theoretic pricing of mortgages, Journal of housing research, 6, 2, 217-244, (1995)
[21] Kau, J.B.; Keenan, D.C., Catastrophic default and credit risk for lending institutions, Journal of finance services research, 15, 2, 87-102, (1999)
[22] Kau, J.B.; Keenan, D.C.; Muller, W.J., An option-based pricing model of private mortgage insurance, Journal of risk and insurance, 60, 2, 288-299, (1993)
[23] Kau, J.B.; Keenan, D.C.; Muller, W.J.; Epperson, J., A generalized valuation model for fixed-rate residential mortgages, Journal of money, credit and banking, 24, 3, 279-299, (1992)
[24] Kau, J.B.; Keenan, D.C.; Muller, W.J.; Epperson, J., The valuation at origination of fixed-rate mortgages with default and prepayment, Journal of real estate finance and economics, 11, 1, 5-36, (1995)
[25] Klein, L.S.; Sirmans, C.F., Reverse mortgages and prepayment risk, Journal of the American real estate and urban economics association, 22, 2, 409-431, (1994)
[26] Koissi, M.C.; Shapiro, A.F.; Hognas, G., Evaluating and extending the lee – carter model for mortality forecasting: bootstrap confidence interval, Insurance: mathematics and economics, 38, 1, 1-20, (2006) · Zbl 1098.62138
[27] Lee, R.D., The lee – carter method for forecasting mortality, with various extensions and applications, North American actuarial journal, 4, 1, 80-93, (2000) · Zbl 1083.62535
[28] Lee, R.D.; Carter, L.R., Modeling and forecasting US mortality, Journal of the American statistical association, 87, 419, 659-675, (1992) · Zbl 1351.62186
[29] Lee, R.; Miller, T., Evaluating the performance of the lee – carter method for forecasting mortality, Demography, 38, 4, 537-549, (2001)
[30] Li, J.S.-H.; Hardy, M.R.; Tan, K.S., On pricing and hedging the no-negative-equity guarantee in equity release mechanisms, The journal of risk and insurance, 77, 2, 499-522, (2010)
[31] Ma, S., Kim, G., Lew, K., 2007, Estimating reverse mortgage insurer’s risk using stochastic models, in: Presented at the Asia-Pacific Risk and Insurance Association 2007 Annual Meeting.
[32] Matsuda, K., 2004, Introduction to option pricing with fourier transform: option pricing with exponential Lévy models, Working Paper, Graduate School and University Center of the City University of New York.
[33] Melnikov, A.; Romaniuk, Y., Evaluating the performance of Gompertz, Makeham and lee – carter mortality models for risk management with unit-linked contracts, Insurance: mathematics and economics, 39, 3, 310-329, (2006) · Zbl 1151.91577
[34] Milevsky, M.A.; Promislow, S.D., Mortality derivatives and the option to annuities, Insurance: mathematics and economics, 29, 3, 299-318, (2001) · Zbl 1074.62530
[35] Mitchell, O.; Piggott, J., Unlocking housing equity in Japan, Journal of the Japanese and international economies, 18, 4, 466-505, (2004)
[36] Mizrach, B., 2008, Jump and co-jump risk in subprime home equity derivatives, Working Paper, Department of Economics, Rutgers University.
[37] Nothaft, F.E., Gao, A.H., Wang, G.H.K., 1995, The stochastic behavior of the Freddie Mac/Fannie Mae conventional mortgage home price index, American Real Estate and Urban Economics Association Annual Meeting, San Francisco.
[38] Phillips, W.; Gwin, S.B., Reverse mortgage, Transactions of the society of actuaries, 44, 289-323, (1992)
[39] Renshaw, A.; Haberman, S., Lee – carter mortality forecasting with age specific enhancement, Insurance: mathematics and economics, 33, 2, 255-272, (2003) · Zbl 1103.91371
[40] Rowlingson, K., Living poor to die rich or spending the kids’ inheritance? attitudes to assets and inheritance in later life, Journal of social policy, 35, 2, 175-192, (2006)
[41] Shreve, S., Stochastic calculus for finance II: continuous-time models, (2004), Springer New York · Zbl 1068.91041
[42] Siu, T.; Tong, H.; Yang, H., On pricing derivatives under GARCH models: a dynamic gerber – shiu approach, North American actuarial journal, 8, 17-31, (2004) · Zbl 1085.91531
[43] Svoboda, S., Interest rate modelling, (2004), Palgrave Macmillan New York
[44] Szymanoski, E.J., Risk and the home equity conversion mortgage, Journal of American real estate and urban economics association, 22, 2, 347-366, (1994)
[45] Tse, Y.K., Modelling reverse mortgages, Asia Pacific journal of management, 12, 2, 79-95, (1995)
[46] Wang, S.S., A class of distortion operators for pricing financial and insurance risks, Journal of risk and insurance, 67, 1, 15-36, (2000)
[47] Wang, L., Valdez, E.A., Piggott, J., 2007, Securitization of longevity risk in reverse mortgages, SSRN Working Paper.
[48] Wang, C.W.; Huang, H.C.; Liu, I.C., A quantitative comparison of the Lee-Carter model with non-Gaussian innovations for long-term mortality data, Geneva papers on risk and insurance-issues and practice, 36, 4, 675-696, (2011)
[49] Weinrobe, M., An insurance plan to guarantee reverse mortgage, Journal of risk and insurance, 55, 4, 644-659, (1988)
[50] Yang, S.S., Securitization and tranching longevity and house price risk for reverse mortgage products, Geneva papers on risk and insurance-issues and practice, 36, 4, 648-674, (2011)
[51] Yang, T.T.; Buist, H.I.; Megbolugbe, F., An analysis of ex-ante probability of mortgage prepayment and default, Real estate economics, 26, 4, 651-676, (1998)
[52] Yang, S.S.; Yue, C.J.; Huang, H.C., Modeling longevity risk using a principal component approach: a comparison with existing stochastic mortality models, Insurance: mathematics and economics, 46, 1, 254-270, (2010) · Zbl 1231.91254
[53] Zhai, D.H., 2000, Reverse mortgage securitizations: understanding and gauging the risks, Structure Finance, Moody’s Investors Service Special Report.
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