On the valuation of reverse mortgages with regular tenure payments
AbstractFor 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 51 (2012)
Issue (Month): 2 ()
Contact details of provider:
Web page: http://www.elsevier.com/locate/inca/505554
Reverse mortgages; Annuity payments; Option pricing; Dimension reduction;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ruth Hancock, 1998. "Can housing wealth alleviate poverty among Britain's older population?," Fiscal Studies, Institute for Fiscal Studies, vol. 19(3), pages 249-272, August.
- Sharon S Yang, 2011. "Securitisation and Tranching Longevity and House Price Risk for Reverse Mortgage Products," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan, vol. 36(4), pages 648-674, October.
- Chen, Hua & Cox, Samuel H. & Wang, Shaun 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, Elsevier, vol. 46(2), pages 371-384, April.
- Michel Denuit & Pierre Devolder & Anne-Cécile Goderniaux, 2007. "Securitization of Longevity Risk: Pricing Survivor Bonds With Wang Transform in the Lee-Carter Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(1), pages 87-113.
- Hong-Chih Huang & Chou-Wen Wang & Yuan-Chi Miao, 2011. "Securitisation of Crossover Risk in Reverse Mortgages," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan, vol. 36(4), pages 622-647, October.
- Olivia S. Mitchell & John Piggott, 2004.
"Unlocking Housing Equity in Japan,"
NBER Working Papers
10340, National Bureau of Economic Research, Inc.
- Mitchell, Olivia S. & Piggott, John, 2004. "Unlocking housing equity in Japan," Journal of the Japanese and International Economies, Elsevier, vol. 18(4), pages 466-505, December.
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Hilliard, Jimmy E. & Reis, Jorge, 1998. "Valuation of Commodity Futures and Options under Stochastic Convenience Yields, Interest Rates, and Jump Diffusions in the Spot," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(01), pages 61-86, March.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Peter Chinloy & Isaac F. Megbolugbe, 1994. "Reverse Mortgages: Contracting and Crossover Risk," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 22(2), pages 367-386.
- Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 299-318, December.
- Brouhns, Natacha & Denuit, Michel & Vermunt, Jeroen K., 2002. "A Poisson log-bilinear regression approach to the construction of projected lifetables," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 373-393, December.
- Ashok Bardhan & Raša Karapandža & Branko Urošević, 2006. "Valuing Mortgage Insurance Contracts in Emerging Market Economies," The Journal of Real Estate Finance and Economics, Springer, vol. 32(1), pages 9-20, February.
- Koissi, Marie-Claire & Shapiro, Arnold F. & Hognas, Goran, 2006. "Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 1-20, February.
- Melnikov, Alexander & Romaniuk, Yulia, 2006. "Evaluating the performance of Gompertz, Makeham and Lee-Carter mortality models for risk management with unit-linked contracts," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 310-329, December.
- Ronald Lee & Timothy Miller, 2001. "Evaluating the performance of the lee-carter method for forecasting mortality," Demography, Springer, vol. 38(4), pages 537-549, November.
- Edward J. Szymanoski, 1994. "Risk and the Home Equity Conversion Mortgage," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 22(2), pages 347-366.
- Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
- Johnny Siu-Hang Li & Mary R. Hardy & Ken Seng Tan, 2010. "On Pricing and Hedging the No-Negative-Equity Guarantee in Equity Release Mechanisms," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 499-522.
- Renshaw, A. E. & Haberman, S., 2003. "Lee-Carter mortality forecasting with age-specific enhancement," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 255-272, October.
- James Kau & Donald Keenan, 1999. "Catastrophic Default and Credit Risk for Lending Institutions," Journal of Financial Services Research, Springer, vol. 15(2), pages 87-102, March.
- Kau, James B, et al, 1992. "A Generalized Valuation Model for Fixed-Rate Residential Mortgages," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 24(3), pages 279-99, August.
- Kau, James B, et al, 1995. "The Valuation at Origination of Fixed-Rate Mortgages with Default and Prepayment," The Journal of Real Estate Finance and Economics, Springer, vol. 11(1), pages 5-36, July.
- Chinloy, Peter & Cho, Man & Megbolugbe, Isaac F, 1997. "Appraisals, Transaction Incentives, and Smoothing," The Journal of Real Estate Finance and Economics, Springer, vol. 14(1-2), pages 89-111, Jan.-Marc.
- Case, Karl E & Shiller, Robert J, 1989.
"The Efficiency of the Market for Single-Family Homes,"
American Economic Review,
American Economic Association, vol. 79(1), pages 125-37, March.
- Karl E. Case & Robert J. Shiller, 1989. "The Efficiency of the Market for Single-Family Homes," NBER Working Papers 2506, National Bureau of Economic Research, Inc.
- Bruce Mizrach, 2008. "Jump and Cojump Risk in Subprime Home Equity Derivatives," Departmental Working Papers 200802, Rutgers University, Department of Economics.
- Linda S. Klein & C.F. Sirmans, 1994. "Reverse Mortgages and Prepayment Risk," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 22(2), pages 409-431.
- Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
- Yang, Sharon S. & Yue, Jack C. & Huang, Hong-Chih, 2010. "Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 254-270, February.
- Yang, Sharon S. & Wang, Chou-Wen, 2013. "Pricing and securitization of multi-country longevity risk with mortality dependence," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 157-169.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.