Breakeven Determination of Loan Limits for Reverse Mortgages under Information Asymmetry

  • Ming Pu
  • Gang-Zhi Fan
  • Yongheng Deng


Since the loan limit of a reverse mortgage is a major concern for the borrower as well as the lender, this paper attempts to develop an option-based model to evaluate the loan limits of reverse mortgages. Our model can identify several crucial determinants for reverse mortgage loan limits, such as initial housing price, expected housing price growth, house price volatility, mortality distribution, and interest rates. We also pay special attention to the important implication of mortgage lenders’ informational advantage over reverse mortgage borrowers concerning housing market risk. In reverse mortgage markets, the elderly borrowers typically hold far less, relative to the lenders, or no information about the lenders’ underlying mortgage pools. Such information asymmetry leads these two categories of market participants to generate different perspectives on the risk of the collateralized properties, which can be identified to be important in determining the maximum loan amounts of reverse mortgages. We further find that the maximum loan amount of a reverse mortgage decreases in the correlation between the returns on the pooled underlying housing properties but increases with the number of the pooled mortgages.


Reverse Mortgages Heterogeneous Beliefs Information Asymmetry Loan Limits 


G21 G22 J14 



We would like to thank Chun-seob Lee, Steven Li, Dogan Tirtiroglu, Seow Eng Ong, Kwong Wing Chau, Zhi Dong, an anonymous referee and participants at the 2011 Asian Real Estate Society-American Real Estate and Urban Economics Society Joint International Conference and the 2011 Asia-Pacific Real Estate Research Symposium for helpful comments. Any errors are our own.


  1. Addae-Dapaah, K., & Leong, K. M. (1996). Housing finance for the ageing Singapore population: the potential of the home equity conversion scheme. Habitat International, 1996(20), 109–120.CrossRefGoogle Scholar
  2. Archer, W. R., Elmer, P. J., Harrison, D. M., & Ling, D. C. (2002). Determinants of multifamily mortgage default. Real Estate Economics, 30(3), 445–473.CrossRefGoogle Scholar
  3. Basak, S. (2000). A model of dynamic equilibrium asset pricing with heterogeneous beliefs and extraneous risk. Journal of Economic Dynamics and Control, 24, 63–95.CrossRefGoogle Scholar
  4. Basak, S., & Croitoru, B. (2000). Equilibrium mispricing in a capital market with portfolio constraints. Review of Financial Studies, 13, 715–748.CrossRefGoogle Scholar
  5. Basak, S., & Croitoru, B. (2006). On the role of arbitrageurs in rational markets. Journal of Financial Economics, 81, 143–173.CrossRefGoogle Scholar
  6. Bishop, T. B. & Shan, H. (2008). “Reverse Mortgages: A Closer Look at HECM Loans,” National Bureau of Economic Research, Available from,%20Shan%20FINAL.pdf.
  7. Bonanno, G., & Nehring, K. (1999). How to make sense of the common prior assumption under incomplete information. International Journal of Game Theory, 28, 409–434.CrossRefGoogle Scholar
  8. Bond, P., Musto, D. K., & Yilmaz, B. (2009). Predatory mortgage lending. Journal of Financial Economics, 94, 412–427.CrossRefGoogle Scholar
  9. Brockett, P. L. (1991). Information theoretic approach to actuarial science: a unification and extension of relevant theory and applications. Transactions of the Society of Actuaries, 43, 73–135.Google Scholar
  10. Brunson, A., Kau, J. B., & Keenan, D. C. (2001). A fixed-rate mortgage valuation in three state variables. Journal of Fixed Income, 11(1), 17–28.CrossRefGoogle Scholar
  11. Chinloy, P., & Megbolugbe, I. F. (1994). Reverse mortgages: contracting and crossover risk. Journal of the American Real Estate and Urban Economics Association, 22, 367–386.CrossRefGoogle Scholar
  12. Chou, K. L., Chow, N. W. S., & Chi, I. (2006). Willingness to consider applying for reverse mortgage in Hong Kong Chinese middle-aged homeowners. Habitat International, 30, 716–727.CrossRefGoogle Scholar
  13. Ciochetti, B. A., & Vandell, K. D. (1999). The performance of commercial mortgages. Real Estate Economics, 27, 27–61.CrossRefGoogle Scholar
  14. Currie, I. D., Durban, M., & Eilers, P. H. C. (2004). Smoothing and forecasting mortality rates. Statistical Modelling, 4(4), 279–298.CrossRefGoogle Scholar
  15. Davis, E. P. (1997). Can Pension Systems Cope? Population Ageing and Retirement Income Provision in the European Union, London, Royal Institute of International Affairs.Google Scholar
  16. Deng, Y. (1997). Mortgage termination: an empirical hazard model with stochastic term structure. Journal of Real Estate Finance and Economics, 14(3), 309–331.CrossRefGoogle Scholar
  17. Deng, Y., Quigley, J., & Van Order, R. (2000). Mortgage terminations, heterogeneity and the exercise of mortgage options. Econometrica, 68(2), 275–307.CrossRefGoogle Scholar
  18. Detemple, J., & Murthy, S. (1997). Equilibrium asset prices and no-arbitrage with portfolio constraints. Review of Financial Studies, 10, 1133–1174.CrossRefGoogle Scholar
  19. Eichholtz, P., Hoesli, M., MacGregor, B., & Nanthakumaran, N. (1995). Real estate portfolio diversification by property type and region. Journal of Property Finance, 6(3), 39–59.CrossRefGoogle Scholar
  20. Epperson, J. F., Kau, J. B., Keenan, B. C., & Muller, W. J. (1985). Pricing default risk in mortgages. Journal of the American Real Estate and Urban Economics Association, 13(3), 261–272.CrossRefGoogle Scholar
  21. Faruqee, H., & Mühleisen, M. (2003). Population aging in Japan: demographic shock and fiscal sustainability. Japan and the World Economy, 15, 185–210.CrossRefGoogle Scholar
  22. Gan, J., & Riddiough, T. J. (2008). Monopoly and information advantage in the residential mortgage market. Review of Financial Studies, 21(6), 2677–2703.CrossRefGoogle Scholar
  23. Hammond, C. M. (1993). Reverse mortgages: a financial planning device for the elderly. Elder Law Journal, 1, 75–112.Google Scholar
  24. Hayashida, C. T., & Sasaki, H. (1986). The Musashino plan: Japan’s home equity conversion program for social, health, and financial services. Journal of Cross-Cultural Gerontology, 3, 255–276.CrossRefGoogle Scholar
  25. Hilliard, J. E., Kau, J. B., & Slawson, V. C. (1998). Valuing prepayment and default in a fixed rate mortgage: a bivariate binomial options pricing technique. Real Estate Economics, 26(3), 431–468.CrossRefGoogle Scholar
  26. Kau, J. B., & Keenan, D. C. (1995). An overview of the option-theoretic pricing of mortgages. Journal of Housing Research, 6, 217–244.Google Scholar
  27. Kau, J. B., Keenan, D. C., Muller, W. J., & Epperson, J. F. (1992). A generalized valuation model for fixed-rate residential mortgages. Journal of Money, Credit, and Banking, 24(3), 279–299.CrossRefGoogle Scholar
  28. Kau, J. B., Keenan, D. C., Muller, W. J., & Epperson, J. F. (1995). The valuation at origination of fixed-rate mortgages with default and prepayment. Journal of Real Estate Finance and Economics, 11(1), 5–36.CrossRefGoogle Scholar
  29. Kau, J. B., Keenan, D. C., Lyubimov, C., Slawson, V. C. (2011). “Asymmetric information in the subprime mortgage market,” Journal of Real Estate Finance and Economics, Forthcoming.Google Scholar
  30. Kutty, N. (1998). The scope for poverty alleviation among elderly homeowners in the US through reverse mortgages. Urban Studies, 35(1), 113–130.CrossRefGoogle Scholar
  31. Lee, R., & Miller, T. (2001). Evaluating the performance of the Lee-Carter method for forecasting mortality. Demography, 38(4), 537–549.CrossRefGoogle Scholar
  32. Leviton, R. (2001). Reverse mortgage decision-making. Journal of Aging & Social Policy, 13, 1–16.CrossRefGoogle Scholar
  33. Li, Y. S. (2005). The challenges of aging toward Chinese society. Public Administration and Management: An Interactive Journal, 10(3), 248–268.Google Scholar
  34. Li, T. (2007). Heterogeneous beliefs, asset prices and volatility in a pure exchange economy. Journal of Economic Dynamics and Control, 31, 1697–1727.CrossRefGoogle Scholar
  35. Loutskina, E., & Strahan, P. E. (2011). Informed and uninformed investment in housing: The downside of diversification. Review of Financial Studies, 24(5), 1447–1480.CrossRefGoogle Scholar
  36. Ma, S., & Deng, Y. (2011). “Evaluation of Reverse Mortgage Programs in Korea,” National University of Singapore Institute of Real Estate Studies Working Paper Series, IRES2011-027.Google Scholar
  37. Mayer, C., & Simons, K. (1994). Reverse mortgages and the liquidity of housing wealth. Journal of the American Real Estate and Urban Economics Association, 22(2), 235–255.CrossRefGoogle Scholar
  38. Merrill, S., Finkel, M., & Kutty, N. (1994). Beneficiaries from reverse mortgage products for elderly home-owners: an analysis of American housing survey data. Journal of the American Real Estate and Urban Economics Association, 22, 257–299.CrossRefGoogle Scholar
  39. Miao, J. J., & Wang, N. (2007). Investment, consumption and hedging under incomplete markets. Journal of Financial Economics, 86, 608–642.CrossRefGoogle Scholar
  40. Miceli, T. J., & Sirmans, C. F. (1994). Reverse mortgages and borrower maintenance risk. Journal of the American Real Estate and Urban Economics Association, 22, 433–450.CrossRefGoogle Scholar
  41. Mitchell, O. S., & Piggott, J. (2004). Unlocking housing equity in Japan. Journal of the Japanese and International Economies, 18, 466–505.CrossRefGoogle Scholar
  42. Quercia, R. G. (1997). House value appreciation among older homeowners: implications for reverse mortgage programs. Journal of Housing Research, 8(2), 201–223.Google Scholar
  43. Rasmussen, D. W., Megbolugbe, I. F., & Morgan, B. A. (1995). Using the 1990 public use microdata sample to estimate potential demand for reverse mortgage products. Journal of Housing Research, 6(1), 1–23.Google Scholar
  44. Sawyer, C. H. (1996). Reverse mortgages: an innovative tool for elder law attorneys. Stetson Law Review, 26, 617–646.Google Scholar
  45. Scheinkman, J., & Xiong, W. (2003). Overconfidence and speculative bubbles. Journal of Political Economy, 111, 1183–1219.CrossRefGoogle Scholar
  46. Shan, H. (2011). Reversing the trend: the recent expansion of the reverse mortgage market. Real Estate Economics, 39(4), 743–768.CrossRefGoogle Scholar
  47. Shreve, S. E. (2004). Stochastic calculus for finance II: Continuous-time models. New York: Springer.Google Scholar
  48. Syzmanoski, E., Jr. (1994). Risk and home equity conversion mortgage. Journal of the American Real Estate and Urban Economics Association, 22, 347–366.CrossRefGoogle Scholar
  49. Tse, Y. K. (1995). Modelling reverse mortgages. Asia Pacific Journal of Management, 12(2), 79–95.CrossRefGoogle Scholar
  50. Von Weizsäcker, R. K. (1996). Distributive implications of an aging society. European Economic Review, 40, 729–746.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of InsuranceSouthwestern University of Finance and EconomicsChengduChina
  2. 2.Department of Real Estate StudiesKonkuk UniversitySeoulKorea
  3. 3.Institute of Real Estate StudiesNational University of Singapore21 Heng Mui Keng Terrace, #04-02Singapore

Personalised recommendations