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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

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  • Chen, Hua
  • Cox, Samuel H.
  • Wang, Shaun S.

Abstract

The purpose of this paper is to build a modeling and pricing framework to investigate the sustainability of the Home Equity Conversion Mortgage (HECM) program in the United States under realistic economic scenarios, i.e., whether the premium payments cover the fair premiums for the inherent risks in the HECM program. We note that earlier HECM models use static mortality tables, neglecting the dynamics of mortality rates and extreme mortality jumps. The earlier models also assume housing prices follow a geometric Brownian motion, which contradicts the fact that housing prices exhibit strong autocorrelation and varying volatility over time. To solve these problems, we propose a generalized Lee-Carter model with asymmetric jump effects to fit the mortality data, and model the house price index via an ARIMA-GARCH process. We then employ the conditional Esscher transform to price the non-recourse provision of reverse mortgages and compare it with the calculated mortgage insurance premiums. The HECM program turns out to be sustainable based on our model setup and parameter settings.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:insuma:v:46:y:2010:i:2:p:371-384
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    References listed on IDEAS

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    Cited by:

    1. Chen, Hua & MacMinn, Richard & Sun, Tao, 2015. "Multi-population mortality models: A factor copula approach," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 135-146.
    2. Shao, Adam W. & Hanewald, Katja & Sherris, Michael, 2015. "Reverse mortgage pricing and risk analysis allowing for idiosyncratic house price risk and longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 76-90.
    3. Yang, Bowen & Li, Jackie & Balasooriya, Uditha, 2015. "Using bootstrapping to incorporate model error for risk-neutral pricing of longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 16-27.
    4. Lee, Yung-Tsung & Wang, Chou-Wen & Huang, Hong-Chih, 2012. "On the valuation of reverse mortgages with regular tenure payments," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 430-441.
    5. Katja Hanewald & Michael Sherris, 2011. "House Price Risk Models for Banking and Insurance Applications," Working Papers 201118, ARC Centre of Excellence in Population Ageing Research (CEPAR), Australian School of Business, University of New South Wales.
    6. repec:bla:jrinsu:v:83:y:2016:i:4:p:877-912 is not listed on IDEAS
    7. Kim, Joseph H.T. & Li, Johnny S.H., 2017. "Risk-neutral valuation of the non-recourse protection in reverse mortgages: A case study for Korea," Emerging Markets Review, Elsevier, vol. 30(C), pages 133-154.
    8. 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.
    9. repec:bla:jrinsu:v:84:y:2017:i:s1:p:393-415 is not listed on IDEAS
    10. Liu, Yanxin & Li, Johnny Siu-Hang, 2015. "The age pattern of transitory mortality jumps and its impact on the pricing of catastrophic mortality bonds," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 135-150.
    11. Katja Hanewald & Michael Sherris, 2013. "Postcode-Level House Price Models for Banking and Insurance Applications," The Economic Record, The Economic Society of Australia, vol. 89(286), pages 411-425, September.
    12. repec:eee:insuma:v:78:y:2018:i:c:p:255-266 is not listed on IDEAS

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