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Valuation of reverse mortgages in the Spanish market for foreign residents

    David Atance   Affiliation
    ; Ana Debón   Affiliation
    ; Iván De La Fuente   Affiliation

Abstract

The continuous growth in life expectancy, besides to the difficult economic and financial situation of the public pension system in Spain, makes reverse mortgages an attractive solution for providing additional income to retirees. However, despite being almost 20 years old, the Spanish market remains immature. Consequently, providers face significant risks, due to factors such as interest rates, housing prices, and longevity. Numerous tourists visit Spain, and many retire there, obtaining legal residence. Therefore, lenders could be interested in marketing reverse mortgages to foreign residents. Nevertheless, the longevity risk faced by these lenders may differ depending on the nationality of the borrower, and profits and losses could vary. Consequently, we propose a methodology for comparing the pricing of reverse mortgages in Spain by considering differences in longevity risk. Specifically, we calculate the amount offered by three types of reverse mortgages to customers of different nationalities, genders, and ages with contracts made in Spain. Our conclusions are pertinent to Spanish lenders since the results indicate that, in general, a Spanish lender would assume a slightly larger risk when lending reverse mortgages to borrowers of the selected nationalities, regardless of other considerations, such as legal issues, which are not addressed in this article.


First published online 31 October 2023

Keyword : reverse mortgage, longevity risk, lump sum, income stream, Lee-Carter, foreign residents, mortality

How to Cite
Atance, D., Debón, A., & De La Fuente, I. (2024). Valuation of reverse mortgages in the Spanish market for foreign residents. Technological and Economic Development of Economy, 30(1), 46–73. https://doi.org/10.3846/tede.2023.20159
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References

Alai, D. H., Chen, H., Cho, D., Hanewald, K., & Sherris, M. (2014). Developing equity release markets: Risk analysis for reverse mortgages and home reversions. North American Actuarial Journal, 18(1), 217–241. https://doi.org/10.1080/10920277.2014.882252

Ang, A., & Piazzesi, M. (2003). A no–arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables. Journal of Monetary Economics, 50(4), 745–787. https://doi.org/10.1016/S0304-3932(03)00032-1

Atance, D., Debón, A., & Navarro, E. (2020). A comparison of forecasting mortality models using resampling methods. Mathematics, 8(9), Article 1550. https://doi.org/10.3390/math8091550

Ayuso, M., Bravo, J. M., & Holzmann, R. (2017a). Addressing longevity heterogeneity in pension scheme design and reform. Journal of Finance and Economics, 6(1), 1–21. https://doi.org/10.2139/ssrn.2879785

Ayuso, M., Bravo, J. M., & Holzmann, R. (2017b). On the heterogeneity in longevity among socioeconomic groups: Scope, trends, and implications for earnings–related pension schemes. Global Journal of Human Social Sciences–Economics, 17(1), 31–57. https://doi.org/10.2139/ssrn.2810471

Ayuso, M., Bravo, J. M., & Holzmann, R. (2021). Getting life expectancy estimates right for pension policy: period versus cohort approach. Journal of Pension Economics & Finance, 20(2), 212–231. https://doi.org/10.1017/S1474747220000050

Banco de España. (2017). Guía de acceso a la hipoteca inversa. https://www.bde.es/f/webbde/Secciones/Publicaciones/Folletos/Ficheros/GUIA.pdf

Barbieri, M., Wilmoth, J. R., Shkolnikov, V. M., Glei, D., Jasilionis, D., Jdanov, D., Boe, C., Riffe, T., Grigoriev, P., & Winant, C. (2015). Data resource profile: the human mortality database (HMD). International Journal of Epidemiology, 44(5), 1549–1556. https://doi.org/10.1093/ije/dyv105

Barrieu, P., Bensusan, H., El Karoui, N., Hillairet, C., Loisel, S., Ravanelli, C., & Salhy, Y. (2012). Understanding, modelling and managing longevity risk: Key issues and main challenges. Scandinavian Actuarial Journal, 2012(3), 203–231. https://doi.org/10.1080/03461238.2010.511034

Black, F., Derman, E., & Toy, W. (1990). A one–factor model of interest rates and its application to treasury bond options. Financial Analysts Journal, 46(1), 33–39. https://doi.org/10.2469/faj.v46.n1.33

BOE España. (2007). Ley 41/2007 de 7 de diciembre por la que se modifica la Ley 2/1981, de 25 de marzo, de Regulación del Mercado Hipotecario y otras normas del sistema hipotecario y financiero, de regulación de las hipotecas inversas y el seguro de dependencia y por la que se establece determinada norma Tributaria. https://www.boe.es/boe/dias/2007/12/08/pdfs/A50593-50614.pdf

BOE España. (2013). Ley 23/2013 de 23 de diciembre, reguladora del Factor de Sostenibilidad y del Índice de Revalorización del Sistema de Pensiones de la Seguridad Social. https://www.boe.es/buscar/doc.php?id=BOE-A-2013-13617

Boj, E., Claramunt, M. M., & Varea, J. (2022). Reverse mortgage and financial sustainability. Technological and Economic Development of Economy, 28(4), 872–892. https://doi.org/10.3846/tede.2022.16617

Booth, H., Hyndman, R. J., Tickle, L., & De Jong, P. (2006). Lee–Carter mortality forecasting: A multi-country comparison of variants and extensions. Demographic Research, 15, 289–310. https://doi.org/10.4054/DemRes.2006.15.9

Booth, H., Maindonald, J., & Smith, L. (2002). Applying Lee–Carter under conditions of variable mortality decline. Population Studies, 56(3), 325–336. https://doi.org/10.1080/00324720215935

Bowers, N., Gerber, H., Hickman, J., Jones, D., & Nesbitt, C. (1987). Actuarial mathematics (vol. 41). The Society of Actuaries. https://doi.org/10.1017/S0071368600009812

Bravo, J. M., Ayuso, M., Holzmann, R., & Palmer, E. (2021). Addressing the life expectancy gap in pension policy. Insurance: Mathematics and Economics, 99, 200–221. https://doi.org/10.1016/j.insmatheco.2021.03.025

Brouhns, N., Denuit, M., & Vermunt, J. K. (2002). A poisson log–bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics, 31(3), 373–393. https://doi.org/10.1016/S0167-6687(02)00185-3

Cairns, A. J., Blake, D., & Dowd, K. (2006). A two–factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance, 73(4), 687–718. https://doi.org/10.1111/j.1539-6975.2006.00195.x

Cairns, A. J., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Ong, A., & Balevich, I. (2009). 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. https://doi.org/10.1080/10920277.2009.10597538

Chen, H., Cox, S. H., & Wang, S. 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, 46(2), 371–384. https://doi.org/10.1016/j.insmatheco.2009.12.003

Chetty, R., Stepner, M., Abraham, S., Lin, S., Scuderi, B., Turner, N., Bergeron, A., & Cutler, D. (2016). The association between income and life expectancy in the United States, 2001–2014. The Journal of the American Medical Association, 315(16), 1750–1766. https://doi.org/10.1001/jama.2016.4226

Chinloy, P., & Megbolugbe, I. F. (1994). Reverse mortgages: contracting and crossover risk. Real Estate Economics, 22(2), 367–386. https://doi.org/10.1111/1540-6229.00638

Cho, D., Hanewald, K., & Sherris, M. (2015). Risk analysis for reverse mortgages with different payout designs. Asia Pacific Journal of Risk and Insurance, 9(1), 77–105. https://doi.org/10.1515/apjri-2014-0012

Coale, A., & Guo, G. (1989). Revised regional model life tables at very low levels of mortality. Population Index, 55, 613–643. https://doi.org/10.2307/3644567

Coale, A. J., & Kisker, E. E. (1990). Defects in data on old–age mortality in the United States: New procedures for calculating mortality schedules and life tables at the highest ages. In Asian and Pacific Population Forum (Vol. 4, pp. 1–31).

Consejo General del Notariado. (2021). Centro de información estadística del notariado. http://www.notariado.org/liferay/web/cien/estadisticas-al-completo

Consumer Financial Protection Bureau. (2012). Report to congress on reverse mortgages. Iowa City, IA.

Cossette, H., Delwarde, A., Denuit, M., Guillot, F., & Marceau, É. (2007). Pension plan valuation and mortality projection: a case study with mortality data. North American Actuarial Journal, 11(2), 1–34. https://doi.org/10.1080/10920277.2007.10597445

Costa-Font, J. (2013). Housing-related well-being in older people: The impact of environmental and financial influences. Urban Studies, 50(4), 657–673. https://doi.org/10.1177/0042098012456247

Cox, J. C., Ingersoll Jr, J. E., & Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica, 53(2), 385–407. https://doi.org/10.2307/1911242

Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229–263. https://doi.org/10.1016/0304-405X(79)90015-1

Choinière-Crèvecoeur, I., & Michaud, P. C. (2023). Reverse mortgages and financial literacy. Journal of Financial Literacy and Wellbeing, 1(1), 79–102. https://doi.org/10.1017/flw.2023.4

Davidoff, T., Gerhard, P., & Post, T. (2017). Reverse mortgages: What homeowners (don’t) know and how it matters. Journal of Economic Behavior & Organization, 133, 151–171. https://doi.org/10.1016/j.jebo.2016.11.007

de la Fuente, I., Navarro, E., & Serna, G. (2023). Proposal for calculating regulatory capital requirements for reverse mortgages. Socio-Economic Planning Sciences, 88, Article 101659. https://doi.org/10.1016/j.seps.2023.101659

de la Fuente, I., Navarro, E., & Serna, G. (2021). Estimating regulatory capital requirements for reverse mortgages. an international comparison. International Review of Economics & Finance, 74, 239–252. https://doi.org/10.1016/j.iref.2021.03.001

de la Fuente, I., Navarro, E., & Serna, G. (2020). Reverse mortgage risks. time evolution of var in lump-sum solutions. Mathematics, 8(11), Article 2043. https://doi.org/10.3390/math8112043

Debón, A., Martínez-Ruiz, F., & Montes, F. (2010). A geostatistical approach for dynamic life tables: The effect of mortality on remaining lifetime and annuities. Insurance: Mathematics and Economics, 47(3), 327–336. https://doi.org/10.1016/j.insmatheco.2010.07.007

Debón, A., Montes, F., & Puig, F. (2008). Modelling and forecasting mortality in Spain. European Journal of Operational Research, 189(3), 624–637. https://doi.org/10.1016/j.ejor.2006.07.050

Debón, A., Montes, F., & Sala, R. (2013). Pricing reverse mortgages in Spain. European Actuarial Journal, 3(1), 23–43. https://doi.org/10.1007/s13385-013-0071-y

Debón, A., Haberman, S., Montes, F., & Otranto, E. (2021). Do different models induce changes in mortality indicators? that is a key question for extending the lee-carter model. International Journal of Environmental Research and Public Health, 18(4). https://doi.org/10.3390/ijerph18042204

Denuit, M., & Goderniaux, A.-C. (2005). Closing and projecting lifetables using log–linear models. Bulletin of the Swiss Association of Actuaries, 29.

Dillingh, R., Prast, H., Rossi, M., & Brancati, C. U. (2013). The psychology and economics of reverse mortgage attitudes: evidence from the Netherlands. Center for Research on Pensions and Welfare Policies.

Di Lorenzo, E., Piscopo, G., Sibillo, M., & Tizziano, R. (2021). Reverse mortgages through artificial intelligence: New opportunities for the actuaries. Decisions in Economics and Finance, 44, 23–35. https://doi.org/10.1007/s10203-020-00274-y

Di Lorenzo, E., Piscopo, G., Sibillo, M., & Tizziano, R. (2022). Reverse mortgage and risk profile awareness: Proposals for securitization. Applied Stochastic Models in Business and Industry, 38(2), 353–369. https://doi.org/10.1002/asmb.2664

Doukhan, P., Pommeret, D., Rynkiewicz, J., & Salhi, Y. (2017). A class of random field memory models for mortality forecasting. Insurance: Mathematics and Economics, 77, 97–110. https://doi.org/10.1016/j.insmatheco.2017.08.010

European Union. (2004). Council Directive 2004/113/EC of 13 december 2004 implementing the principle of equal treatment between men and women in the access to and supply of goods and services. Brussels, Belgium.

Eurostat. (2019). Ageing Europe looking at the lives of older people in the EU. https://ec.europa.eu/eurostat/en/web/products-statistical-books/-/KS-02-19-681

Fornero, E., Rossi, M., & Urzí Brancati, M. C. (2016). Explaining why, right or wrong, (Italian) households do not like reverse mortgages. Journal of Pension Economics & Finance, 15(2), 180–202. https://doi.org/10.1017/S1474747215000013

Guillen, M., & Vidiella-i-Anguera, A. (2005). Forecasting Spanish natural life expectancy. Risk Analysis, 25(5), 1161–1170. https://doi.org/10.1111/j.1539-6924.2005.00671.x

Haberman, S., & Renshaw, A. (2009). On age-period-cohort parametric mortality rate projections. Insurance: Mathematics and Economics, 45(2), 255–270. https://doi.org/10.1016/j.insmatheco.2009.07.006

Haberman, S., & Renshaw, A. (2011). A comparative study of parametric mortality projection models. Insurance: Mathematics and Economics, 48(1), 35–55. https://doi.org/10.1016/j.insmatheco.2010.09.003

Hainaut, D. (2018). A neural–network analyzer for mortality forecast. ASTIN Bulletin, 48(2), 481–508. https://doi.org/10.1017/asb.2017.45

Hancock, R. (1998a). Housing wealth, income and financial wealth of older people in Britain. Ageing & Society, 18(1), 5–33. https://doi.org/10.1017/S0144686X97006685

Hancock, R. (1998b). Can housing wealth alleviate poverty among Britain’s older population? Fiscal Studies, 19(3), 249–272. https://doi.org/10.1111/j.1475-5890.1998.tb00287.x

Hobcraft, J., Menken, J., & Preston, S. (1985). Age, period, and cohort effects in demography: A review. In Cohort analysis in social research (pp. 89–135). Springer. https://doi.org/10.1007/978-1-4613-8536-3_4

Hong, W. H., Yap, J. H., Selvachandran, G., Thong, P. H., & Son, H. L. (2021). Forecasting mortality rates using hybrid Lee–Carter model, artificial neural network and random forest. Complex & Intelligent Systems, 7(1), 163–189. https://doi.org/10.1007/s40747-020-00185-w

Huang, H.-C., Wang, C.-W., & Miao, Y.-C. (2011). Securitisation of crossover risk in reverse mortgages. The Geneva Papers on Risk and Insurance–Issues and Practice, 36(4), 622–647. https://doi.org/10.1057/gpp.2011.23

Human Mortality Database. (2021). University of California, USA, Max Planck Institute for Demographic Research, Germany. www.mortality.org

Hunt, A., & Blake, D. (2020). Identifiability in age/period/cohort mortality models. Annals of Actuarial Science, 14(2), 500–536. https://doi.org/10.1017/S1748499520000123

Hyndman, R., Athanasopoulos, G., Bergmeir, C., Caceres, G., Chhay, L., O’Hara-Wild, M., Petropoulos, F., Razbash, S., Wang, E., & Yasmeen, F. (2021). Forecast: Forecasting functions for time series and linear models. R package version 8.15.

Hyndman, R. J., & Khandakar, Y. (2008). Automatic time series forecasting: the forecast package for R. Journal of Statistical Software, 26(3), 1–22. https://doi.org/10.18637/jss.v027.i03

Ji, M., Hardy, M., & Li, J. S.-H. (2012). A semi-markov multiple state model for reverse mortgage terminations. Annals of Actuarial Science, 6(2), 235–257. https://doi.org/10.1017/S1748499512000061

Jones, B. L., & Mereu, J. A. (2000). A family of fractional age assumptions. Insurance: Mathematics and Economics, 27(2), 261–276. https://doi.org/10.1016/S0167-6687(00)00052-4

Jones, B. L., & Mereu, J. A. (2002). A critique of fractional age assumptions. Insurance: Mathematics and Economics, 30(3), 363–370. https://doi.org/10.1016/S0167-6687(02)00104-X

Kibele, E., Scholz, R., & Shkolnikov, V. M. (2008). Low migrant mortality in Germany for men aged 65 and older: Fact or artifact? European Journal of Epidemiology, 23(6), 389–393. https://doi.org/10.1007/s10654-008-9247-1

Kogure, A., Li, J., & Kamiya, S. (2014). A bayesian multivariate risk-neutral method for pricing reverse mortgages. North American Actuarial Journal, 18(1), 242–257. https://doi.org/10.1080/10920277.2013.872983

Lee, R. (2000). The Lee–Carter method for forecasting mortality, with various extensions and applications. North American Actuarial Journal, 4(1), 80–91. https://doi.org/10.1080/10920277.2000.10595882

Lee, R. D., & Carter, L. R. (1992). Modeling and forecasting US mortality. Journal of the American Statistical Association, 87(419), 659–671. https://doi.org/10.1080/01621459.1992.10475265

Lee, Y.-T., Kung, K.-L., & Liu, I.-C. (2018). Profitability and risk profile of reverse mortgages: A cross–system and cross–plan comparison. Insurance: Mathematics and Economics, 78, 255–266. https://doi.org/10.1016/j.insmatheco.2017.09.019

Lee, Y. T., & Shi, T. (2022). Valuation of reverse mortgages with surrender: A utility approach. The Journal of Real Estate Finance and Economics, 65, 593–621. https://doi.org/10.1007/s11146-021-09869-7

Lee, Y.-T., Wang, C.-W., & Huang, H.-C. (2012). On the valuation of reverse mortgages with regular tenure payments. Insurance: Mathematics and Economics, 51(2), 430–441. https://doi.org/10.1016/j.insmatheco.2012.06.008

Levantesi, S., & Pizzorusso, V. (2019). Application of machine learning to mortality modeling and forecasting. Risks, 7(1), 26. https://doi.org/10.3390/risks7010026

Lima, E., Riffe, T., Queiroz, B., & Acrani, L. T. (2017). An evaluation of adult death registration coverage in the Human Mortality Database and World Health Organization mortality data. IUSSP, Cape Town.

Mayer, C., & Simons, K. (1994). Home equity conversions and the liquidity of housing wealth. Journal of the American Real Estate and Urban Economics Association, 22(2), 235–255. https://doi.org/10.1111/1540-6229.00634

Ministerio de Fomento España. (2020). Valor tasado de la vivienda. https://www.fomento.gob.es/BE2/?nivel=2orden=35000000

Niepmann, F., & Schmidt–Eisenlohr, T. (2022). Foreign currency loans and credit risk: Evidence from US banks. Journal of International Economics, 135, Article 103558. https://doi.org/10.1016/j.jinteco.2021.103558

Nigri, A., Levantesi, S., Marino, M., Scognamiglio, S., & Perla, F. (2019). A deep learning integrated Lee–Carter model. Risks, 7(1), Article 33. https://doi.org/10.3390/risks7010033

Pavía, J. M., & Lledó, J. (2022). Estimation of the combined effects of ageing and seasonality on mortality risk: An application to Spain. Journal of the Royal Statistical Society Series A: Statistics in Society, 185(2), 471–497. https://doi.org/10.1111/rssa.12769

Perks, W. (1932). On some experiments in the graduation of mortality statistics. Journal of the Institute of Actuaries, 63(1), 12–57. https://doi.org/10.1017/S0020268100046680

Perla, F., Richman, R., Scognamiglio, S., & Wüthrich, M. V. (2021). Time–series forecasting of mortality rates using deep learning. Scandinavian Actuarial Journal, 2021(7), 572–598. https://doi.org/10.1080/03461238.2020.1867232

Pitacco, E., Denuit, M., Haberman, S., & Olivieri, A. (2009). Modelling longevity dynamics for pensions and annuity business. Oxford University Press.

R Core Team. (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.

Reed, R., & Gibler, K. M. (2003). The case for reverse mortgages in Australia: Applying the USA experience. In PRRES 2003: Proceedings of the 9th Annual Conference of the Pacific Rim Real Estate Society 2003 (pp. 1–13). Pacific Rim Real Estate Society.

Renshaw, A., Haberman, S., & Hatzopoulos, P. (1996). The modelling of recent mortality trends in United Kingdom male assured lives. British Actuarial Journal, 2(2), 449–477. https://doi.org/10.1017/S1357321700003470

Renshaw, A. E., & Haberman, S. (2006). A cohort–based extension to the Lee–Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38(3), 556–570. https://doi.org/10.1016/j.insmatheco.2005.12.001

Richman, R., & Wüthrich, M. V. (2021). A neural network extension of the Lee–Carter model to multiple populations. Annals of Actuarial Science, 15(2), 346–366. https://doi.org/10.1017/S1748499519000071

Riffe, T. (2015). Reading Human Fertility Database and Human Mortality Database data into R (Technical report TR-2015-004). MPIDR. https://doi.org/10.4054/MPIDR-TR-2015-004

Shan, H. (2011). Reversing the trend: The recent expansion of the reverse mortgage market. Real Estate Economics, 39(4), 743–768. https://doi.org/10.1111/j.1540-6229.2011.00310.x

Shao, A. W., Hanewald, K., & Sherris, M. (2015). Reverse mortgage pricing and risk analysis allowing for idiosyncratic house price risk and longevity risk. Insurance: Mathematics and Economics, 63, 76–90. https://doi.org/10.1016/j.insmatheco.2015.03.026

Sharma, T., French, D., & McKillop, D. (20202. Risk and equity release mortgages in the UK. The Journal of Real Estate Finance and Economics, 64, 274–297. https://doi.org/10.1007/s11146-020-09793-2

Thatcher, A. R., Kannisto, V., & Vaupel, J. W. (1998). The force of mortality at ages 80 to 120. Odense University Press.

Turner, H., & Firth, D. (2020). Generalized nonlinear models in R: An overview of the gnm package. R package version 1.1-1.

Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5(2), 177–188. https://doi.org/10.1016/0304-405X(77)90016-2

Villegas, A. M., Kaishev, V. K., & Millossovich, P. (2018). StMoMo: An R package for stochastic mortality modeling. Journal of Statistical Software, 84(3), 1–38. https://doi.org/10.18637/jss.v084.i03

Wang, C.-W., Huang, H.-C., & Lee, Y.-T. (2016). On the valuation of reverse mortgage insurance. Scandinavian Actuarial Journal, 2016(4), 293–318. https://doi.org/10.1080/03461238.2014.925967

Wang, L., Valdez, E. A., & Piggott, J. (2008). Securitization of longevity risk in reverse mortgages. North American Actuarial Journal, 12(4), 345–371. https://doi.org/10.1080/10920277.2008.10597529

Wang, S. S. (2000). A class of distortion operators for pricing financial and insurance risks. Journal of Risk and Insurance, 67(1), 15–36. https://doi.org/10.2307/253675

Whait, R. B., Lowies, B., Rossini, P., McGreal, S., & Dimovski, B. (2019). The reverse mortgage conundrum: Perspectives of older households in Australia. Habitat International, 94, Article 102073. https://doi.org/10.1016/j.habitatint.2019.102073

Wills, S., & Sherris, M. (2008). Integrating financial and demographic longevity risk models: An Australian model for financial applications (UNSW Australian School of Business Research Paper, 2008ACTL05).

Yang, S. S. (2011). Securitisation and tranching longevity and house price risk for reverse mortgage products. The Geneva Papers on Risk and Insurance–Issues and Practice, 36(4), 648–674. https://doi.org/10.1057/gpp.2011.26