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European Actuarial Journal
Published in: European Actuarial Journal 1/2013

01-07-2013 | Original Research Paper

Pricing reverse mortgages in Spain

Authors: A. Debón, F. Montes, R. Sala

Published in: European Actuarial Journal | Issue 1/2013

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Abstract

In Spain, as in other European countries, the continuous ageing of the population creates a need for long-term care services and their financing. However, in Spain the development of this kind of services is still embryonic. The aim of this article is to obtain a calculation method for reverse mortgages in Spain based on the fit and projection of dynamic tables for Spanish mortality, using the Lee and Carter model. Mortality and life expectancy for the next 20 years are predicted using the fitted model, and confidence intervals are obtained from the prediction errors of parameters for the mortality index of the model. The last part of the article illustrates an application of the results to calculate the reverse mortgage model promoted by the Spanish Instituto de Crédito Oficial (Spanish State Financial Agency), for which the authors have developed a computer application.
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Footnotes
1
Instituto de Crédito Oficial is a State-owned corporate entity attached to the Ministry of Economy and Finance through the Secretariat of State for the Economy. It has the status of the State’s Financial Agency in Spain. http://​www.​ico.​es.
 
2
National Institute of Statistics, http://​www.​ine.​es.
 
Literature
1.
Blay-Berrueta D (2007) Sistemas de cofinaciaciación de la dependencia: seguro privado frente a hipoteca inversa. Cuadernos de la Fundación, Fundación Mapfre Estudios, Madrid.
2.
Booth H (2006) Demographic forecasting: 1980 to 2005 in review. Int J Forecast 22(3):547–582CrossRef
3.
Booth H, Hyndman R, Tickle L, de Jong P (2006) Lee–Carter mortality forecasting: a multi-country comparison of variants and extensions. Demogr Res 15(9):289–310CrossRef
4.
Booth H, Maindonald J, Smith L (2002) Applying Lee–Carter under conditions of variable mortality decline. Popul Stud 56(3):325–336CrossRef
5.
Booth H, Tickle L (2003) The future aged: new projections of Australia’s ederly population. Popul Stud 22(4):38–44
6.
Brouhns N, Denuit M, Keilegom IV (2005) Bootstrapping Poisson log-bilinear model for mortality forecasting. Scand Actuar J 2005(3):212–224MATHCrossRef
7.
Brouhns N, Denuit M, Vermunt J (2002) A Poisson log-bilinear regression approach to the construction of projected lifetables. Insur Math Econ 31(3):373–393MathSciNetMATHCrossRef
8.
Carter L, Lee R (1992) Modeling and forecasting US sex differentials in mortality. Int J Forecast 8(3):393–411CrossRef
9.
Carter L, Prkawetz A (2001) Examining structural shifs in mortality using the Lee–Carter method. Mpidr wp 2001–2007, Center for Demography and Ecology Information, University of Wisconsin-Madison.
10.
Chinloy P, Megbolugbe I (1994) Reverse mortgages: contracting and crossover. J Am Real Estate Urban Econ Assoc 22(2):367–386CrossRef
11.
Coale A, Guo G (1989) Revisited regional model life tables at very low levels of mortality. Popul Index 55:613–643CrossRef
12.
Coale A, Kisker E (1990) Defects in data old age mortality in the United States: New procedures for calculating approximately accurate mortality schedules and lifes tables at the highest ages. Asian Pac Popul Forum 4:1–31
13.
Cossette H, Delwarde A, Denuit M, Guillot F, Étienne M (2007) Pension plan valuation and mortality projection: a case study with mortality data. N Am Actuar J 11(2):1–34.
14.
Costa-Font J (2009) Ageing in place? exploring elderly people’s housing preferences in Spain. Urban Stud 46(2):295–316CrossRef
15.
Costa-Font J (2013) Housing-related well-being in older people: the impact of environmental and financial influences. Urban Stud 50(4):657–673
16.
17.
18.
D’Amato V, Haberman S, Piscopo G, Russolillo M (2012) Modelling dependent data for longevity projections. Insur Math Econ 51(3):694–701MathSciNetCrossRef
19.
Davidoff T (2012) Can ‘high costs’ justify weak demand for the home equity conversion mortgage? Technical report, available at SSRN
20.
Davidoff T, Welke G (2007) Selection and moral hazard in the reverse mortgage market. Technical report, Haas School of Business, UC Berkeley
21.
Debón A, Montes F, Mateu J, Porcu E, Bevilacqua M (2008) Modelling residuals dependence in dymanic life tables. Comput Stat Data Anal 52(3):3128–3147MATHCrossRef
22.
Debón A, Montes F, Puig F (2008) Modelling and forecasting mortality in Spain. Eur J Oper Res 189(3):624–637MATHCrossRef
23.
Debón A, Montes F, Sala R (2009) Tablas de mortalidad dinámicas. Una aplicación a la hipoteca inversa en España. Fundación ICO. Publicaciones de la Universitat de Valéncia, Valencia
24.
Debón A, Montes F, Martínez-Ruiz F (2011) Statistical methods to compare mortality for a group with non-divergent populations: an application to Spanish regions. Eur Actuar J 1:291–308MathSciNetCrossRef
25.
Delwarde A, Denuit M, Eilers P (2007) Smoothing the Lee–Carter and poisson log-bilinear models for mortality forecasting: a penalized log-likelihood approach. Stat Modell 7(1):29–48MathSciNetCrossRef
26.
Denuit M (2007) Distribution of the random future life expectancies in log-bilinear mortality projections models. Lifetime Data Anal 13(3):381–397MathSciNetMATHCrossRef
27.
Denuit M, Goderniaux A (2004) Closing and projecting lifetables using log-linear models. Mitteilungen. der Schweizerischen Aktuarvereingung 1:29–49
28.
Felipe A, Guillén M, Pérez-Marín A (2002) Recent mortality trends in the Spanish population. Br Actuar J 8(4):757–786.
29.
Forfar D, McCutcheon J, Wilkie A (1988) On graduation by mathematical formula. J Inst Actuar 115(459):1–149CrossRef
30.
Guillen M, Vidiella-i-Anguera A (2005) Forecasting Spanish natural life expectancy. Risk Anal 25(5):1161–1170CrossRef
31.
Heligman L, Pollard J (1980) The age pattern of mortality. J Inst Actuar 107:49–80CrossRef
32.
33.
Horiuchi S, Wilmoth J (1998) Decelaration in the age pattern of mortality at older ages. Demography 35:391–412CrossRef
34.
Hyndman RJ (2008) Forecast: forecasting functions for time series. R package version 1.11
35.
Koissi M, Shapiro A, Hgns G (2006) Evaluating and extending the Lee–Carter model for mortality forecasting confidence interval. Insur Math Econ 38(1):1–20MATHCrossRef
36.
Kutty N (1998) The scope for poverty alleviation among elderly home-owners in the United States through reverse mortgages. Urban Stud 35(1):113–129CrossRef
37.
Lee R (2000) The Lee–Carter method for forecasting mortality, with various extensions and applications. N Am Actuar J 4(1):80–91MathSciNetMATHCrossRef
38.
Lee R, Carter L (1992) Modelling and forecasting US mortality. J Am Stat Assoc 87(419):659–671
39.
Lee R, Nault F (1993) Modeling and forecasting provincial mortality in Canada. Montreal world congress of the International Union for Scientific Study of Population
40.
Lee R, Rofman R (1994) Modelación y Proyección de la mortalidad en Chile. Notas Poblacin 22(59):182–213
41.
Li N, Lee R (2005) Coherent mortality forecast for a group of populations: an extension of the Lee–Carter method. Demography 42(3):575–593CrossRef
42.
Li S-H, Hardy M, Tan K (2009) Uncertainty in mortality forecasting: an extensin to the classical Lee–Carter approach. Astin Bull 31:137–164MathSciNetCrossRef
43.
44.
Liu X, Braun WJ (2010) Investigating mortality uncertainty using the block bootstrap. J Probab Stat 2010:385–399
45.
McNown R, Rogers A (1989) Forecasting mortality: a parametrized time series aproach. Demography 26(4):645–660CrossRef
46.
McNown R, Rogers A (1992) Forecasting cause-specific mortality using time series methods. Int J Forecast 8(3):413–432
47.
Miceli T, Sirmans C (1994) Reverse mortgages and borrower maintenance risk. J Am Real Estate Urban Econ Assoc 22(2):433–450CrossRef
48.
Pedroza C (2006) A bayesian forecasting model: predicting US male mortality. Biostatistics 7(4):530–550MATHCrossRef
49.
Renshaw A, Haberman S (2003) Lee–Carter mortality forecasting: a parallel generalized linear modelling aproach for England and Wales mortality projections. J R Stat Soc C 52(1):119–137MathSciNetMATHCrossRef
50.
51.
Renshaw A, Haberman S (2003) On the forecasting of mortality reduction factors. Insur Math Econ 32(3):379–401MATHCrossRef
52.
Renshaw A, Haberman S (2006) A cohort-based extension to the Lee–Carter model for mortality reduction factors. Insur Math Econ 38(3):556–570MathSciNetMATHCrossRef
53.
Renshaw A, Haberman S (2008) On simulation-based approaches to risk measurement in mortality with specific reference to poisson Lee–Carter modelling. Insur Math Econ 42(2):797–816MATHCrossRef
54.
Shiller R, Weiss A (2000) Moral hazard in home equity conversion. Real Estate Econ 28(1):1–31CrossRef
55.
Skarr D (2008) Financial planner’s guide to the FHA insured home equity conversion mortgage. J Financ Plan 21(5):68–75
56.
Sánchez-Álvarez I, Lpez-Ares S, Quiroga-García R (2007) Diseño de hipotecas inversas en el mercado español. Proyecto 205/05 3, Instituto de Mayores y Servicios Sociales
57.
Taffin C (2006) La hipoteca inversa o vitalicia. Informes externos, Asociación Hipotecaria Española
58.
Thatcher A, Kannisto V, Andreev K (2002) The survivor ratio method for estimating numbers at high ages. Demogr Res 6(1):1–18CrossRef
59.
Thatcher A, Kannisto V, Vaupel J (1998) The force of mortality at ages 80 to 120. Odense University Press, Odense
60.
Tuljapurkar S, Li N, Boe C (2000) A universal pattern of mortality decline in the G7 countries. Nature 405(6788):789–792CrossRef
61.
Wang L, Valdez E, Piggott J (2008) Securization of longevity risk in reverse mortgages. N Am Actuar J 12(4):345–370MathSciNetCrossRef
62.
Wilmoth J (1993) Computational methods for fitting and extrapolating the Lee–Carter model of mortality change. Technical report, Departament of Demography, University of California, Berkeley
63.
Wilmoth J (1996) Health and mortality among elderly populations, chapter mortality projections for Japan: a comparison of four methods. Oxford University Press, Oxford, pp 266–287
Metadata
Title
Pricing reverse mortgages in Spain
Authors
A. Debón
F. Montes
R. Sala
Publication date
01-07-2013
Publisher
Springer-Verlag
Published in
European Actuarial Journal / Issue 1/2013
Print ISSN: 2190-9733
Electronic ISSN: 2190-9741
DOI
https://doi.org/10.1007/s13385-013-0071-y

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