Life insurance valuation using exotic options
DOI:
https://doi.org/10.46661/revmetodoscuanteconempresa.4500Keywords:
exotic option, life insurance, digital option, exercise probabilityAbstract
This paper presents the analysis and valuation of an individual, temporary, and leveled-prime life insurance. It starting point is an analogy between contract rules and a financial exotic option. In particular, a cash or nothing option. Several cases are presented from a person with different age and gender, and sensitivity to different probability distributions are tested using Monte Carlo simulation. All cases are adjusted to Argentinean recent data in order to estimate exercise prices, main variable to estimate the contract value. Prime market values used on this work are more than double than the theoretical value found on the exotic option while comparing them to identical contract conditions such as insured amount, time frame and demographic conditions of the individual.
Downloads
References
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637-654. https://doi.org/10.1086/260062
Boletín Oficial de la República Argentina (2018). Legislación y Avisos Oficiales. Superintendencia de Seguros de la Nación. Resolución 697/2018. Recuperado de https://www.boletinoficial.gob.ar/detalleAviso/primera/188883/20180726.
Breslow, N., & Crowley, J. (1974). A Large Sample Study of the Life Table and Product Limit Estimates under Random Censorship. The Annals of Statistics, 2(3), 437-453. https://doi.org/10.1214/aos/1176342705
Casparri, M.T., & García, J. (2010). Algunas innovaciones financieras para La gestión del riesgo global. Buenos Aires: Editorial de la Facultad de Ciencias Económicas de la Universidad de Buenos Aires, Argentina.
Cummins, J.D. (1990). Asset pricing models and insurance ratemaking. ASTIN Bulletin: The Journal of the IAA, 20(2), 125-166. https://doi.org/10.2143/AST.20.2.2005438
Cummins, J.D. (1991). Statistical and financial models of insurance pricing and the insurance firm. The Journal of Risk and Insurance, 58(2), 261-302. https://doi.org/10.2307/253237
D'Arcy, S.P., & Doherty, N.A. (1988). The financial theory of pricing property-liability insurance contracts. SS Huebner Foundation for Insurance Education, Wharton School, University of Pennsylvania. https://doi.org/10.2143/ast.18.2.2014953
del Pozo, E.M. (2001). Modelos de opciones aplicados al seguro (No. 01-09). Madrid: Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
Fernández, P., & Ariño, M.A. (1996). Derivados exóticos. Documento de investigación 308. Centro Internacional de Investigación Financiera (CIIF) y División de Investigación IESE, Universidad de Navarra.
Gaarder, E. (2007). Derivatives: Models on Models. Chichester, United Kingdom: John Wiley & Sons.
García, J.J., Sancha, M.P., Tejero, C., & Toscano, D. (2000). Opciones “exóticas”. Boletín Económico de ICE, 2673, 1-8.
Gatzert, N., & Schmeiser, H. (2006). Implicit options in life insurance: Valuation and risk management. Zeitschrift für die gesamte Versicherungswissenschaft, 95(1), 111-128. https://doi.org/10.1007/BF03353443
Gompertz, B. (1825). On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies. Philosophical Transactions of the Royal Society of London, 115, 513-583. https://doi.org/10.1098/rstl.1825.0026
Hull, J. (2012). Options, Futures and other Derivatives (12ª ed.). Harlow, United Kingdom: Pearson Education Global Edition.
Hull, J. (2014). Introducción a los mercados de futuros y opciones (8ª ed.). Madrid, España: Editorial Pearson.
Kolb, R. (2003). Futures, Options, and Swaps. Oxford, United Kingdom: Blackwell Publishing.
Kolb, R., & Overdahl, J. (2010). Financial derivatives. Pricing and risk management. New Jersey, United States: John Wiley & Sons.
Ley Nº 17.418 (1967). Ley de Seguros. Boletín Oficial de la República, Buenos Aires, Argentina, 30 de agosto de 1967.
Luoma, A., Puustelli, A., & Koskinen, L. (2008). Bayesian analysis of participating life insurance contracts with American-style options. In Proceedings of AFIR Colloquium. http://www.actuaries.org/AFIR/Colloquia/Rome2/Koskinen_Luoma_Puustelli.pdf
Makeham, W.M. (1860). On the Law of Mortality and the Construction of Annuity Tables. The Assurance Magazine and Journal of the Institute of Actuaries, 8(6), 301-310. https://doi.org/10.1017/s204616580000126x
Melinsky, Pellegrinelli y Asoc. (2019). Tablas de mortalidad. Recuperado de http://www.melpel.com.ar/?p=678. Fecha de consulta: 01/08/2019.
Merton, R.C. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science, 4(1), 141-183. https://doi.org/10.2307/3003143
National Vital Statistics Report (2006). United States Life Tables 2003, by Elizabeth Arias. National Vital Statistics Reports, 54(14), 1-40. https://www.cdc.gov/nchs/data/nvsr/nvsr54/nvsr54_14.pdf
Whaley, R. (2006). Derivatives: Markets, Valuation and Risk Management. New Jersey, United States: John Wiley & Sons.
Wilmott, P. (2009). Frequently Asked Questions in Quantitative Finance. London, United Kingdom: John Wiley & Sons.
Yin, R. (2005). Estudo de caso: planejamento e métodos (3ª ed.). Porto Alegre, Brasil: Bookman.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Submission of manuscripts implies that the work described has not been published before (except in the form of an abstract or as part of thesis), that it is not under consideration for publication elsewhere and that, in case of acceptance, the authors agree to automatic transfer of the copyright to the Journal for its publication and dissemination. Authors retain the authors' right to use and share the article according to a personal or instutional use or scholarly sharing purposes; in addition, they retain patent, trademark and other intellectual property rights (including research data).
All the articles are published in the Journal under the Creative Commons license CC-BY-SA (Attribution-ShareAlike). It is allowed a commercial use of the work (always including the author attribution) and other derivative works, which must be released under the same license as the original work.
Up to Volume 21, this Journal has been licensing the articles under the Creative Commons license CC-BY-SA 3.0 ES. Starting from Volume 22, the Creative Commons license CC-BY-SA 4.0 is used.
