Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences pp 233-248 | Cite as
Expected Present and Final Value of an Annuity when some Non-Central Moments of the Capitalization Factor are Unknown: Theory and an Application using R
- 671 Downloads
Abstract
The aim of this chapter is the development of three approaches for obtaining the value of an n-payment annuity, with payments of 1 unit each, when the interest rate is random. To calculate the value of these annuities, we are going to assume that only some non-central moments of the capitalization factor are known. The first technique consists in using a tetraparametric function which depends on the arctangent function. The second expression is derived from the so-called quadratic discounting whereas the third approach is based on the approximation of the mathematical expectation of the ratio of two random variables by Mood et al. (1974). A comparison of these methodologies through an application, using the R statistical software, shows that all of them lead to different results.
Keywords
Annuity Random interest rate Tetraparametric function Discount factor Mood et al. approximationReferences
- Calot, G., 1974. Curso de Estadística Descriptiva. Ed. Paraninfo, Madrid.Google Scholar
- Cruz Rambaud, S., Maturo, F., Sánchez Pérez, A.M., 2015. Approach of the value of an annuity when non-central moments of the capitalization factor are known: an R application with interest rates following normal and beta distributions. Ratio Mathematica 28, 15–30.Google Scholar
- Cruz Rambaud, S., Sánchez Pérez, A.M., 2016. Una aproximación del valor de una renta cuando el tipo de interés es aleatorio. XXIV Jornadas de Asepuma y XII Encuentro Internacional Granada (Spain), July 7–8.Google Scholar
- Cruz Rambaud, S., Valls Martínez, M.C., 2002. La determinación de la tasa de actualización para la valoración de empresas. Análisis Financiero 87-2, 72–85.Google Scholar
- Fisz, M., 1963. Probability Theory and Mathematical Statistics. John Wiley and Sons, Inc, New York.zbMATHGoogle Scholar
- Mira Navarro, J.C., 2014. Introducción a las Operaciones Financieras. Creative Commons, http://www.miramegias.com/emodulos/fileadmin/pdfs/mof.pdf.
- Mood, A.M., Graybill, F.A., Boes, D.C., 1974. Introduction to the Theory of Statistics. 3rd Ed. Boston: McGraw Hill.Google Scholar
- Rice, J.A., 2006. Mathematical Statistics and Data Analysis. 2nd Ed. California: Duxbury Press.Google Scholar
- Suárez Suárez, A.S., 2005. Decisiones Óptimas de Inversión y Financiación en la Empresa. 2nd Ed. Madrid, Ed. Pirámide.Google Scholar
- Villalón, J.G., Martínez Barbeito, J., Seijas Macías, J.A., 2009. Sobre la evolución de los tantos de interés. XVII Jornadas de Asepuma y V Encuentro Internacional 17, 1–502.Google Scholar