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

Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez

Abstract


This paper proposes an expression of the value of an annuity with payments of 1 unit each when the interest rate is random. In order to attain this objective, we proceed on the assumption that the non-central moments of the capitalization factor are known. Specifically, to calculate the value of these annuities, we propose two different expressions. First, we suppose that the random interest rate is normally distributed; then, we assume that it follows the beta distribution. A practical application of these two methodologies is also implemented using the R statistical software.

Keywords


annuity; random interest rate; non-central moments

Full Text:

PDF

References


Calot, G. (1974). Curso de estadística descriptiva. Madrid: Ed. Paraninfo.

Cruz Rambaud, S. and Valls Martínez, M.C. (2002). “La determinación de la tasa de actualización para la valoración de empresas”. Análisis Financiero, 87, 72-85.

Fisz, M. (1963). Probability theory and mathematical statistics, 3rd Edition. New York: John Wiley and Sons, Inc.

Mood, A.M.; Graybill, F.A. and Boes, D.C. (1974). Introduction to the theory of statistics, 3rd Edition. New York: McGraw Hill.

Rice, J.A. (1995). Mathematical statistics and data analysis (2nd Ed.). California: Ed. Duxbury Press.

Spiegel, M.R. (1975). Probability and Statistics. United States of America: Ed. McGraw-Hill.

Suárez Suárez, A.S. (2005). Decisiones óptimas de inversión y financiación en la empresa. Madrid: Ed. Pirámide.

Villalón, J.G.; Martínez Barbeito, J. and Seijas Macías, J.A. (2009). "Sobre la evolución de los tantos de interés”. XVII Jornadas de Asepuma y V Encuentro Internacional, 17, 1, 502.




DOI: http://dx.doi.org/10.23755/rm.v28i1.25

Refbacks

  • There are currently no refbacks.


Copyright (c) 2015 Salvador Cruz Rambaud, Fabrizio Maturo, Ana María Sánchez

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.