Abstract
The aim of this paper is to design the package of the R statistical software called “Annuity Random Interest Rate”, referred hereinafter as AnnuityRIR, in order to calculate the value of an n-annuity with payments of one unit each when the interest rate is random. To do this, we have employed different approaches; the two main methodologies treated in this study consider that all non-central moments of the capitalization factor are known, or contrarily some of them are unknown. Consequently, five different approaches have been developed and the practical application of the proposed methods is reflected in this paper by pricing an annuity with a random risk-free interest rate during the last ten years. The version is available from CRAN: https://cran.r-project.org/web/packages/AnnuityRIR/index.html.
Highlights
An annuity is a sequence of n payments separated by the same interval of time (Gerber 1997)
This paper introduces and illustrates some new approaches to estimate the present value of an n-payment unitary annuity with random interest rate
The approaches proposals presented in this paper have been developed by using different and alternative procedures mainly based on the knowledge of some non-central moments of the random interest rate
Summary
An annuity is a sequence of n payments separated by the same interval of time (Gerber 1997). The appraisal of an investment, or the development of loan repayments schemes, in this paper, we will not derive the interest rate as a stochastic process over time but we will use the distribution function of the random variable obtained starting from the current values exhibited by the interest rate. In this way, the employment of interest rates as a part of the stochastic discount factors allows a more accurate pricing of any operation (Date et al 2007; Dufresne 2007). We will introduce some new methodologies to calculate the present value of an annuity (immediate and due)
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