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AnnuityRIR: an R-package to approximate the value of an annuity according to the non-central moments of the capitalization factor

Author

Listed:
  • Salvador Cruz Rambaud

    (University of Almería)

  • Fabrizio Maturo

    (University of Campania Luigi Vanvitelli)

  • Ana Maria Sánchez Pérez

    (University of Almería)

  • Massimo Squillante

    (University of Sannio)

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 .

Suggested Citation

  • Salvador Cruz Rambaud & Fabrizio Maturo & Ana Maria Sánchez Pérez & Massimo Squillante, 2023. "AnnuityRIR: an R-package to approximate the value of an annuity according to the non-central moments of the capitalization factor," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(3), pages 347-366, October.
    • Handle: RePEc:spr:qualqt:v:57:y:2023:i:3:d:10.1007_s11135-020-01058-7
    DOI: 10.1007/s11135-020-01058-7
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    References listed on IDEAS

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    1. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, February.
    2. Date, P. & Mamon, R. & Wang, I.C., 2007. "Valuation of cash flows under random rates of interest: A linear algebraic approach," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 84-95, July.
    3. Zaks, Abraham, 2001. "Annuities under random rates of interest," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 1-11, February.
    4. De Schepper, A. & De Vylder, F. & Goovaerts, M. & Kaas, R., 1992. "Interest randomness in annuities certain," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 271-281, December.
    5. De Schepper, A. & Goovaerts, M., 1992. "Some further results on annuities certain with random interest," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 283-290, December.
    6. Daniel Dufresne, 2007. "Stochastic Life Annuities," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(1), pages 136-157.
    7. Burnecki, Krzysztof & Marciniuk, Agnieszka & Weron, Aleksander, 2003. "Annuities under random rates of interest--revisited," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 457-460, July.
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