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An alternative approach to the calibration of the Vasicek and CIR interest rate models via generating functions

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  • Marianito R. Rodrigo
  • Rogemar S. Mamon

Abstract

We propose a new method to calibrate the Vasicek and Cox--Ingersoll--Ross interest rate models from bond prices. We define an appropriate generating function and derive recursive relations between the derivatives of the generating function and the bond prices. The parameters of the Vasicek and CIR models are then obtained by solving a system of linearly independent equations arising from the recursive relations. We include numerical results that show the method's accuracy when bond prices generated from the exact formulas are used.

Suggested Citation

  • Marianito R. Rodrigo & Rogemar S. Mamon, 2014. "An alternative approach to the calibration of the Vasicek and CIR interest rate models via generating functions," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1961-1970, November.
    • Handle: RePEc:taf:quantf:v:14:y:2014:i:11:p:1961-1970
    DOI: 10.1080/14697688.2013.765062
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    References listed on IDEAS

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    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. Anna Rita Bacinello & Fulvio Ortu & Patrizia Stucchi, 1996. "Valuation of sinking-fund bonds in the Vasicek and CIR frameworks*Financial support from Murst Fondo 40% on 'Modelli di struttura a termine dei tassi d'interesse' is gratefully acknowledged," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(4), pages 269-394.
    3. Robert J. Elliott & John van der Hoek, 2001. "Stochastic flows and the forward measure," Finance and Stochastics, Springer, vol. 5(4), pages 511-525.
    4. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
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    Cited by:

    1. Zhao, Yixing & Mamon, Rogemar & Gao, Huan, 2018. "A two-decrement model for the valuation and risk measurement of a guaranteed annuity option," Econometrics and Statistics, Elsevier, vol. 8(C), pages 231-249.

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