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A Bayesian Analysis of the Cox-Ingersoll-Ross Model

Author

Listed:
  • Dante Amengual

    (Centro de Estudios Monetarios y Financieros)

  • Lluc Puig-Codina

    (Banco de España and University of Alicante)

Abstract

The Cox-Ingersoll-Ross model (CIR) is a diffusion process with widespread applications in economics, finance and population biology. In this paper we first obtain a full Gibbs Sampler for the exact CIR process observed at equidistant times. We do not require the imposition of the Feller condition. We show how to carry out smoothing and handling of missing data. Additionally, the introduction of a tailored single Metropolis-Hastings step allows us to handle irregular and random time intervals. Secondly, we obtain several asymptotic properties which include Local Asymptotic Normality, consistency and asymptotic normality of conditional maximum likelihood estimation and a Bernstein-von Mises theorem. Lastly, we provide an empirical illustration using U.S. Treasury yields under a variety of priors and a comparison with other models such as the Vasicek and the 3/2 models.

Suggested Citation

  • Dante Amengual & Lluc Puig-Codina, 2026. "A Bayesian Analysis of the Cox-Ingersoll-Ross Model," Working Papers 2640, Banco de España.
    • Handle: RePEc:bde:wpaper:2640e
    DOI: https://doi.org/10.53479/44785
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    Keywords

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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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