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Interest rates calibration with a CIR model

Author

Listed:
  • Giuseppe Orlando
  • Rosa Maria Mininni
  • Michele Bufalo

Abstract

Purpose - The purpose of this paper is to model interest rates from observed financial market data through a new approach to the Cox–Ingersoll–Ross (CIR) model. This model is popular among financial institutions mainly because it is a rather simple (uni-factorial) and better model than the former Vasicek framework. However, there are a number of issues in describing interest rate dynamics within the CIR framework on which focus should be placed. Therefore, a new methodology has been proposed that allows forecasting future expected interest rates from observed financial market data by preserving the structure of the original CIR model, even with negative interest rates. The performance of the new approach, tested on monthly-recorded interest rates data, provides a good fit to current data for different term structures. Design/methodology/approach - To ensure a fitting close to current interest rates, the innovative step in the proposed procedure consists in partitioning the entire available market data sample, usually showing a mixture of probability distributions of the same type, in a suitable number of sub-sample having a normal/gamma distribution. An appropriate translation of market interest rates to positive values has been introduced to overcome the issue of negative/near-to-zero values. Then, the CIR model parameters have been calibrated to the shifted market interest rates and simulated the expected values of interest rates by a Monte Carlo discretization scheme. We have analysed the empirical performance of the proposed methodology for two different monthly-recorded EUR data samples in a money market and a long-term data set, respectively. Findings - Better results are shown in terms of the root mean square error when a segmentation of the data sample in normally distributed sub-samples is considered. After assessing the accuracy of the proposed procedure, the implemented algorithm was applied to forecast next-month expected interest rates over a historical period of 12 months (fixed window). Through an error analysis, it was observed that our algorithm provides a better fitting of the predicted expected interest rates to market data than the exponentially weighted moving average model. A further confirmation of the efficiency of the proposed algorithm and of the quality of the calibration of the CIR parameters to the observed market interest rates is given by applying the proposed forecasting technique. Originality/value - This paper has the objective of modelling interest rates from observed financial market data through a new approach to the CIR model. This model is popular among financial institutions mainly because it is a rather simple (uni-factorial) and better model than the former Vasicek model (Section 2). However, there are a number of issues in describing short-term interest rate dynamics within the CIR framework on which focus should be placed. A new methodology has been proposed that allows us to forecast future expected short-term interest rates from observed financial market data by preserving the structure of the original CIR model. The performance of the new approach, tested on monthly data, provides a good fit for different term structures. It is shown how the proposed methodology overcomes both the usual challenges (e.g. simulating regime switching, clustered volatility and skewed tails), as well as the new ones added by the current market environment (particularly the need to model a downward trend to negative interest rates).

Suggested Citation

  • Giuseppe Orlando & Rosa Maria Mininni & Michele Bufalo, 2019. "Interest rates calibration with a CIR model," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 20(4), pages 370-387, September.
  • Handle: RePEc:eme:jrfpps:jrf-05-2019-0080
    DOI: 10.1108/JRF-05-2019-0080
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    Citations

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    Cited by:

    1. Giuseppe Orlando & Rosa Maria Mininni & Michele Bufalo, 2020. "Forecasting interest rates through Vasicek and CIR models: A partitioning approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(4), pages 569-579, July.
    2. Bufalo, Michele & Orlando, Giuseppe, 2023. "A three-factor stochastic model for forecasting production of energy materials," Finance Research Letters, Elsevier, vol. 51(C).
    3. Wulan Anggraeni & Sudradjat Supian & Sukono & Nurfadhlina Binti Abdul Halim, 2022. "Earthquake Catastrophe Bond Pricing Using Extreme Value Theory: A Mini-Review Approach," Mathematics, MDPI, vol. 10(22), pages 1-22, November.
    4. Marco Di Francesco & Kevin Kamm, 2021. "How to handle negative interest rates in a CIR framework," Papers 2106.03716, arXiv.org.
    5. Wulan Anggraeni & Sudradjat Supian & Sukono & Nurfadhlina Abdul Halim, 2023. "Single Earthquake Bond Pricing Framework with Double Trigger Parameters Based on Multi Regional Seismic Information," Mathematics, MDPI, vol. 11(3), pages 1-44, January.
    6. Mohamed Ben Alaya & Ahmed Kebaier & Djibril Sarr, 2021. "Deep Calibration of Interest Rates Model," Papers 2110.15133, arXiv.org, revised Sep 2024.
    7. Giuseppe Orlando & Michele Bufalo, 2022. "A generalized two‐factor square‐root framework for modeling occurrences of natural catastrophes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(8), pages 1608-1622, December.
    8. Giuseppe Orlando & Michele Bufalo, 2021. "Interest rates forecasting: Between Hull and White and the CIR#—How to make a single‐factor model work," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(8), pages 1566-1580, December.
    9. Giuseppe Orlando & Michele Bufalo, 2021. "Empirical Evidences on the Interconnectedness between Sampling and Asset Returns’ Distributions," Risks, MDPI, vol. 9(5), pages 1-35, May.
    10. Ascione, Giacomo & Mehrdoust, Farshid & Orlando, Giuseppe & Samimi, Oldouz, 2023. "Foreign Exchange Options on Heston-CIR Model Under Lévy Process Framework," Applied Mathematics and Computation, Elsevier, vol. 446(C).

    More about this item

    Keywords

    Calibration; Forecasting and simulation; Interest rates; CIR model; G12; E43; E47;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications

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