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Application of the CIR Model for Spot Short Interest Rates Modelling on the Polish Market

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Cyclostationarity: Theory and Methods – IV (CSTA 2017)

Part of the book series: Applied Condition Monitoring ((ACM,volume 16))

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Abstract

The paper examines the estimation of the instantaneous Polish short term interest rate using one of the most popular stochastic differential models for studying the short interest rates, i.e. the Cox, Ingersoll, Ross model (1985) (henceforth CIR). We propose a new approach to estimating an instantaneous short interest rate: our attention is shifted from the whole term structure of the interest rate to the artificial notation of the short rate. In particular, the method focusing on determining a relationship between an observed instantaneous short interest rate and a certain (abstract) unobserved instantaneous rate which is defined as an interest rate demanded over an infinitesimally short period under the risk-neutral measure. To estimate the CIR model, we use a state space model in which estimates of the latent variables and model parameters are obtained by applying an Expectation-Maximisation algorithm combined with particle filters (PF). In practice, the instantaneous rate is identified with an overnight rate, therefore during the research we have adopted daily domestic interbank lending rates which are represented by interest rates on overnight deposits (WIBOR ON). To facilitate the discussion, simulated data are also employed. The obtained results prove the correctness and attractiveness of the method under consideration.

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Notes

  1. 1.

    It is worth noting that Bessel function approaches the plus infinity rapidly, which hinders the optimization routines. However the issue will not be addressed in this paper.

  2. 2.

    We use the Euler discretization with correction, known as “the full truncation scheme” studied in (Higham et al. 2002).

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Acknowledgements

This work is supported by the National Centre of Science granted on the basis of decision number DEC-2013/11/D/HS4/04014.

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Authors and Affiliations

  1. Kielce University of Technology, Kielce, Poland

    Katarzyna Brzozowska-Rup

Authors
  1. Katarzyna Brzozowska-Rup
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Correspondence to Katarzyna Brzozowska-Rup .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, National School of Engineers of Sfax, Sfax, Tunisia

    Fakher Chaari

  2. Institute of Mathematics, Cracow Technical University, Krakow, Poland

    Jacek Leskow

  3. Faculty of GeoEngineering, Mining and Geology, Wrocław University of Science and Technology, Wroclaw, Poland

    Radoslaw Zimroz

  4. Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wroclaw, Poland

    Agnieszka Wyłomańska

  5. AGH University of Science and Technology, Krakow, Poland

    Anna Dudek

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Brzozowska-Rup, K. (2020). Application of the CIR Model for Spot Short Interest Rates Modelling on the Polish Market. In: Chaari, F., Leskow, J., Zimroz, R., Wyłomańska, A., Dudek, A. (eds) Cyclostationarity: Theory and Methods – IV. CSTA 2017. Applied Condition Monitoring, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-030-22529-2_11

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  • DOI: https://doi.org/10.1007/978-3-030-22529-2_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22528-5

  • Online ISBN: 978-3-030-22529-2

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