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The Carma Interest Rate Model

Author

Listed:
  • ARNE ANDRESEN

    (Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, No-7491 Trondheim, Norway)

  • FRED ESPEN BENTH

    (Center of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway)

  • STEEN KOEKEBAKKER

    (Department of Economics and Finance, University of Agder, Service Box 422, 4604 Kristiansand, Norway)

  • VALERIY ZAKAMULIN

    (Department of Economics and Finance, University of Agder, Service Box 422, 4604 Kristiansand, Norway)

Abstract

In this paper, we present a multi-factor continuous-time autoregressive moving-average (CARMA) model for the short and forward interest rates. This model is able to present an adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provides closed-form solutions to bond prices, yields, bond option prices, and the term structure of forward rate volatility. We demonstrate the capabilities of our model by calibrating it to a panel of spot rates and the empirical volatility of forward rates simultaneously, making the model consistent with both the spot rate dynamics and forward rate volatility structure.

Suggested Citation

  • Arne Andresen & Fred Espen Benth & Steen Koekebakker & Valeriy Zakamulin, 2014. "The Carma Interest Rate Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 1-27.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:02:n:s0219024914500083
    DOI: 10.1142/S0219024914500083
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    References listed on IDEAS

    as
    1. Nicola Anderson & John Sleath, 2001. "New estimates of the UK real and nominal yield curves," Bank of England working papers 126, Bank of England.
    2. David K. Backus & Silverio Foresi & Chris Telmer, "undated". "Discrete time models of bond pricing," GSIA Working Papers 251, Carnegie Mellon University, Tepper School of Business.
    3. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, December.
    4. David K. Backus & Stanley E. Zin, 1994. "Reverse Engineering the Yield Curve," NBER Working Papers 4676, National Bureau of Economic Research, Inc.
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    Citations

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    Cited by:

    1. Vicky Fasen‐Hartmann & Sebastian Kimmig, 2020. "Robust estimation of stationary continuous‐time arma models via indirect inference," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(5), pages 620-651, September.
    2. Vicky Fasen, 2016. "Dependence Estimation for High-frequency Sampled Multivariate CARMA Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 292-320, March.
    3. Lorenzo Mercuri & Andrea Perchiazzo & Edit Rroji, 2020. "Finite Mixture Approximation of CARMA(p,q) Models," Papers 2005.10130, arXiv.org, revised May 2020.
    4. Mercuri, Lorenzo & Perchiazzo, Andrea & Rroji, Edit, 2024. "A Hawkes model with CARMA(p,q) intensity," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 1-26.
    5. Brouty, Xavier & Garcin, Matthieu, 2024. "Fractal properties, information theory, and market efficiency," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    6. Péter Kevei, 2018. "Asymptotic moving average representation of high-frequency sampled multivariate CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 467-487, April.

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