IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v17y2014i02ns0219024914500083.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024914500083
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024914500083?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. David K. Backus & Stanley E. Zin, 1994. "Reverse Engineering the Yield Curve," Working Papers 94-09, New York University, Leonard N. Stern School of Business, Department of Economics.
    3. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    4. Nicola Anderson & John Sleath, 2001. "New estimates of the UK real and nominal yield curves," Bank of England working papers 126, Bank of England.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lorenzo Mercuri & Andrea Perchiazzo & Edit Rroji, 2020. "Finite Mixture Approximation of CARMA(p,q) Models," Papers 2005.10130, arXiv.org, revised May 2020.
    2. 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.
    3. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Joyce, Michael & Kaminska, Iryna & Lildholdt, Peter, 2008. "Understanding the real rate conundrum: an application of no-arbitrage finance models to the UK real yield curve," Bank of England working papers 358, Bank of England.
    2. Luca Benati, 2006. "Affine term structure models for the foreign exchange risk premium," Bank of England working papers 291, Bank of England.
    3. Joyce, Michael A.S. & Lildholdt, Peter & Sorensen, Steffen, 2010. "Extracting inflation expectations and inflation risk premia from the term structure: A joint model of the UK nominal and real yield curves," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 281-294, February.
    4. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
    5. Wolfgang Lemke & Deutsche Bundesbank, 2006. "Term Structure Modeling and Estimation in a State Space Framework," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-28344-7, October.
    6. Peter Lildholdt & Nikolaos Panigirtzoglou & Chris Peacock, 2007. "An affine macro-factor model of the UK yield curve," Bank of England working papers 322, Bank of England.
    7. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 50-71.
    8. François R. Velde, 2009. "Chronicle of a Deflation Unforetold," Journal of Political Economy, University of Chicago Press, vol. 117(4), pages 591-634, August.
    9. Zvi Wiener & Helena Pompushko, 2006. "The Estimation of Nominal and Real Yield Curves from Government," Bank of Israel Working Papers 2006.03, Bank of Israel.
    10. Wen Xu, 2016. "Estimation of Dynamic Panel Data Models with Stochastic Volatility Using Particle Filters," Econometrics, MDPI, vol. 4(4), pages 1-13, October.
    11. Alejandro Rodriguez & Esther Ruiz, 2009. "Bootstrap prediction intervals in state–space models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(2), pages 167-178, March.
    12. Parrini, Alessandro, 2013. "Importance Sampling for Portfolio Credit Risk in Factor Copula Models," MPRA Paper 103745, University Library of Munich, Germany.
    13. Jean-Luc Gaffard, 2014. "Crise de la théorie et crise de la politique économique. Des modèles d'équilibre général stochastique aux modèles de dynamique hors de l'équilibre," Revue économique, Presses de Sciences-Po, vol. 65(1), pages 71-96.
    14. Salman Huseynov, 2021. "Long and short memory in dynamic term structure models," CREATES Research Papers 2021-15, Department of Economics and Business Economics, Aarhus University.
    15. Tsionas, Mike G., 2021. "Bayesian forecasting with the structural damped trend model," International Journal of Production Economics, Elsevier, vol. 234(C).
    16. Tommaso Proietti, 2002. "Some Reflections on Trend-Cycle Decompositions with Correlated Components," Econometrics 0209002, University Library of Munich, Germany.
    17. Tobias Hartl & Roland Jucknewitz, 2022. "Approximate state space modelling of unobserved fractional components," Econometric Reviews, Taylor & Francis Journals, vol. 41(1), pages 75-98, January.
    18. Broto Carmen & Ruiz Esther, 2009. "Testing for Conditional Heteroscedasticity in the Components of Inflation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(2), pages 1-30, May.
    19. Marczak, Martyna & Proietti, Tommaso, 2016. "Outlier detection in structural time series models: The indicator saturation approach," International Journal of Forecasting, Elsevier, vol. 32(1), pages 180-202.
    20. Oreste Napolitano & Alberto Montagnoli, 2010. "The European Unemployment Gap and the Role of Monetary Policy," Economics Bulletin, AccessEcon, vol. 30(2), pages 1346-1358.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:ijtafx:v:17:y:2014:i:02:n:s0219024914500083. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.