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Multifractal modeling of short-term interest rates

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  • M. Rypdal
  • O. L{\o}vsletten
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    Abstract

    We propose a multifractal model for short-term interest rates. The model is a version of the Markov-Switching Multifractal (MSM), which incorporates the well-known level effect observed in interest rates. Unlike previously suggested models, the level-MSM model captures the power-law scaling of the structure functions and the slowly decaying dependency in the absolute value of returns. We apply the model to the Norwegian Interbank Offered Rate with three months maturity (NIBORM3) and the U.S. Treasury Bill with three months maturity (TBM3). The performance of the model is compared to level-GARCH models, level-EGARCH models and jump-diffusions. For the TBM3 data the multifractal out-performs all the alternatives considered.

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    File URL: http://arxiv.org/pdf/1111.5265
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    Paper provided by arXiv.org in its series Papers with number 1111.5265.

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    Date of creation: Nov 2011
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    Handle: RePEc:arx:papers:1111.5265

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    1. Thomas Lux, 2006. "The Markov-Switching Multifractal Model of Asset Returns: GMM Estimation and Linear Forecasting of Volatility," Working Papers, Warwick Business School, Finance Group wp06-19, Warwick Business School, Finance Group.
    2. Ola L{\o}vsletten & Martin Rypdal, 2011. "Approximated maximum likelihood estimation in multifractal random walks," Papers 1112.0105, arXiv.org, revised Feb 2012.
    3. Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1999. "A Multifractal Model of Assets Returns," New York University, Leonard N. Stern School Finance Department Working Paper Seires, New York University, Leonard N. Stern School of Business- 99-072, New York University, Leonard N. Stern School of Business-.
    4. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 385-407, March.
    5. Laurent Calvet, 2000. "Forecasting Multifractal Volatility," Harvard Institute of Economic Research Working Papers, Harvard - Institute of Economic Research 1902, Harvard - Institute of Economic Research.
    6. Koedijk, C.G. & Nissen, F. & Schotman, P.C. & Wolff, C.C.P., 1997. "The dynamics of short-term interest rate volatility reconsidered," Open Access publications from Tilburg University, Tilburg University urn:nbn:nl:ui:12-3108628, Tilburg University.
    7. Bali, Turan G. & Wu, Liuren, 2006. "A comprehensive analysis of the short-term interest-rate dynamics," Journal of Banking & Finance, Elsevier, Elsevier, vol. 30(4), pages 1269-1290, April.
    8. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 12(04), pages 627-627, November.
    9. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, Elsevier, vol. 5(2), pages 177-188, November.
    10. Laurent Calvet & Adlai Fisher, 2003. "Regime-Switching and the Estimation of Multifractal Processes," NBER Working Papers 9839, National Bureau of Economic Research, Inc.
    11. Bacry, E. & Kozhemyak, A. & Muzy, Jean-Francois, 2008. "Continuous cascade models for asset returns," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 32(1), pages 156-199, January.
    12. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, Elsevier, vol. 106(1), pages 27-65, January.
    13. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, Elsevier, vol. 77(2), pages 343-377, April.
    14. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, American Finance Association, vol. 47(3), pages 1209-27, July.
    15. Yongmiao Hong & Haitao Li & Feng Zhao, 2004. "Out-of-Sample Performance of Discrete-Time Spot Interest Rate Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 22, pages 457-473, October.
    16. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, Econometric Society, vol. 57(2), pages 307-33, March.
    17. Laurent E. Calvet, 2004. "How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 49-83.
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