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Applying Heath-Jarrow-Morton Model to Forecasting the US Treasury Daily Yield Curve Rates

Author

Listed:
  • Valerii Maltsev

    (Department of Mathematics and Statistics, University of Konstanz, 78464 Konstanz, Germany
    These authors contributed equally to this work.)

  • Michael Pokojovy

    (Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USA
    These authors contributed equally to this work.)

Abstract

The Heath-Jarrow-Morton (HJM) model is a powerful instrument for describing the stochastic evolution of interest rate curves under no-arbitrage assumption. An important feature of the HJM approach is the fact that the drifts can be expressed as functions of respective volatilities and the underlying correlation structure. Aimed at researchers and practitioners, the purpose of this article is to present a self-contained, but concise review of the abstract HJM framework founded upon the theory of interest and stochastic partial differential equations in infinite dimensions. To illustrate the predictive power of this theory, we apply it to modeling and forecasting the US Treasury daily yield curve rates. We fit a non-parametric model to real data available from the US Department of the Treasury and illustrate its statistical performance in forecasting future yield curve rates.

Suggested Citation

  • Valerii Maltsev & Michael Pokojovy, 2021. "Applying Heath-Jarrow-Morton Model to Forecasting the US Treasury Daily Yield Curve Rates," Mathematics, MDPI, vol. 9(2), pages 1-25, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:114-:d:475951
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    References listed on IDEAS

    as
    1. Tang, Cheng Yong & Chen, Song Xi, 2009. "Parameter estimation and bias correction for diffusion processes," Journal of Econometrics, Elsevier, vol. 149(1), pages 65-81, April.
    2. Cheridito, Patrick & Filipovic, Damir & Kimmel, Robert L., 2007. "Market price of risk specifications for affine models: Theory and evidence," Journal of Financial Economics, Elsevier, vol. 83(1), pages 123-170, January.
    3. Luca Vincenzo Ballestra & Graziella Pacelli & Davide Radi, 2016. "A Note On Fergusson And Platen: “Application Of Maximum Likelihood Estimation To Stochastic Short Rate Models”," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(04), pages 1-7, December.
    4. Andrew Jeffrey, 2004. "Nonparametric Estimation of a Multifactor Heath-Jarrow-Morton Model: An Integrated Approach," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 251-289.
    5. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    6. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    7. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    8. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, February.
    9. Ram Bhar & Carl Chiarella, 1995. "The Estimation of the Heath-Jarrow-Morton Model by Use of Kalman Filtering Techniques," Working Paper Series 54, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    10. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    11. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Chiara Sabelli & Michele Pioppi & Luca Sitzia & Giacomo Bormetti, 2018. "Multi-curve HJM modelling for risk management," Quantitative Finance, Taylor & Francis Journals, vol. 18(4), pages 563-590, April.
    13. Thorsten Schmidt, 2006. "An Infinite Factor Model For Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 43-68.
    14. Ewa Broszkiewicz-Suwaj & Aleksander Weron, 2005. "Calibration of the multifactor HJM model for energy market," HSC Research Reports HSC/05/03, Hugo Steinhaus Center, Wroclaw University of Technology.
    15. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    16. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    17. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    18. Dybvig, Philip H & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1996. "Long Forward and Zero-Coupon Rates Can Never Fall," The Journal of Business, University of Chicago Press, vol. 69(1), pages 1-25, January.
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