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Projecting the Forward Rate Flow on a Finite Dimensional Manifold


  • Erhan Bayraktar

    (Princeton University)

  • Li Chen

    (Princeton University)

  • H. Vincent Poor

    (Princeton University)


Given an Heath-Jarrow-Morton (HJM) interest rate model and a parametrized family of finite dimensional forward rate curves, this paper provides us a way to project this infinite dimensional HJM forward rate curve to the finite dimensional manifold. This projection characterizes banks' behavior of calibrating forward curves by applying a certain family of curves (e.g., Nelson-Seigel family). Moreover, we derive the Stratonovich dynamics of the projected finite dimensional forward curve. This leads an implicit algorithm for parametric estimation of the original HJM model. We have demonstrated the feasibility of this method by applying generalized method of moments and methods of simulated moments.

Suggested Citation

  • Erhan Bayraktar & Li Chen & H. Vincent Poor, 2003. "Projecting the Forward Rate Flow on a Finite Dimensional Manifold," Finance 0303007, EconWPA.
  • Handle: RePEc:wpa:wuwpfi:0303007
    Note: Type of Document - Tex; prepared on IBM PC - PC-TEX/UNIX Sparc TeX; to print on HP/PostScript/Franciscan monk; pages: 8 ; figures: none. We never published this piece and now we would like to reduce our mailing and xerox cost by posting it.

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    References listed on IDEAS

    1. Duffee, Gregory R, 1999. "Estimating the Price of Default Risk," Review of Financial Studies, Society for Financial Studies, vol. 12(1), pages 197-226.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    3. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    4. Li Chen & H. Vincent Poor, 2003. "Markovian Quadratic Term Structure Models For Risk-free And Defaultable Rates," Finance 0303008, EconWPA.
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    Cited by:

    1. Roncoroni, Andrea & Galluccio, Stefano & Guiotto, Paolo, 2010. "Shape factors and cross-sectional risk," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2320-2340, November.

    More about this item


    HJM Model; Finite-dimensional Manifolds; Nelson_Siegel Family;

    JEL classification:

    • C39 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Other

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