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Projecting The Forward Rate Flow Onto A Finite Dimensional Manifold

Author

Listed:
  • ERHAN BAYRAKTAR

    (Department of Mathematics, University of Michigan, 2074 East Hall, Ann Arbor, MI 48109-1109, USA)

  • LI CHEN

    (Lehman Brothers, Fixed Income Derivatives Research, 745 Seventh Avenue, New York, NY 10019, USA)

  • H. VINCENT POOR

    (Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA)

Abstract

Given a Heath–Jarrow–Morton (HJM) interest rate model $\mathcal{M}$ and a parametrized family of finite dimensional forward rate curves $\mathcal{G}$, this paper provides a technique for projecting the infinite dimensional forward rate curve rt given by $\mathcal{M}$ onto the finite dimensional manifold $\mathcal{G}$. The Stratonovich dynamics of the projected finite dimensional forward curve are derived and it is shown that, under the regularity conditions, the given Stratonovich differential equation has a unique strong solution. Moreover, this projection leads to an efficient algorithm for implicit parametric estimation of the infinite dimensional HJM model. The feasibility of this method is demonstrated by applying the generalized method of moments.

Suggested Citation

  • Erhan Bayraktar & Li Chen & H. Vincent Poor, 2006. "Projecting The Forward Rate Flow Onto A Finite Dimensional Manifold," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(05), pages 777-785.
    • Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:05:n:s0219024906003743
    DOI: 10.1142/S0219024906003743
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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

    Keywords

    Interest rate models; consistency problems; calibration of HJM models; infinite dimensional stochastic differential equations;
    All these keywords.

    JEL classification:

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

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