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On the construction of finite dimensional realizations for nonlinear forward rate models

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  • Camilla Landén

    ()
    (Department of Mathematics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden Manuscript)

  • Tomas Björk

    ()
    (Department of Finance, Stockholm School of Economics, Box 6501, SE-113 83 Stockholm, Sweden)

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    Abstract

    We consider interest rate models of Heath-Jarrow-Morton type where the forward rates are driven by a multidimensional Wiener process, and where the volatility structure is allowed to be a smooth functional of the present forward rate curve. In a recent paper [3], Björk and Svensson give necessary and sufficient conditions for the existence of a finite dimensional Markovian state space realization (FDR) for such a forward rate model, and in the present paper we provide a general method for the actual construction of an FDR. We illustrate the method by constructing FDR:s for a number of concrete models. These FDR:s generalize previous results by allowing for a more general volatility structure. Furthermore the dimension of the realizations obtained by using our method is typically smaller than that of the corresponding previously known realizations.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 6 (2002)
    Issue (Month): 3 ()
    Pages: 303-331

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    Handle: RePEc:spr:finsto:v:6:y:2002:i:3:p:303-331

    Note: received: January 2001; final version received: August 2001
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    Web page: http://www.springerlink.com/content/101164/

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    Related research

    Keywords: HJM models; factor models; forward rates; state space models; Markovian realizations;

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    Cited by:
    1. Mikael Elhouar, 2008. "Finite-dimensional Realizations of Regime-switching HJM Models," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 15(4), pages 331-354.
    2. Björk, Tomas, 2003. "On the Geometry of Interest Rate Models," Working Paper Series in Economics and Finance 545, Stockholm School of Economics.
    3. Carl Chiarella & Samuel Chege Maina & Christina Nikitopoulos-Sklibosios, 2010. "Markovian Defaultable HJM Term Structure Models with Unspanned Stochastic Volatility," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 283, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Gaspar, Raquel M., 2004. "On Finite Dimensional Realizations of Forward Price Term Structure Models," Working Paper Series in Economics and Finance 569, Stockholm School of Economics.
    5. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, Oxford University Press, edition 3, number 9780199574742, October.
    6. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 6.

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