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The Fractional OU Process: Term Structure Theory and Application

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  • Esben Hoeg

    (Aarhus School of Business)

  • Per Frederiksen

    (Jyske Bank)

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    Abstract

    The paper revisits dynamic term structure models (DTSMs) and proposes a new way in dealing with the limitation of the classical affine models. In particular, this paper expands the flexibility of the DTSMs by applying a fractional Brownian motion as the governing force of the state variable instead of the standard Brownian motion. This is a new direction in pricing non defaultable bonds with offspring in the arbitrage free pricing of weather derivatives based on fractional Brownian motions. By applying fractional Ito calculus and a fractional version of the Girsanov transform, a no arbitrage price of the bond is recovered by solving a fractional version of the fundamental bond pricing equation. Besides this theoretical contribution, the paper proposes an estimation methodology based on the Kalman filter approach, which is applied to the US term structure of interest rates

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    Bibliographic Info

    Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2006 with number 194.

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    Date of creation: 04 Jul 2006
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    Handle: RePEc:sce:scecfa:194

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    Web page: http://comp-econ.org/
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    Related research

    Keywords: Fractional bond pricing equation; fractional Brownian motion; fractional Ornstein-Uhlenbeck process; long memory; Kalman Filter;

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    2. Tkacz, Greg, 2000. "Estimating the Fractional Order of Integration of Interest Rates Using a Wavelet OLS Estimator," Working Papers 00-5, Bank of Canada.
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    23. Fred Espen Benth, 2003. "On arbitrage-free pricing of weather derivatives based on fractional Brownian motion," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(4), pages 303-324.
    24. Morten Ørregaard Nielsen & Per Frederiksen, 2008. "Fully Modified Narrow-Band Least Squares Estimation of Stationary Fractional Cointegration," Working Papers 1171, Queen's University, Department of Economics.
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