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The Fractional Ornstein-Uhlenbeck Process: Term Structure Theory and Application

Author

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  • Høg, Espen P.

    (Department of Accounting, Aarhus School of Business)

  • Frederiksen, Per H.

    (Jyske Bank)

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.

Suggested Citation

  • Høg, Espen P. & Frederiksen, Per H., 2006. "The Fractional Ornstein-Uhlenbeck Process: Term Structure Theory and Application," Finance Research Group Working Papers F-2006-01, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    • Handle: RePEc:hhb:aarbfi:2006-01
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    References listed on IDEAS

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    3. Peter Løchte Jørgensen & Domenico De Giovanni, 2010. "Time Charters with Purchase Options in Shipping: Valuation and Risk Management," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(5), pages 399-430.
    4. De Giovanni, Domenico, 2007. "Lapse Rate Modeling: A Rational Expectation Approach," Finance Research Group Working Papers F-2007-03, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    5. Høg, Esben, 2008. "Volatility and realized quadratic variation of differenced returns : A wavelet method approach," Finance Research Group Working Papers F-2008-06, University of Aarhus, Aarhus School of Business, Department of Business Studies.

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