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Statistically consistent term structures have affine geometry

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  • Paul Kruhner
  • Shijie Xu

Abstract

This paper is concerned with finite dimensional models for the entire term structure for energy futures. As soon as a finite dimensional set of possible yield curves is chosen, one likes to estimate the dynamic behaviour of the yield curve evolution from data. The estimated model should be free of arbitrage which is known to result in some drift condition. If the yield curve evolution is modelled by a diffusion, then this leaves the diffusion coefficient open for estimation. From a practical perspective, this requires that the chosen set of possible yield curves is compatible with any obtained diffusion coefficient. In this paper, we show that this compatibility enforces an affine geometry of the set of possible yield curves.

Suggested Citation

  • Paul Kruhner & Shijie Xu, 2023. "Statistically consistent term structures have affine geometry," Papers 2308.02246, arXiv.org.
    • Handle: RePEc:arx:papers:2308.02246
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    References listed on IDEAS

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    1. Hans Buehler, 2006. "Consistent Variance Curve Models," Finance and Stochastics, Springer, vol. 10(2), pages 178-203, April.
    2. Fred Espen Benth & Paul Krühner, 2018. "Approximation of forward curve models in commodity markets with arbitrage-free finite-dimensional models," Finance and Stochastics, Springer, vol. 22(2), pages 327-366, April.
    3. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    4. Hans Buehler, 2006. "Consistent Variance Curve Models," Finance and Stochastics, Springer, vol. 10(2), pages 178-203, April.
    5. repec:eme:mfppss:03074350510769703 is not listed on IDEAS
    6. Fred Espen Benth & Jan Kallsen & Thilo Meyer-Brandis, 2007. "A Non-Gaussian Ornstein-Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(2), pages 153-169.
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