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General Quadratic Term Structures of Bond, Futures and Forward Prices

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Abstract

For finite dimensional factor models, the paper studies general quadratic term structures. These term structures include as special cases the affine term structures and the Gaussian quadratic term structures, previously studied in the literature. We show, however, that there are other, non-Gaussian, quadratic term structures and derive sufficient conditions for the existence of these general quadratic term structures for bond, futures and forward prices. As forward prices are martingales under the T-forward measure, their term structure equation depends on properties of bond prices' term structure. We exploit the connection with the bond prices term structure and show that even in quadratic short rate settings we can have affine term structures for forward prices. Finally, we show how the study of futures prices is naturally embedded in a study of forward prices and show that the difference between the two prices have to do with the correlation between bond prices and the price process of the underlying to the forward contract and this difference may be deterministic in some (non-trivial) stochastic interest rate settings.

Suggested Citation

  • Gaspar, Raquel M., 2004. "General Quadratic Term Structures of Bond, Futures and Forward Prices," SSE/EFI Working Paper Series in Economics and Finance 559, Stockholm School of Economics.
    • Handle: RePEc:hhs:hastef:0559
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    11. Miltersen, Kristian R. & Schwartz, Eduardo S., 1998. "Pricing of Options on Commodity Futures with Stochastic Term Structures of Convenience Yields and Interest Rates," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(1), pages 33-59, March.
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    Cited by:

    1. Roger Lord & Christian Kahl, 2006. "Optimal Fourier Inversion in Semi-analytical Option Pricing," Tinbergen Institute Discussion Papers 06-066/2, Tinbergen Institute, revised 05 Jun 2007.
    2. Roger Lord & Christian Kahl, 2006. "Why the Rotation Count Algorithm works," Tinbergen Institute Discussion Papers 06-065/2, Tinbergen Institute.
    3. Lech A. Grzelak & Cornelis W. Oosterlee & Sacha Van Weeren, 2012. "Extension of stochastic volatility equity models with the Hull--White interest rate process," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 89-105, July.
    4. Gaspar, Raquel M. & Schmidt, Thorsten, 2005. "Quadratic Portfolio Credit Risk models with Shot-noise Effects," SSE/EFI Working Paper Series in Economics and Finance 616, Stockholm School of Economics.
    5. Aneta Hryckiewicz & Piotr Mielus & Karolina Skorulska & Malgorzata Snarska, 2018. "Does a bank levy increase frictions on the interbank market?," KAE Working Papers 2018-033, Warsaw School of Economics, Collegium of Economic Analysis.
    6. Gaspar, Raquel M., 2004. "On Finite Dimensional Realizations of Forward Price Term Structure Models," SSE/EFI Working Paper Series in Economics and Finance 569, Stockholm School of Economics.
    7. Zorana Grbac & Laura Meneghello & Wolfgang J. Runggaldier, 2015. "Derivative pricing for a multi-curve extension of the Gaussian, exponentially quadratic short rate model," Papers 1512.03259, arXiv.org, revised Jun 2016.
    8. Cody Hyndman & Xinghua Zhou, 2014. "Explicit solutions of quadratic FBSDEs arising from quadratic term structure models," Papers 1410.1220, arXiv.org, revised Dec 2014.
    9. Mia Hinnerich, 2015. "Consistent Parallel And Proportional Shifts In The Term Structure Of Futures Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 1-25.

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    More about this item

    Keywords

    term structure; bond price; futures price; forward price; affine term structure; quadratic term structure;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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