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General Quadratic Term Structures of Bond, Futures and Forward Prices

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  • Gaspar, Raquel M.

    ()
    (Dept. of Finance, Stockholm School of Economics)

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.

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Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 559.

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Length: 57 pages
Date of creation: 30 Mar 2004
Date of revision:
Handle: RePEc:hhs:hastef:0559

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Keywords: term structure; bond price; futures price; forward price; affine term structure; quadratic term structure;

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References

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  1. Damir Filipović, 2002. "Separable Term Structures And The Maximal Degree Problem," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 341-349.
  2. Markus Leippold & Liuren Wu, 2002. "Asset Pricing Under The Quadratic Class," Finance 0207015, EconWPA.
  3. 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(01), pages 33-59, March.
  4. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  5. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348.
  6. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
  7. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
  8. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  9. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
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Cited by:
  1. Roger Lord & Christian Kahl, 2006. "Why the Rotation Count Algorithm works," Tinbergen Institute Discussion Papers 06-065/2, Tinbergen Institute.
  2. Gaspar, Raquel M. & Schmidt, Thorsten, 2005. "Quadratic Portfolio Credit Risk models with Shot-noise Effects," Working Paper Series in Economics and Finance 616, Stockholm School of Economics.
  3. 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.

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