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Entropy and information in the interest rate term structure

Author

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  • D. C. Brody
  • L. P. Hughston

Abstract

Associated with every positive interest term structure there is a probability density function over the positive half-line. This fact can be used to turn the problem of term structure analysis into a problem in the comparison of probability distributions, an area well developed in statistics, known as information geometry. The information-theoretic and geometric aspects of term structures thus arising are here illustrated. In particular, we introduce a new term structure calibration methodology based on maximization of entropy, and also present some new families of interest rate models arising naturally in this context.

Suggested Citation

  • D. C. Brody & L. P. Hughston, 2002. "Entropy and information in the interest rate term structure," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 70-80.
    • Handle: RePEc:taf:quantf:v:2:y:2002:i:1:p:70-80
    DOI: 10.1088/1469-7688/2/1/306
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    Cited by:

    1. El Karoui, Nicole & Jeanblanc, Monique & Jiao, Ying, 2010. "What happens after a default: The conditional density approach," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1011-1032, July.
    2. Gzyl, Henryk & Mayoral, Silvia, 2016. "Determination of zero-coupon and spot rates from treasury data by maximum entropy methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 38-50.
    3. Frieden, B. Roy & Hawkins, Raymond J., 2010. "Asymmetric information and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(2), pages 287-295.
    4. Mengütürk, Levent Ali, 2018. "Gaussian random bridges and a geometric model for information equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 465-483.
    5. Hawkins, Raymond J. & Aoki, Masanao & Roy Frieden, B., 2010. "Asymmetric information and macroeconomic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3565-3571.
    6. Dorje C. Brody & Lane P. Hughston, 2018. "Social Discounting And The Long Rate Of Interest," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 306-334, January.
    7. Hackworth, J.F., 2008. "Uncertainty and the yield curve," Economics Letters, Elsevier, vol. 98(3), pages 259-268, March.
    8. Dorje C. Brody & Lane P. Hughston, 2013. "Social Discounting and the Long Rate of Interest," Papers 1306.5145, arXiv.org, revised Sep 2015.

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