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Characterizing Gaussian Models of the Term Structure of Interest Rates

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  • D. P. Kennedy

Abstract

Models of the term structure of interest rates are considered for which, under the martingale measure, instantaneous forward rates are Gaussian. The possible forms of the covariance structure are characterized under appropriate formulations of the Markov property. It is demonstrated that imposing Markovian assumptions limits severely the covariances that may be obtained and that the strongest such formulation together with stationarity implies that the whole forward rate surface is necessarily a Gaussian random field described by just three parameters. Copyright Blackwell Publishers Inc. 1997.

Suggested Citation

  • D. P. Kennedy, 1997. "Characterizing Gaussian Models of the Term Structure of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 107-118.
  • Handle: RePEc:bla:mathfi:v:7:y:1997:i:2:p:107-118
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    1. Casassus, Jaime & Collin-Dufresne, Pierre & Goldstein, Bob, 2005. "Unspanned stochastic volatility and fixed income derivatives pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2723-2749, November.
    2. Tao L. Wu & Shengqiang Xu, 2014. "A Random Field LIBOR Market Model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(6), pages 580-606, June.
    3. Belal E. Baaquie, 1998. "Quantum Field Theory of Treasury Bonds," Papers cond-mat/9809199, arXiv.org.
    4. Santa-Clara, Pedro & Sornette, Didier, 2001. "The Dynamics of the Forward Interest Rate Curve with Stochastic String Shocks," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 149-185.
    5. Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2016. "The stochastic string model as a unifying theory of the term structure of interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 217-237.
    6. Albeverio, Sergio & Lytvynov, Eugene & Mahnig, Andrea, 2004. "A model of the term structure of interest rates based on Lévy fields," Stochastic Processes and their Applications, Elsevier, vol. 114(2), pages 251-263, December.
    7. Kerkhof, F.L.J. & Pelsser, A., 2002. "Observational Equivalence of Discrete String Models and Market Models," Discussion Paper 2002-28, Tilburg University, Center for Economic Research.
    8. Lijun Bo & Ying Jiao & Xuewei Yang, 2011. "Credit derivatives pricing with default density term structure modelled by Lévy random fields," Working Papers hal-00651397, HAL.
    9. Demers, Jean-Guy, 2009. "Multiple zone power forwards: A value at risk framework," Energy Economics, Elsevier, vol. 31(5), pages 714-726, September.
    10. Bisht Deepak & Laha, A. K., 2017. "Pricing Option on Commodity Futures under String Shock," IIMA Working Papers WP 2017-07-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    11. Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2015. "Stochastic string models with continuous semimartingales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 229-246.
    12. Secomandi, Nicola & Seppi, Duane J., 2014. "Real Options and Merchant Operations of Energy and Other Commodities," Foundations and Trends(R) in Technology, Information and Operations Management, now publishers, vol. 6(3-4), pages 161-331, July.
    13. Longstaff, Francis A & Santa-Clara, Pedro & Schwartz, Eduardo S, 2000. "The Relative Valuation of Caps and Swaptions: Theory and Empirical Evidence," University of California at Los Angeles, Anderson Graduate School of Management qt65f1914p, Anderson Graduate School of Management, UCLA.
    14. Belal E. Baaquie & Marakani Srikant & Mitch Warachka, 2002. "A Quantum Field Theory Term Structure Model Applied to Hedging," Papers cond-mat/0206457, arXiv.org.
    15. Vladislav Kargin, 2003. "Portfolio Management for a Random Field of Bond Returns," Finance 0310007, University Library of Munich, Germany.
    16. Roncoroni, Andrea & Galluccio, Stefano & Guiotto, Paolo, 2010. "Shape factors and cross-sectional risk," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2320-2340, November.
    17. Longstaff, Francis A. & Santa-Clara, Pedro & Schwartz, Eduardo S., 2001. "Throwing away a billion dollars: the cost of suboptimal exercise strategies in the swaptions market," Journal of Financial Economics, Elsevier, vol. 62(1), pages 39-66, October.
    18. repec:wsi:ijtafx:v:06:y:2003:i:05:n:s0219024903001980 is not listed on IDEAS
    19. Vladislav Kargin, 2002. "On Bond Portfolio Management," Papers math/0208130, arXiv.org, revised Mar 2003.
    20. Kimmel, Robert L., 2004. "Modeling the term structure of interest rates: A new approach," Journal of Financial Economics, Elsevier, vol. 72(1), pages 143-183, April.
    21. Pandher, Gurupdesh, 2007. "Arbitrage-free valuation of interest rate securities under forward curves with stochastic speed and acceleration," Journal of Economic Theory, Elsevier, vol. 137(1), pages 432-459, November.
    22. Buraschi, Andrea & Corielli, Francesco, 2005. "Risk management implications of time-inconsistency: Model updating and recalibration of no-arbitrage models," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2883-2907, November.

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