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A General Characterization of Quadratic Term Structure Models


  • Li Chen

    (Princeton University)

  • H. Vincent Poor

    (Princeton University)


In this paper, we define a strongly regular quadratic Gaussian process to characterize quadratic term structure models (QTSMs) in a general Markov setting. The key of this definition is to keep the analytical tractability of QTSMs which has the quadratic term structure of the yield curve. In order to keep this property, under the regularity condition, we have proven that no jumps are allowed in the infinitesimal generator of the underlying state process. The coefficient functions defined in the quadratic Gaussian relationship can be decided by the multi-variate Riccati Equations with a unique admissible parameter set. Based on this result, we discuss the pricing problems of QTSMs under default-free and defaultable rates.

Suggested Citation

  • Li Chen & H. Vincent Poor, 2002. "A General Characterization of Quadratic Term Structure Models," Finance 0211008, EconWPA.
  • Handle: RePEc:wpa:wuwpfi:0211008
    Note: Type of Document - Tex; prepared on IBM PC - PC-TEX; to print on PostScript; pages: 40 . We never published this piece and now we would like to reduce our mailing and xerox cost by posting it.

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    References listed on IDEAS

    1. Nicole El Karoui & Monique Jeanblanc-Picqué, 1998. "Optimization of consumption with labor income," Finance and Stochastics, Springer, vol. 2(4), pages 409-440.
    2. Kramkov, D.O., 1994. "Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets," Discussion Paper Serie B 294, University of Bonn, Germany.
    3. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    4. Föllmer, Hans & Kramkov, D. O., 1997. "Optional decompositions under constraints," SFB 373 Discussion Papers 1997,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. I. Klein & L. C. G. Rogers, 2007. "Duality In Optimal Investment And Consumption Problems With Market Frictions," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 225-247.
    6. Domenico Cuoco & Hong Liu, 2000. "A Martingale Characterization of Consumption Choices and Hedging Costs with Margin Requirements," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 355-385.
    7. Cuoco, Domenico, 1997. "Optimal Consumption and Equilibrium Prices with Portfolio Constraints and Stochastic Income," Journal of Economic Theory, Elsevier, vol. 72(1), pages 33-73, January.
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    Cited by:

    1. Peng Cheng & Olivier Scaillet, 2002. "Linear-Quadratic Jump-Diffusion Modeling with Application to Stochastic Volatility," FAME Research Paper Series rp67, International Center for Financial Asset Management and Engineering.
    2. Sergei Levendorskii, 2002. "Pseudo-diffusions and Quadratic term structure models," Papers cond-mat/0212249,, revised Apr 2004.

    More about this item


    Quadratic Term Structure models; Markov Semigroup theory; Affine process;

    JEL classification:

    • C39 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Other
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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