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A general characterization of one factor affine term structure models


  • Damir Filipovic

    () (Department of Mathematics, ETH, CH-8092 Zurich, Switzerland Manusript)


We give a complete characterization of affine term structure models based on a general nonnegative Markov short rate process. This applies to the classical CIR model but includes as well short rate processes with jumps. We provide a link to the theory of branching processes and show how CBI-processes naturally enter the field of term structure modelling. Using Markov semigroup theory we exploit the full structure behind an affine term structure model and provide a deeper understanding of some well-known properties of the CIR model. Based on these fundamental results we construct a new short rate model with jumps, which extends the CIR model and still gives closed form expressions for bond options.

Suggested Citation

  • Damir Filipovic, 2001. "A general characterization of one factor affine term structure models," Finance and Stochastics, Springer, vol. 5(3), pages 389-412.
  • Handle: RePEc:spr:finsto:v:5:y:2001:i:3:p:389-412
    Note: received: June 2000, final version received: October 2000

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    References listed on IDEAS

    1. Ioannis Karatzas & Jaksa Cvitanic, 1999. "On dynamic measures of risk," Finance and Stochastics, Springer, vol. 3(4), pages 451-482.
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    3. Helyette Geman & D. Madan, 2004. "Pricing in Incomplete Markets : From Absence of Good Deals to Acceptable Risk," Post-Print halshs-00144406, HAL.
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    Cited by:

    1. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen, 2010. "Real-world jump-diffusion term structure models," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 23-37.
    2. Vicente, José & Tabak, Benjamin M., 2008. "Forecasting bond yields in the Brazilian fixed income market," International Journal of Forecasting, Elsevier, vol. 24(3), pages 490-497.
    3. 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.
    4. Ronnie L. Loeffen & Pierre Patie, 2010. "Absolute ruin in the Ornstein-Uhlenbeck type risk model," Papers 1006.2712,
    5. Steven Heston, 2007. "A model of discontinuous interest rate behavior, yield curves, and volatility," Review of Derivatives Research, Springer, vol. 10(3), pages 205-225, December.
    6. Ying Jiao & Chunhua Ma & Simone Scotti, 2016. "Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling," Working Papers hal-01275397, HAL.
    7. Matyas Barczy & Mohamed Ben Alaya & Ahmed Kebaier & Gyula Pap, 2017. "Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations," Papers 1711.02140,
    8. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 23.
    9. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    10. Tetsuya Ishikawa & Scott Robertson, 2017. "Optimal Investment and Pricing in the Presence of Defaults," Papers 1703.00062,
    11. Enlin Pan & Liuren Wu, 2004. "Taking Positive Interest Rates Seriously," Finance 0409013, EconWPA.
    12. Martin Keller-Ressel & Thomas Steiner, 2008. "Yield curve shapes and the asymptotic short rate distribution in affine one-factor models," Finance and Stochastics, Springer, vol. 12(2), pages 149-172, April.
    13. Ying Jiao & Chunhua Ma & Simone Scotti, 2016. "Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling," Papers 1602.05541,, revised Feb 2016.
    14. Andrey Itkin & Peter Carr, 2010. "Pricing swaps and options on quadratic variation under stochastic time change models—discrete observations case," Review of Derivatives Research, Springer, vol. 13(2), pages 141-176, July.
    15. Massoud Heidari & Liuren WU, 2002. "Are Interest Rate Derivatives Spanned by the Term Structure of Interest Rates?," Finance 0207013, EconWPA.
    16. Matyas Barczy & Mohamed Ben Alaya & Ahmed Kebaier & Gyula Pap, 2016. "Asymptotic properties of maximum likelihood estimator for the growth rate for a jump-type CIR process based on continuous time observations," Papers 1609.05865,, revised Aug 2017.
    17. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance,in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742 Elsevier.

    More about this item


    Affine Term Structure Models; CBI-Processes; Infinitely Decomposable Processes; Non-continuous Markovian Short Rates;

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects


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