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A general characterization of one factor affine term structure models

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  • Damir Filipovic

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

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    Abstract

    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.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 5 (2001)
    Issue (Month): 3 ()
    Pages: 389-412

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    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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    Related research

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

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    Cited by:
    1. 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.
    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. Peter Carr & Liuren Wu, 2002. "Time-Changed Levy Processes and Option Pricing," Finance 0207011, EconWPA.
    4. Enlin Pan & Liuren Wu, 2004. "Taking Positive Interest Rates Seriously," Finance 0409013, EconWPA.
    5. 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.
    6. Ronnie L. Loeffen & Pierre Patie, 2010. "Absolute ruin in the Ornstein-Uhlenbeck type risk model," Papers 1006.2712, arXiv.org.
    7. 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.
    8. Massoud Heidari & Liuren WU, 2002. "Are Interest Rate Derivatives Spanned by the Term Structure of Interest Rates?," Finance 0207013, EconWPA.
    9. 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.
    10. 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.
    11. 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.

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