IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb373/200344.html
   My bibliography  Save this paper

On Markovian Short Rates in Term Structure Models Driven by Jump-Diffusion Processes

Author

Listed:
  • Gapeev, Pavel V.
  • Küchler, Uwe

Abstract

We study a bond market model and related term structure of interest rates where prices of zero coupon bonds are driven by a jump-diffusion process. We present a criterion on the deterministic forward rate volatilities under which the short rate process is Markovian and give sufficient conditions on the bond price volatility structure depending on the short rate for existing a finite-dimensional Markovian realization of the term structure model.

Suggested Citation

  • Gapeev, Pavel V. & Küchler, Uwe, 2003. "On Markovian Short Rates in Term Structure Models Driven by Jump-Diffusion Processes," SFB 373 Discussion Papers 2003,44, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:200344
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/22258/1/dpsfb200344.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53, January.
    2. R. Bhar & C. Chiarella, 1997. "Transformation of Heath?Jarrow?Morton models to Markovian systems," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 1-26, March.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    4. Inui, Koji & Kijima, Masaaki, 1998. "A Markovian Framework in Multi-Factor Heath-Jarrow-Morton Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(3), pages 423-440, September.
    5. Andrew Carverhill, 1994. "When Is The Short Rate Markovian?," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 305-312, October.
    6. Hiroshi Shirakawa, 1991. "Interest Rate Option Pricing With Poisson‐Gaussian Forward Rate Curve Processes," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 77-94, October.
    7. Tomas Björk & Lars Svensson, 2001. "On the Existence of Finite‐Dimensional Realizations for Nonlinear Forward Rate Models," Mathematical Finance, Wiley Blackwell, vol. 11(2), pages 205-243, April.
    8. Andrew Mark Jeffrey, 1995. "Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics," Yale School of Management Working Papers ysm46, Yale School of Management.
    9. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    10. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239, April.
    11. Björk, Tomas & Gombani, Andrea, 1997. "Minimal Realizations of Forward Rates," SSE/EFI Working Paper Series in Economics and Finance 182, Stockholm School of Economics.
    12. Carl Chiarella & Oh Kang Kwon, 2001. "Forward rate dependent Markovian transformations of the Heath-Jarrow-Morton term structure model," Finance and Stochastics, Springer, vol. 5(2), pages 237-257.
    13. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure1," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72, January.
    14. Küchler, Uwe, 2003. "On integrals with respect to Levy processes," SFB 373 Discussion Papers 2003,12, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gapeev, Pavel V., 2004. "On arbitrage and Markovian short rates in fractional bond markets," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 211-222, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gapeev Pavel V. & Küchler Uwe, 2006. "On Markovian short rates in term structure models driven by jump-diffusion processes," Statistics & Risk Modeling, De Gruyter, vol. 24(2), pages 1-17, December.
    2. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2005.
    3. Stefan Tappe, 2019. "Existence of affine realizations for L\'evy term structure models," Papers 1907.02363, arXiv.org.
    4. Damir Filipovi'c & Stefan Tappe, 2019. "Existence of L\'evy term structure models," Papers 1907.03561, arXiv.org.
    5. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742, Decembrie.
    6. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 6, July-Dece.
    7. Camilla Landén & Tomas Björk, 2002. "On the construction of finite dimensional realizations for nonlinear forward rate models," Finance and Stochastics, Springer, vol. 6(3), pages 303-331.
    8. Carl Chiarella & Christina Nikitopoulos Sklibosios & Erik Schlögl, 2007. "A Markovian Defaultable Term Structure Model With State Dependent Volatilities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 155-202.
    9. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011.
    10. Carl Chiarella & Oh-Kang Kwon, 2001. "State Variables and the Affine Nature of Markovian HJM Term Structure Models," Research Paper Series 52, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. Carl Chiarella & Christina Sklibosios, 2003. "A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 10(2), pages 87-127, September.
    12. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.
    13. Eckhard Platen & Stefan Tappe, 2011. "Affine Realizations for Levy Driven Interest Rate Models with Real-World Forward Rate Dynamics," Research Paper Series 289, Quantitative Finance Research Centre, University of Technology, Sydney.
    14. Damir Filipović & Stefan Tappe, 2008. "Existence of Lévy term structure models," Finance and Stochastics, Springer, vol. 12(1), pages 83-115, January.
    15. Björk, Tomas & Landén, Camilla & Svensson, Lars, 2002. "Finite dimensional Markovian realizations for stochastic volatility forward rate models," SSE/EFI Working Paper Series in Economics and Finance 498, Stockholm School of Economics, revised 07 May 2002.
    16. Dai, Qiang & Singleton, Kenneth J., 2003. "Fixed-income pricing," 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 20, pages 1207-1246, Elsevier.
    17. Stefan Tappe, 2019. "An alternative approach on the existence of affine realizations for HJM term structure models," Papers 1907.03256, arXiv.org.
    18. Tomas Björk & Lars Svensson, 2001. "On the Existence of Finite‐Dimensional Realizations for Nonlinear Forward Rate Models," Mathematical Finance, Wiley Blackwell, vol. 11(2), pages 205-243, April.
    19. Falini, Jury, 2010. "Pricing caps with HJM models: The benefits of humped volatility," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1358-1367, December.
    20. Björk, Tomas, 2000. "A Geometric View of Interest Rate Theory," SSE/EFI Working Paper Series in Economics and Finance 419, Stockholm School of Economics, revised 21 Dec 2000.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:sfb373:200344. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sfhubde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.