IDEAS home Printed from https://ideas.repec.org/p/uts/ppaper/2015-7.html
   My bibliography  Save this paper

Real-World Forward Rate Dynamics With Affine Realizations

Author

Abstract

We investigate the existence of affine realizations for Lévy driven interest rate term structure models under the real-world probability measure, which so far has only been studied under an assumed risk-neutral probability measure. For models driven by Wiener processes, all results obtained under the risk-neutral approach concerning the existence of affine realizations are transferred to the general case. A similar result holds true for models driven by compound Poisson processes with finite jump size distributions. However, in the presence of jumps with infinite activity we obtain severe restrictions on the structure of the market price of risk; typically, it must even be constant.

Suggested Citation

  • Eckhard Platen & Steffan Tappe, 2015. "Real-World Forward Rate Dynamics With Affine Realizations," Published Paper Series 2015-7, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    • Handle: RePEc:uts:ppaper:2015-7
    as

    Download full text from publisher

    File URL: https://www.tandfonline.com/doi/abs/10.1080/07362994.2015.1019629
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
    2. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53, January.
    3. 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.
    4. 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.
    5. 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.
    6. 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..
    7. Damir Filipović & Stefan Tappe, 2008. "Existence of Lévy term structure models," Finance and Stochastics, Springer, vol. 12(1), pages 83-115, January.
    8. Ernst Eberlein & Jean Jacod & Sebastian Raible, 2005. "Lévy term structure models: No-arbitrage and completeness," Finance and Stochastics, Springer, vol. 9(1), pages 67-88, January.
    9. Ernst Eberlein & Fehmi Özkan, 2003. "The Defaultable Lévy Term Structure: Ratings and Restructuring," Mathematical Finance, Wiley Blackwell, vol. 13(2), pages 277-300, April.
    10. Alan Brace & Marek Musiela, 1994. "A Multifactor Gauss Markov Implementation Of Heath, Jarrow, And Morton," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 259-283, July.
    11. Ernst Eberlein & Wolfgang Kluge, 2006. "Valuation Of Floating Range Notes In Lévy Term‐Structure Models," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 237-254, April.
    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. Toshiyuki Nakayama & Stefan Tappe, 2022. "Distance between closed sets and the solutions to stochastic partial differential equations," Papers 2205.00279, arXiv.org, revised Oct 2024.
    2. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2019. "Affine multiple yield curve models," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 568-611, April.
    3. Tappe, Stefan, 2016. "Affine realizations with affine state processes for stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2062-2091.
    4. Stefan Tappe, 2019. "Existence of affine realizations for stochastic partial differential equations driven by L\'evy processes," Papers 1907.00335, arXiv.org.
    5. Stefan Tappe, 2019. "Affine realizations with affine state processes for stochastic partial differential equations," Papers 1907.00336, arXiv.org.
    6. Claudio Fontana & Eckhard Platen & Stefan Tappe, 2024. "Real-world models for multiple term structures: a unifying HJM framework," Papers 2411.01983, arXiv.org.

    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. 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.
    2. Stefan Tappe, 2019. "Existence of affine realizations for L\'evy term structure models," Papers 1907.02363, arXiv.org.
    3. Damir Filipovi'c & Stefan Tappe, 2019. "Existence of L\'evy term structure models," Papers 1907.03561, arXiv.org.
    4. Lijun Bo & Ying Jiao & Xuewei Yang, 2011. "Credit derivatives pricing with default density term structure modelled by L\'evy random fields," Papers 1112.2952, arXiv.org.
    5. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    6. 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, January-A.
    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. Jean Jacod & Philip Protter, 2010. "Risk-neutral compatibility with option prices," Finance and Stochastics, Springer, vol. 14(2), pages 285-315, April.
    9. Stefan Tappe, 2019. "Existence of affine realizations for stochastic partial differential equations driven by L\'evy processes," Papers 1907.00335, arXiv.org.
    10. Lijun Bo & Ying Jiao & Xuewei Yang, 2014. "Credit derivatives pricing with default density term structure modelled by Lévy random fields," Post-Print hal-00651397, HAL.
    11. 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.
    12. Özkan Fehmi & Schmidt Thorsten, 2005. "Credit risk with infinite dimensional Lévy processes," Statistics & Risk Modeling, De Gruyter, vol. 23(4), pages 281-299, April.
    13. Damir Filipović & Stefan Tappe, 2008. "Existence of Lévy term structure models," Finance and Stochastics, Springer, vol. 12(1), pages 83-115, January.
    14. Francesca Biagini & Maximilian Härtel, 2014. "Behavior Of Long-Term Yields In A Lévy Term Structure," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(03), pages 1-24.
    15. 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.
    16. 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.
    17. Tappe, Stefan, 2016. "Affine realizations with affine state processes for stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2062-2091.
    18. Micha{l} Barski & Jerzy Zabczyk, 2015. "Forward rate models with linear volatilities," Papers 1512.05321, arXiv.org.
    19. Carl Chiarella & Samuel Chege Maina & Christina Nikitopoulos-Sklibosios, 2010. "Markovian Defaultable HJM Term Structure Models with Unspanned Stochastic Volatility," Research Paper Series 283, Quantitative Finance Research Centre, University of Technology, Sydney.
    20. 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.

    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:uts:ppaper:2015-7. 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: Duncan Ford (email available below). General contact details of provider: https://edirc.repec.org/data/sfutsau.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.