IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1804.07556.html
   My bibliography  Save this paper

Affine processes beyond stochastic continuity

Author

Listed:
  • Martin Keller-Ressel
  • Thorsten Schmidt
  • Robert Wardenga

Abstract

In this paper we study time-inhomogeneous affine processes beyond the common assumption of stochastic continuity. In this setting times of jumps can be both inaccessible and predictable. To this end we develop a general theory of finite dimensional affine semimartingales under very weak assumptions. We show that the corresponding semimartingale characteristics have affine form and that the conditional characteristic function can be represented with solutions to measure differential equations of Riccati type. We prove existence of affine Markov processes and affine semimartingales under mild conditions and elaborate on examples and applications including affine processes in discrete time.

Suggested Citation

  • Martin Keller-Ressel & Thorsten Schmidt & Robert Wardenga, 2018. "Affine processes beyond stochastic continuity," Papers 1804.07556, arXiv.org, revised Dec 2018.
    • Handle: RePEc:arx:papers:1804.07556
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1804.07556
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    2. Don H. Kim & Jonathan H. Wright, 2014. "Jumps in Bond Yields at Known Times," NBER Working Papers 20711, National Bureau of Economic Research, Inc.
    3. Christa Cuchiero & Damir Filipovi'c & Eberhard Mayerhofer & Josef Teichmann, 2009. "Affine processes on positive semidefinite matrices," Papers 0910.0137, arXiv.org, revised Apr 2011.
    4. Claudio Fontana & Thorsten Schmidt, 2016. "General dynamic term structures under default risk," Papers 1603.03198, arXiv.org, revised Nov 2017.
    5. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-664, May.
    6. Piazzesi, Monika, 2001. "An Econometric Model of the Yield Curve With Macroeconomic Jump Effects," University of California at Los Angeles, Anderson Graduate School of Management qt5946p7hn, Anderson Graduate School of Management, UCLA.
    7. Lembke B., 1918. "√ a. p," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 111(1), pages 709-712, February.
    8. repec:bla:jfinan:v:59:y:2004:i:1:p:227-260 is not listed on IDEAS
    9. Alain BÉlanger & Steven E. Shreve & Dennis Wong, 2004. "A General Framework For Pricing Credit Risk," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 317-350, July.
    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. Claudio Fontana & Zorana Grbac & Sandrine Gümbel & Thorsten Schmidt, 2020. "Term structure modelling for multiple curves with stochastic discontinuities," Post-Print hal-03898927, HAL.
    2. Sandrine Gumbel & Thorsten Schmidt, 2020. "Machine learning for multiple yield curve markets: fast calibration in the Gaussian affine framework," Papers 2004.07736, arXiv.org, revised Apr 2020.
    3. Sandrine Gümbel & Thorsten Schmidt, 2020. "Machine Learning for Multiple Yield Curve Markets: Fast Calibration in the Gaussian Affine Framework," Risks, MDPI, vol. 8(2), pages 1-18, May.
    4. Mar'ia Fernanda del Carmen Agoitia Hurtado & Thorsten Schmidt, 2018. "Time-inhomogeneous polynomial processes," Papers 1806.03887, arXiv.org.
    5. Alan Brace & Karol Gellert & Erik Schlögl, 2024. "SOFR term structure dynamics—Discontinuous short rates and stochastic volatility forward rates," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(6), pages 936-985, June.
    6. Karol Gellert & Erik Schlogl, 2021. "Short Rate Dynamics: A Fed Funds and SOFR Perspective," Research Paper Series 420, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Claudio Fontana & Zorana Grbac & Sandrine Gumbel & Thorsten Schmidt, 2018. "Term structure modeling for multiple curves with stochastic discontinuities," Papers 1810.09882, arXiv.org, revised Dec 2019.

    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. Claudio Fontana & Zorana Grbac & Sandrine Gumbel & Thorsten Schmidt, 2018. "Term structure modeling for multiple curves with stochastic discontinuities," Papers 1810.09882, arXiv.org, revised Dec 2019.
    2. Claudio Fontana & Zorana Grbac & Sandrine Gümbel & Thorsten Schmidt, 2020. "Term structure modelling for multiple curves with stochastic discontinuities," Finance and Stochastics, Springer, vol. 24(2), pages 465-511, April.
    3. Sandrine Gumbel & Thorsten Schmidt, 2021. "Defaultable term structures driven by semimartingales," Papers 2103.01577, arXiv.org, revised Aug 2021.
    4. Claudio Fontana & Zorana Grbac & Sandrine Gümbel & Thorsten Schmidt, 2020. "Term structure modelling for multiple curves with stochastic discontinuities," Post-Print hal-03898927, HAL.
    5. Xin Guo & Robert A. Jarrow & Yan Zeng, 2009. "Credit Risk Models with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 320-332, May.
    6. Fontana, Claudio & Schmidt, Thorsten, 2018. "General dynamic term structures under default risk," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3353-3386.
    7. repec:wyi:journl:002109 is not listed on IDEAS
    8. Tolulope Fadina & Thorsten Schmidt, 2019. "Default Ambiguity," Risks, MDPI, vol. 7(2), pages 1-17, June.
    9. Frank Gehmlich & Thorsten Schmidt, 2014. "Dynamic Defaultable Term Structure Modelling beyond the Intensity Paradigm," Papers 1411.4851, arXiv.org, revised Jul 2015.
    10. Tahir Choulli & Catherine Daveloose & Michèle Vanmaele, 2020. "A martingale representation theorem and valuation of defaultable securities," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1527-1564, October.
    11. Hilscher, Jens & Raviv, Alon, 2014. "Bank stability and market discipline: The effect of contingent capital on risk taking and default probability," Journal of Corporate Finance, Elsevier, vol. 29(C), pages 542-560.
    12. Chava, Sudheer & Jarrow, Robert, 2008. "Modeling loan commitments," Finance Research Letters, Elsevier, vol. 5(1), pages 11-20, March.
    13. Nan Chen & S. G. Kou, 2009. "Credit Spreads, Optimal Capital Structure, And Implied Volatility With Endogenous Default And Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 343-378, July.
    14. Elisa Luciano, 2007. "Copula-Based Default Dependence Modelling: Where Do We Stand?," ICER Working Papers - Applied Mathematics Series 21-2007, ICER - International Centre for Economic Research.
    15. Chen, An-Sing & Chu, Hsiang-Hui & Hung, Pi-Hsia & Cheng, Miao-Sih, 2020. "Financial risk and acquirers' stockholder wealth in mergers and acquisitions," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    16. Tsung-Kang Chen & Yijie Tseng & Yu-Ting Hsieh, 2015. "Real Earnings Management Uncertainty and Corporate Credit Risk," European Accounting Review, Taylor & Francis Journals, vol. 24(3), pages 413-440, September.
    17. Luca Benzoni & Lorenzo Garlappi & Robert S. Goldstein, 2019. "Asymmetric Information, Dynamic Debt Issuance, and the Term Structure of Credit Spreads," Working Paper Series WP-2019-8, Federal Reserve Bank of Chicago.
    18. Viviana Fanelli & Silvana Musti, 2007. "Modelling Credit Spreads evolution using the Cox Process within the HJM framework," Quaderni DSEMS 27-2007, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia.
    19. Giesecke, Kay & Longstaff, Francis A. & Schaefer, Stephen & Strebulaev, Ilya, 2011. "Corporate bond default risk: A 150-year perspective," Journal of Financial Economics, Elsevier, vol. 102(2), pages 233-250.
    20. Jean-Pierre Fouque & Ronnie Sircar & Knut Sølna, 2006. "Stochastic Volatility Effects on Defaultable Bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(3), pages 215-244.
    21. Kraft, Holger & Steffensen, Mogens, 2008. "How to invest optimally in corporate bonds: A reduced-form approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(2), pages 348-385, February.

    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:arx:papers:1804.07556. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.