IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2207.03883.html

An introduction to rating triggers for collateral-inclusive XVA in an ICTMC framework

Author

Listed:
  • Kevin Kamm

Abstract

In this paper, we model the rating process of an entity as a piecewise homogeneous continuous time Markov chain. We focus specifically on calibrating the model to both historical data (rating transition matrices) and market data (CDS quotes), relying on a simple change of measure to switch from the historical probability to the risk-neutral one. We overcome some of the imperfections of the data by proposing a novel calibration procedure, which leads to an improvement of the entire scheme. We apply our model to compute bilateral credit and debit valuation adjustments of a netting set under a CSA with thresholds depending on ratings of the two parties.

Suggested Citation

  • Kevin Kamm, 2022. "An introduction to rating triggers for collateral-inclusive XVA in an ICTMC framework," Papers 2207.03883, arXiv.org.
    • Handle: RePEc:arx:papers:2207.03883
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2207.03883
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kevin Kamm & Michelle Muniz, 2022. "A novel approach to rating transition modelling via Machine Learning and SDEs on Lie groups," Papers 2205.15699, arXiv.org.
    2. Cornelis W Oosterlee & Lech A Grzelak, 2019. "Mathematical Modeling and Computation in Finance:With Exercises and Python and MATLAB Computer Codes," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number q0236, February.
    3. Lando, David & Skodeberg, Torben M., 2002. "Analyzing rating transitions and rating drift with continuous observations," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 423-444, March.
    Full references (including those not matched with items on IDEAS)

    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. Nguyen, Thu Ha & Lan, Yihui & Treepongkaruna, Sirimon & Zhong, Rui, 2023. "Credit rating downgrades and stock price crash risk: International evidence," Finance Research Letters, Elsevier, vol. 55(PB).
    2. Pesaran, M. Hashem & Schuermann, Til & Treutler, Bjorn-Jakob & Weiner, Scott M., 2006. "Macroeconomic Dynamics and Credit Risk: A Global Perspective," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(5), pages 1211-1261, August.
    3. Schechtman, Ricardo, 2013. "Default matrices: A complete measurement of banks’ consumer credit delinquency," Journal of Financial Stability, Elsevier, vol. 9(4), pages 460-474.
    4. P. Lencastre & F. Raischel & P. G. Lind, 2014. "The effect of the number of states on the validity of credit ratings," Papers 1409.2661, arXiv.org.
    5. José Eduardo Gómez González & Ines Paola Orozco Hinojosa, 2010. "Un modelo de alerta temprana para el sistema financiero colombiano," Revista ESPE - Ensayos sobre Política Económica, Banco de la Republica de Colombia, vol. 28(62), pages 124-147, June.
    6. Trueck, Stefan & Rachev, Svetlozar T., 2008. "Rating Based Modeling of Credit Risk," Elsevier Monographs, Elsevier, edition 1, number 9780123736833.
    7. Weißbach, Rafael & Mollenhauer, Thomas, 2011. "Modelling Rating Transitions," VfS Annual Conference 2011 (Frankfurt, Main): The Order of the World Economy - Lessons from the Crisis 48698, Verein für Socialpolitik / German Economic Association.
    8. Figlewski, Stephen & Frydman, Halina & Liang, Weijian, 2012. "Modeling the effect of macroeconomic factors on corporate default and credit rating transitions," International Review of Economics & Finance, Elsevier, vol. 21(1), pages 87-105.
    9. Griselda Deelstra & Lech A. Grzelak & Felix L. Wolf, 2022. "Sensitivities and Hedging of the Collateral Choice Option," Papers 2207.10373, arXiv.org, revised Aug 2022.
    10. José E. Gómez-González & Nicholas M. Kiefer., 2009. "Evidence of Non-Markovian Behavior in the Process of Bank Rating Migrations," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 46(133), pages 33-50.
    11. Georges Dionne & Geneviève Gauthier & Khemais Hammami & Mathieu Maurice & Jean‐Guy Simonato, 2010. "Default Risk in Corporate Yield Spreads," Financial Management, Financial Management Association International, vol. 39(2), pages 707-731, June.
    12. Rebekka Topp & Robert Perl, 2010. "Through‐the‐Cycle Ratings Versus Point‐in‐Time Ratings and Implications of the Mapping Between Both Rating Types," Financial Markets, Institutions & Instruments, John Wiley & Sons, vol. 19(1), pages 47-61, February.
    13. Tobias Behrens & Gero Junike & Wim Schoutens, 2023. "Failure of Fourier pricing techniques to approximate the Greeks," Papers 2306.08421, arXiv.org, revised Nov 2024.
    14. Valerio Vacca, 2011. "An unexpected crisis? Looking at pricing effectiveness of different banks," Temi di discussione (Economic working papers) 814, Bank of Italy, Economic Research and International Relations Area.
    15. Kiefer, Nicholas M. & Larson, C. Erik, 2007. "A simulation estimator for testing the time homogeneity of credit rating transitions," Journal of Empirical Finance, Elsevier, vol. 14(5), pages 818-835, December.
    16. Jing Wang & Shuaiqiang Liu & Cornelis Vuik, 2025. "Controllable Generation of Implied Volatility Surfaces with Variational Autoencoders," Papers 2509.01743, arXiv.org.
    17. Arnaud_de_Servigny & Norbert_Jobst, 2005. "An Empirical Analysis of Equity Default Swaps (I): Univariate Insights," International Finance 0503007, University Library of Munich, Germany.
    18. Duffie, Darrell & Saita, Leandro & Wang, Ke, 2007. "Multi-period corporate default prediction with stochastic covariates," Journal of Financial Economics, Elsevier, vol. 83(3), pages 635-665, March.
    19. Jones, Stewart & Johnstone, David & Wilson, Roy, 2015. "An empirical evaluation of the performance of binary classifiers in the prediction of credit ratings changes," Journal of Banking & Finance, Elsevier, vol. 56(C), pages 72-85.
    20. Wozabal, David & Hochreiter, Ronald, 2012. "A coupled Markov chain approach to credit risk modeling," Journal of Economic Dynamics and Control, Elsevier, vol. 36(3), pages 403-415.

    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:2207.03883. 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.