IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/60155.html
   My bibliography  Save this paper

A Markov chain model for contagion

Author

Listed:
  • Dassios, Angelos
  • Zhao, Hongbiao

Abstract

We introduce a bivariate Markov chain counting process with contagion for modelling the clustering arrival of loss claims with delayed settlement for an insurance company. It is a general continuous-time model framework that also has the potential to be applicable to modelling the clustering arrival of events, such as jumps, bankruptcies, crises and catastrophes in finance, insurance and economics with both internal contagion risk and external common risk. Key distributional properties, such as the moments and probability generating functions, for this process are derived. Some special cases with explicit results and numerical examples and the motivation for further actuarial applications are also discussed. The model can be considered a generalisation of the dynamic contagion process introduced by Dassios and Zhao (2011).

Suggested Citation

  • Dassios, Angelos & Zhao, Hongbiao, 2014. "A Markov chain model for contagion," LSE Research Online Documents on Economics 60155, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:60155
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/60155/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. E. Bacry & S. Delattre & M. Hoffmann & J. F. Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 65-77, January.
    2. Chavez-Demoulin, V. & McGill, J.A., 2012. "High-frequency financial data modeling using Hawkes processes," Journal of Banking & Finance, Elsevier, vol. 36(12), pages 3415-3426.
    3. Emmanuel Bacry & Sylvain Delattre & Marc Hoffmann & Jean-François Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Post-Print hal-01313995, HAL.
    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. Jang, Jiwook & Dassios, Angelos & Zhao, Hongbiao, 2018. "Moments of renewal shot-noise processes and their applications," LSE Research Online Documents on Economics 87428, London School of Economics and Political Science, LSE Library.

    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. Kyungsub Lee, 2022. "Application of Hawkes volatility in the observation of filtered high-frequency price process in tick structures," Papers 2207.05939, arXiv.org.
    2. Swishchuk, Anatoliy & Zagst, Rudi & Zeller, Gabriela, 2021. "Hawkes processes in insurance: Risk model, application to empirical data and optimal investment," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 107-124.
    3. Anatoliy Swishchuk & Aiden Huffman, 2018. "General Compound Hawkes Processes in Limit Order Books," Papers 1812.02298, arXiv.org.
    4. Hainaut, Donatien, 2016. "Impact of volatility clustering on equity indexed annuities," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 367-381.
    5. Donatien Hainaut, 2016. "A model for interest rates with clustering effects," Post-Print hal-01393994, HAL.
    6. Hainaut, Donatien & Goutte, Stephane, 2018. "A switching microstructure model for stock prices," LIDAM Discussion Papers ISBA 2018014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Hainaut, Donatien, 2016. "A bivariate Hawkes process for interest rate modeling," Economic Modelling, Elsevier, vol. 57(C), pages 180-196.
    8. Hyun Jin Jang & Kiseop Lee & Kyungsub Lee, 2020. "Systemic risk in market microstructure of crude oil and gasoline futures prices: A Hawkes flocking model approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(2), pages 247-275, February.
    9. Angelos Dassios & Hongbiao Zhao, 2014. "A Markov Chain Model for Contagion," Risks, MDPI, vol. 2(4), pages 1-22, November.
    10. Herrera, Rodrigo & González, Sergio & Clements, Adam, 2018. "Mutual excitation between OECD stock and oil markets: A conditional intensity extreme value approach," The North American Journal of Economics and Finance, Elsevier, vol. 46(C), pages 70-88.
    11. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    12. Amirhossein Sadoghi & Jan Vecer, 2022. "Optimal liquidation problem in illiquid markets," Post-Print hal-03696768, HAL.
    13. Buccioli, Alice & Kokholm, Thomas & Nicolosi, Marco, 2019. "Expected shortfall and portfolio management in contagious markets," Journal of Banking & Finance, Elsevier, vol. 102(C), pages 100-115.
    14. Donatien Hainaut, 2016. "A bivariate Hawkes process based model, for interest rates," Post-Print hal-01458162, HAL.
    15. Donatien Hainaut, 2016. "A model for interest rates with clustering effects," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1203-1218, August.
    16. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    17. Bo Jing & Shenghong Li & Yong Ma, 2020. "Pricing VIX options with volatility clustering," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(6), pages 928-944, June.
    18. Emmanuel Bacry & Jean-Francois Muzy, 2014. "Second order statistics characterization of Hawkes processes and non-parametric estimation," Papers 1401.0903, arXiv.org, revised Feb 2015.
    19. Marcello Rambaldi & Emmanuel Bacry & Jean-Franc{c}ois Muzy, 2018. "Disentangling and quantifying market participant volatility contributions," Papers 1807.07036, arXiv.org.
    20. Thomas Deschatre & Xavier Warin, 2023. "A Common Shock Model for multidimensional electricity intraday price modelling with application to battery valuation," Papers 2307.16619, arXiv.org.

    More about this item

    Keywords

    risk model; contagion risk; bivariate point process; Markov chain model; discretised dynamic contagion process; dynamic contagion process;
    All these keywords.

    JEL classification:

    • F3 - International Economics - - International Finance
    • G3 - Financial Economics - - Corporate Finance and Governance

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ehl:lserod:60155. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.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.