IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v21y2019i4d10.1007_s11009-018-9678-4.html
   My bibliography  Save this article

A Bivariate Mutually-Excited Switching Jump Diffusion (BMESJD) for Asset Prices

Author

Listed:
  • Donatien Hainaut

    (Université Catholique de Louvain)

  • Griselda Deelstra

    (Université libre de Bruxelles)

Abstract

We propose a new approach for bivariate financial time series modelling which allows for mutual excitation between shocks. Jumps are triggered by changes of regime of a hidden Markov chain whose matrix of transition probabilities is constructed in order to approximate a bivariate Hawkes process. This model, called the Bivariate Mutually-Excited Switching Jump Diffusion (BMESJD) presents several interesting features. Firstly, compared to alternative approaches for modelling the contagion between jumps, the calibration is easier and performed with a modified Hamilton’s filter. Secondly, the BMESJD allows for simultaneous jumps when markets are highly stressed. Thirdly, a family of equivalent probability measures under which the BMESJD dynamics are preserved, is well identified. Finally, the BMESJD is a continuous time process that is well adapted for pricing options with two underlying assets.

Suggested Citation

  • Donatien Hainaut & Griselda Deelstra, 2019. "A Bivariate Mutually-Excited Switching Jump Diffusion (BMESJD) for Asset Prices," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1337-1375, December.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:4:d:10.1007_s11009-018-9678-4
    DOI: 10.1007/s11009-018-9678-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-018-9678-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-018-9678-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Donatien Hainaut & David B. Colwell, 2016. "A structural model for credit risk with switching processes and synchronous jumps," The European Journal of Finance, Taylor & Francis Journals, vol. 22(11), pages 1040-1062, September.
    2. Donatien Hainaut & Renaud MacGilchrist, 2012. "Strategic asset allocation with switching dependence," Annals of Finance, Springer, vol. 8(1), pages 75-96, February.
    3. Jakob Gulddahl Rasmussen, 2013. "Bayesian Inference for Hawkes Processes," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 623-642, September.
    4. Honda, Toshiki, 2003. "Optimal portfolio choice for unobservable and regime-switching mean returns," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 45-78, October.
    5. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    6. Massimo Guidolin & Allan Timmermann, 2008. "International asset allocation under regime switching, skew, and kurtosis preferences," The Review of Financial Studies, Society for Financial Studies, vol. 21(2), pages 889-935, April.
    7. Donatien Hainaut & Franck Moraux, 2019. "A switching self-exciting jump diffusion process for stock prices," Annals of Finance, Springer, vol. 15(2), pages 267-306, June.
    8. Yinghui Dong & Kam C. Yuen & Guojing Wang & Chongfeng Wu, 2016. "A Reduced-Form Model for Correlated Defaults with Regime-Switching Shot Noise Intensities," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 459-486, June.
    9. Aït-Sahalia, Yacine & Cacho-Diaz, Julio & Laeven, Roger J.A., 2015. "Modeling financial contagion using mutually exciting jump processes," Journal of Financial Economics, Elsevier, vol. 117(3), pages 585-606.
    10. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    11. Gabriele Stabile & Giovanni Luca Torrisi, 2010. "Risk Processes with Non-stationary Hawkes Claims Arrivals," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 415-429, September.
    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. Lirong Cui & Bei Wu & Juan Yin, 2022. "Moments for Hawkes Processes with Gamma Decay Kernel Functions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1565-1601, September.

    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. Hainaut, Donatien & Deelstra, Griselda, 2018. "A Bivariate Mutually-Excited Switching Jump Diffusion (BMESJD) for asset prices," LIDAM Discussion Papers ISBA 2018011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Donatien Hainaut & Franck Moraux, 2019. "A switching self-exciting jump diffusion process for stock prices," Annals of Finance, Springer, vol. 15(2), pages 267-306, June.
    3. Chen, Zhiping & Li, Gang & Zhao, Yonggan, 2014. "Time-consistent investment policies in Markovian markets: A case of mean–variance analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 293-316.
    4. Branger, Nicole & Kraft, Holger & Meinerding, Christoph, 2014. "Partial information about contagion risk, self-exciting processes and portfolio optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 18-36.
    5. Donatien Hainaut & Yang Shen & Yan Zeng, 2018. "How do capital structure and economic regime affect fair prices of bank’s equity and liabilities?," Annals of Operations Research, Springer, vol. 262(2), pages 519-545, March.
    6. Hainaut, Donatien, 2014. "Impulse control of pension fund contributions, in a regime switching economy," European Journal of Operational Research, Elsevier, vol. 239(3), pages 810-819.
    7. 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).
    8. Jianmin Shi, 2020. "Optimal control of multiple Markov switching stochastic system with application to portfolio decision," Papers 2010.16102, arXiv.org.
    9. Ashwaq Ali Zarban & David Colwell & Donna Mary Salopek, 2024. "Pricing a Defaultable Zero-Coupon Bond under Imperfect Information and Regime Switching," Mathematics, MDPI, vol. 12(17), pages 1-19, September.
    10. Jianmin Shi, 2023. "Dynamic asset allocation with multiple regime‐switching markets," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(2), pages 1741-1755, April.
    11. Hematizadeh, Roksana & Tajaddini, Reza & Hallahan, Terrence, 2022. "Dynamic asset allocation strategy using a state-dependent Markov model: Applications to international equity markets," Journal of International Money and Finance, Elsevier, vol. 128(C).
    12. Donatien Hainaut & Yan Shen & Yan Zeng, 2016. "How do capital structure and economic regime affect fair prices of bank's equity and liabilities?," Post-Print hal-01394133, HAL.
    13. Charles Guy Njike Leunga & Donatien Hainaut, 2022. "Valuation of Annuity Guarantees Under a Self-Exciting Switching Jump Model," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 963-990, June.
    14. Campani, Carlos Heitor & Garcia, René & Lewin, Marcelo, 2021. "Optimal portfolio strategies in the presence of regimes in asset returns," Journal of Banking & Finance, Elsevier, vol. 123(C).
    15. Hainaut, Donatien, 2023. "A mutually exciting rough jump diffusion for financial modelling," LIDAM Discussion Papers ISBA 2023011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    16. Donatien Hainaut & Renaud MacGilchrist, 2012. "Strategic asset allocation with switching dependence," Annals of Finance, Springer, vol. 8(1), pages 75-96, February.
    17. Aloui, Chaker & Hammoudeh, Shawkat & Hamida, Hela Ben, 2015. "Price discovery and regime shift behavior in the relationship between sharia stocks and sukuk: A two-state Markov switching analysis," Pacific-Basin Finance Journal, Elsevier, vol. 34(C), pages 121-135.
    18. Arouri, Mohamed & M’saddek, Oussama & Nguyen, Duc Khuong & Pukthuanthong, Kuntara, 2019. "Cojumps and asset allocation in international equity markets," Journal of Economic Dynamics and Control, Elsevier, vol. 98(C), pages 1-22.
    19. Loriana Pelizzon & Monica Billio & Mila Getmansky, 2008. "Crisis and Hedge Fund Risk," Working Papers 2008_10, Department of Economics, University of Venice "Ca' Foscari".
    20. Bernardi, Mauro & Catania, Leopoldo, 2018. "Portfolio optimisation under flexible dynamic dependence modelling," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 1-18.

    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:spr:metcap:v:21:y:2019:i:4:d:10.1007_s11009-018-9678-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.