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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
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    References listed on IDEAS

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    1. Jakob Gulddahl Rasmussen, 2013. "Bayesian Inference for Hawkes Processes," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 623-642, September.
    2. 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.
    3. 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.
    4. 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.
    5. Donatien Hainaut & Renaud MacGilchrist, 2012. "Strategic asset allocation with switching dependence," Annals of Finance, Springer, vol. 8(1), pages 75-96, February.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
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    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.

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