Methodology and Computing in Applied Probability

, Volume 21, Issue 4, pp 1337–1375 | Cite as

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

  • Donatien HainautEmail author
  • Griselda Deelstra


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.


Switching process Self-excited process Jump-diffusions 

Mathematics Subject Classification (2010)

60G46 60G55 91G40 


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Donatien Hainaut thanks for its support the Chair “Data Analytics and Models for insurance” of BNP Paribas Cardif, hosted by ISFA (Université Claude Bernard, Lyon) and managed by the “Fondation Du Risque”.


  1. Aït-Sahalia Y, Cacho-Diaz J, Laeven RJA (2015) Modeling financial contagion using mutually exciting jump processes. J Financ Econ 117:585–606CrossRefGoogle Scholar
  2. Boswijk P, Laeven RJA, Lalu A (2015) Asset returns with self-exciting jumps: option pricing and estimation with a continuum of moments. Working paperGoogle Scholar
  3. Carr P, Wu L (2016) Leverage effect, volatility feedback, and self-exciting market disruptions. Forthcoming in Journal of Financial and Quantitative AnalysisGoogle Scholar
  4. Chen K, Poon S-H (2013) Variance swap premium under stochastic volatility and self-exciting jumps. Working paper SSRN-id2200172Google Scholar
  5. Chourdakis K (2005) Switching Lévy models in continuous time: Finite distributions and option pricing. Working paper SSRN: 838924Google Scholar
  6. Dong Y, Yuen KC, Wang G, Wu C (2016) A reduced-form model for correlated defaults with regime-switching shot noise intensities. Methodol Comput Appl Probab 18(2):459–486MathSciNetCrossRefGoogle Scholar
  7. Embrechts P, Liniger T, Lu L (2011) Multivariate Hawkes processes: an application to financial data. J Appl Probab 48(A):367–378MathSciNetCrossRefGoogle Scholar
  8. Guidolin M, Timmermann A (2008) International asset allocation under regime switching, Skew, and Kurtosis Preferences. Rev Financ Stud 21(2):889–935CrossRefGoogle Scholar
  9. Hainaut D, Colwell D (2016) A structural model for credit risk with switching processes and synchronous jumps. Eur J Financ 22(11):1040–1062CrossRefGoogle Scholar
  10. Hainaut D, Deelstra G (2018) A self-exciting switching jump diffusion (SESJD): properties, calibration and hitting time. Forthcoming in Quantitative Finance, MathSciNetCrossRefGoogle Scholar
  11. Hainaut D, Macgilchrist R (2012) Strategic asset allocation with switching dependence. Ann Financ 8(1):75–96MathSciNetCrossRefGoogle Scholar
  12. Hainaut D, Moraux F (2017) A switching self-exciting jump diffusion process for stock prices. UCL working paperGoogle Scholar
  13. Hamilton JD (1989) A new approach to the economic analysis of non stationary time series and the business cycle. Econometrica 57(2):357–384MathSciNetCrossRefGoogle Scholar
  14. Hawkes A (1971) Sprectra of some mutually exciting point processes. J R Statist Soc Series B 33:438–443. CrossRefzbMATHGoogle Scholar
  15. Honda T (2003) Optimal portfolio choice for unobservable and regime-switching mean returns. J Econ Dyn Control 28:45–78MathSciNetCrossRefGoogle Scholar
  16. Margrabe W (1978) The Value of an option to exchange one asset for another. J Financ 33(1):177–186CrossRefGoogle Scholar
  17. Rasmussen JG (2013) Bayesian inference for Hawkes processes. Methodol Comput Appl Probab 15(3):623–642MathSciNetCrossRefGoogle Scholar
  18. Stabile G, Torrisi GL (2010) Risk processes with non-stationary Hawkes claims arrivals. Methodol Comput Appl Probab 12(3):623–642MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ISBAUniversité Catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Department of MathematicsUniversité libre de BruxellesBruxellesBelgium

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