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