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To this aim, we study the approaches of Luciano and Semeraro (J Comput Appl Math 233:1937\u20131953, 2010) and Ballotta and Bonfiglioli (Eur J Financ 22:1320\u20131350, 2016) to construct multivariate processes. We explore several calibration methods that can be used to fine-tune the models, and that deal with the observed trade-off between marginal and correlation fit. We carry out a thorough empirical analysis to evaluate the ability of the models to fit market data, price exotic derivatives, and embed a rich dependence structure. By merging theoretical aspects with the results of the empirical test, we provide tools to make suitable decisions about the models and calibration techniques to employ in a real context.<\/jats:p>","DOI":"10.1007\/s00291-025-00815-0","type":"journal-article","created":{"date-parts":[[2025,4,11]],"date-time":"2025-04-11T05:37:31Z","timestamp":1744349851000},"page":"1379-1420","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Multivariate L\u00e9vy models: calibration and pricing"],"prefix":"10.1007","volume":"47","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-5028-7411","authenticated-orcid":false,"given":"Giovanni","family":"Amici","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6533-3055","authenticated-orcid":false,"given":"Paolo","family":"Brandimarte","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesco","family":"Messeri","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2075-8196","authenticated-orcid":false,"given":"Patrizia","family":"Semeraro","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,4,11]]},"reference":[{"key":"815_CR1","doi-asserted-by":"crossref","unstructured":"Alfeus M, He X-J, Zhu S-P (2020) Regularization effect on model calibration. 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