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The proposed framework captures the typical risk characteristics of FX markets and is coherent with the symmetries of FX rates. Moreover, due to the self-exciting behavior of CBI processes, the volatilities of FX rates exhibit self-exciting dynamics. By relying on the theory of affine processes, we show that our approach is analytically tractable and that the model structure is invariant under a suitable class of risk-neutral measures. A semi-closed pricing formula for currency options is obtained by Fourier methods. We propose two calibration methods, also by relying on deep-learning techniques, and show that a simple specification of the model can achieve a good fit to market data on a currency triangle.<\/jats:p>","DOI":"10.1007\/s10479-022-04982-z","type":"journal-article","created":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T05:02:41Z","timestamp":1664341361000},"page":"127-152","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["CBI-time-changed L\u00e9vy processes for multi-currency modeling"],"prefix":"10.1007","volume":"336","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9592-3873","authenticated-orcid":false,"given":"Claudio","family":"Fontana","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alessandro","family":"Gnoatto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guillaume","family":"Szulda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,9,28]]},"reference":[{"issue":"3","key":"4982_CR1","doi-asserted-by":"publisher","first-page":"1181","DOI":"10.1016\/j.ejor.2017.02.018","volume":"260","author":"L Ballotta","year":"2017","unstructured":"Ballotta, L., Deelstra, G., & Ray\u00e9e, G. 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