{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:36:25Z","timestamp":1787322985731,"version":"3.56.0"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"name":"Chaire Risques Financiers"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Finan. Math."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>In this paper, we prove a large deviations principle for the class of multidimensional affine stochastic volatility models considered in [C. Gourieroux and R. Sufana (2010), J. Bus. Econom. Statist., 28, pp. 438--451], where the volatility matrix is modeled by a Wishart process. This class extends the very popular Heston model to the multivariate setting, thus allowing us to model the joint behavior of a basket of stocks or several exchange rates. We then use the large deviations principle to obtain an asymptotic approximation for the implied volatilities of various options and to develop an asymptotically optimal importance sampling algorithm, to reduce the number of simulations when using Monte Carlo methods for price derivatives. The theory is illustrated with foreign exchange option pricing examples.<\/jats:p>","DOI":"10.1137\/18m1197588","type":"journal-article","created":{"date-parts":[[2019,12,17]],"date-time":"2019-12-17T14:13:30Z","timestamp":1576592010000},"page":"942-976","source":"Crossref","is-referenced-by-count":1,"title":["Long-Time Large Deviations for the Multiasset Wishart Stochastic Volatility Model and Option Pricing"],"prefix":"10.1137","volume":"10","author":[{"given":"Aur\u00e9lien","family":"Alfonsi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Krief","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Tankov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,12,17]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1214\/12-AAP863"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"A. Alfonsi (2015),\n                      Affine diffusions and related processes: Simulation, theory and applications\n                      , Bocconi and Springer Ser. 6, Springer, Cham, Switzerland.","DOI":"10.1007\/978-3-319-05221-2"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2016.04.026"},{"key":"atypb4","unstructured":"A. Benabid, H. Bensusan, and N. El Karoui (2008),\n                      Wishart Stochastic Volatility: Asymptotic Smile and Numerical Framework\n                      , preprint, hal-00458014v2."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01259552"},{"key":"atypb6","doi-asserted-by":"crossref","unstructured":"I. J. Clark (2011),\n                      Foreign Exchange Option Pricing: A Practitioner's Guide\n                      , Wiley, Chichester, England.","DOI":"10.1002\/9781119208679"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1214\/10-AAP710"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/s11147-008-9018-x"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1080\/14697680701668418"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.1993.10485320"},{"key":"atypb11","doi-asserted-by":"crossref","unstructured":"A. Dembo and O. Zeitouni (1998),\n                      Large Deviations Techniques and Applications\n                      , 2nd ed., Appl. Math. 38, Springer, New York.","DOI":"10.1007\/978-1-4612-5320-4"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-010-0147-3"},{"key":"atypb13","doi-asserted-by":"crossref","unstructured":"A. Genin and P. Tankov (2019),\n                      Optimal importance sampling for L\u00e9vy processes\n                      , Stochastic Process. Appl., to appear.","DOI":"10.1016\/j.spa.2018.12.019"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1080\/07474930600713234"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1198\/jbes.2009.08105"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-007-0053-5"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/6.2.327"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1137\/16M1069651"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1080\/17442508.2012.720687"},{"key":"atypb20","doi-asserted-by":"crossref","unstructured":"H. Pham (2007),\n                      Some applications and methods of large deviations in finance and insurance\n                      , in Paris-Princeton Lectures on Mathematical Finance 2004, Springer, Berlin, pp. 191-244.","DOI":"10.1007\/978-3-540-73327-0_5"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2009.10.010"},{"key":"atypb22","unstructured":"R. T. 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