{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:39:15Z","timestamp":1787323155550,"version":"3.56.0"},"reference-count":36,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>We propose a stable nonparametric method for constructing an option pricing model of exponential L\u00e9vy type, consistent with a given data set of option prices. After demonstrating the ill-posedness of the usual and least squares version of this inverse problem, we suggest to regularize the calibration problem by reformulating it as the problem of finding an exponential L\u00e9vy model that minimizes the sum of the pricing error and the relative entropy with respect to a prior exponential L\u00e9vy model. We prove the existence of solutions for the regularized problem and show that it yields solutions which are continuous with respect to the data, stable with respect to the choice of prior, and which converge to the minimum entropy least squares solution of the initial problem when the noise level in the data vanishes.<\/jats:p>","DOI":"10.1137\/040616267","type":"journal-article","created":{"date-parts":[[2006,2,23]],"date-time":"2006-02-23T21:00:22Z","timestamp":1140728422000},"page":"1-25","source":"Crossref","is-referenced-by-count":56,"title":["Retrieving L\u00e9vy Processes from Option Prices: Regularization of an Ill-posed Inverse Problem"],"prefix":"10.1137","volume":"45","author":[{"given":"Rama","family":"Cont","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Tankov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012903424423"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011354913068"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"Marco Avellaneda, The minimum\u2010entropy algorithm and related methods for calibrating asset\u2010pricing models, Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998), 1998, 545\u201356399i:90013","DOI":"10.4171\/dms\/1-3\/53"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1142\/S0219024998000242"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1142\/S0219024901000882"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1080\/135048697334827"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3700-6"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/9.1.69"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.21314\/JCF.2005.130"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.21314\/JCF.1999.043"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1029962753"},{"key":"R12","unstructured":"R. Cont,\n                      Model uncertainty and its impact on the pricing of derivative instruments\n                      , Math. Finance, to appear."},{"key":"R13","volume-title":"Financial modelling with jump processes","author":"Cont Rama","year":"2004"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.21314\/JCF.2004.123"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142903436186"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/19\/1\/306"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176996454"},{"key":"R18","first-page":"18","volume":"7","author":"Dupire B.","year":"1994","journal-title":"RISK"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00093"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144500358232"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/0730079"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00079"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(00)00011-9"},{"key":"R24","unstructured":"Thomas Goll, Ludger R\u00fcschendorf, Minimal distance martingale measures and optimal portfolios consistent with observed market prices, Stochastics Monogr., Vol. 12, Taylor & Francis, London, 2002, 141\u20131542004f:60099"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(81)90026-0"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.21314\/JCF.1998.022"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-003-0294-y"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.21314\/JCF.1997.002"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1007\/s007800200097"},{"key":"R30","unstructured":"L. Nguyen,\n                      Calibration de Mod\u00e8les Financiers par Minimisation d\u2019Entropie Relative et Mod\u00e8les avec Sauts\n                      , Ph.D. thesis, Ecole Nationale de Ponts et Chauss\u00e9es, Paris, France, 2003."},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1968.24.525"},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1994.tb00079.x"},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00005"},{"key":"R34","unstructured":"K. Sato,\n                      L\u00e9vy Processes and Infinitely Divisible Distributions\n                      , Cambridge University Press, Cambridge, UK, 1999."},{"key":"R35","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1996.tb05220.x"},{"key":"R36","unstructured":"P. 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