{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:39:59Z","timestamp":1760143199241,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,25]],"date-time":"2024-01-25T00:00:00Z","timestamp":1706140800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12071479"],"award-info":[{"award-number":["12071479"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper, we recover the European option volatility function \u03c3(t) of the underlying asset and the fractional order \u03b1 of the time fractional derivatives under the time fractional Vasicek model. To address the ill-posed nature of the inverse problem, we employ Tikhonov regularization. The Alternating Direction Multiplier Method (ADMM) is utilized for the simultaneous recovery of the parameter \u03b1 and the volatility function \u03c3(t). In addition, the existence of a solution to the minimization problem has been demonstrated. Finally, the effectiveness of the proposed approach is verified through numerical simulation and empirical analysis.<\/jats:p>","DOI":"10.3390\/a17020054","type":"journal-article","created":{"date-parts":[[2024,1,25]],"date-time":"2024-01-25T06:54:12Z","timestamp":1706165652000},"page":"54","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Simultaneous Calibration of European Option Volatility and Fractional Order under the Time Fractional Vasicek Model"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-2402-9453","authenticated-orcid":false,"given":"Yunkang","family":"Du","sequence":"first","affiliation":[{"name":"School of Mathematics, Renmin University of China, Beijing 100872, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zuoliang","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mathematics, Renmin University of China, Beijing 100872, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1086\/260062","article-title":"The pricing of options and corporate liabilities","volume":"81","author":"Black","year":"1973","journal-title":"J. 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