{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T00:17:13Z","timestamp":1770337033951,"version":"3.49.0"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","funder":[{"DOI":"10.13039\/501100000780","name":"European Union","doi-asserted-by":"crossref","award":["FP7-PEOPLE-2012-ITN project STRIKE (Novel Methods in Computational Finance) 304617"],"award-info":[{"award-number":["FP7-PEOPLE-2012-ITN project STRIKE (Novel Methods in Computational Finance) 304617"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Slovak Research Grant Agency","award":["VEGA 1\/0780\/15"],"award-info":[{"award-number":["VEGA 1\/0780\/15"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Market illiquidity,\nfeedback effects, presence of transaction costs, risk from unprotected portfolio and other nonlinear effects in PDE-based option pricing models can be described by solutions to the generalized Black\u2013Scholes parabolic equation with a diffusion term nonlinearly depending on the option price itself.\nIn this paper, different linearization techniques such as Newton's method and the analytic asymptotic approximation formula are adopted and compared for a wide class of nonlinear Black\u2013Scholes equations including, in particular, the market illiquidity model and the risk-adjusted pricing model. Accuracy and time complexity of both numerical methods are compared.\nFurthermore, market quotes data was used to calibrate model parameters.<\/jats:p>","DOI":"10.1515\/cmam-2015-0035","type":"journal-article","created":{"date-parts":[[2015,11,26]],"date-time":"2015-11-26T17:01:30Z","timestamp":1448557290000},"page":"35-50","source":"Crossref","is-referenced-by-count":4,"title":["Comparison of the Analytical Approximation Formula and Newton's Method for Solving a Class of Nonlinear Black\u2013Scholes Parabolic Equations"],"prefix":"10.1515","volume":"16","author":[{"given":"Karol","family":"\u010euri\u0161","sequence":"first","affiliation":[{"name":"National Bank of Slovakia, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shih-Hau","family":"Tan","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Greenwich, London, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Choi-Hong","family":"Lai","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Greenwich, London, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"\u0160ev\u010dovi\u010d","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Statistics, Division of Applied Mathematics, Comenius University, Bratislava, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2015,11,26]]},"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/16\/1\/article-p35.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0035\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0035\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T21:33:46Z","timestamp":1680298426000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0035\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,26]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,1]]},"published-print":{"date-parts":[[2016,1,1]]}},"alternative-id":["10.1515\/cmam-2015-0035"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2015-0035","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2015,11,26]]}}}