{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T06:10:07Z","timestamp":1777875007270,"version":"3.51.4"},"reference-count":17,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,12,1]]},"abstract":"Abstract<\/jats:title>\n \n In this note, we describe a new approach to the option pricing problem by introducing the notion of the safe (and acceptable) price for the writer of an option, in contrast to the fair price used in the Black\u2013Scholes model.\nOur starting point is that the option pricing problem is closely related with the hedging problem by practical techniques.\nRecalling that the Black\u2013Scholes model does not give us the price of the option but the initial value of a replicating portfolio, we observe easily that this has a serious disadvantage because it assumes the building of this replicating portfolio continuously in time, and this is a disadvantage of any model that assumes such a construction.\nHere we study the problem from the practical point of view concerning mainly the over-the-counter market.\nThis approach is not affected by the number of the underlying assets and is particularly useful for incomplete markets.\nIn the usual Black\u2013Scholes or binomial approach or some other approaches, one assumes that one can invest or borrow at the same risk-free rate\n \n \n \n \n r<\/m:mi>\n ><\/m:mo>\n 0<\/m:mn>\n <\/m:mrow>\n <\/m:math>\n \n r>0<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , which is not true in general.\nEven if this is the case, one can immediately observe that this risk-free rate is not a universal constant but is different among different people or institutions.\nSo the fair price of an option is not so much fair!\nMoreover, the two sides are not, in general, equivalent against the risk; therefore, the notion of a fair price has no meaning at all.\nWe also define a variant of the usual binomial model, by estimating safe upward and downward rates\n \n \n \n \n u<\/m:mi>\n ,<\/m:mo>\n d<\/m:mi>\n <\/m:mrow>\n <\/m:math>\n \n u,d<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , trying to give a cheaper safe or acceptable price for the option.\n <\/jats:p>","DOI":"10.1515\/mcma-2022-2122","type":"journal-article","created":{"date-parts":[[2022,9,27]],"date-time":"2022-09-27T16:18:40Z","timestamp":1664295520000},"page":"307-318","source":"Crossref","is-referenced-by-count":3,"title":["On the practical point of view of option pricing"],"prefix":"10.1515","volume":"28","author":[{"given":"Nikolaos","family":"Halidias","sequence":"first","affiliation":[{"name":"Department of Statistics and Actuarial-Financial Mathematics , University of the Aegean , Karlovassi 83200, Samos , Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2022,9,28]]},"reference":[{"key":"2026043020441019009_j_mcma-2022-2122_ref_001","doi-asserted-by":"crossref","unstructured":"P. Carr, K. Ellis and V. Gupta,\nStatic hedging of exotic options,\nJ. Finance 53 (1998), no. 3, 1\u201326.","DOI":"10.1111\/0022-1082.00048"},{"key":"2026043020441019009_j_mcma-2022-2122_ref_002","doi-asserted-by":"crossref","unstructured":"R.-R. Chen, S.-L. Chung and T. T. Yang,\nOption pricing in a multi-asset, complete market economy,\nJ. Financ. Quant. Anal. 37 (2002), no. 4, 649\u2013666.","DOI":"10.2307\/3595015"},{"key":"2026043020441019009_j_mcma-2022-2122_ref_003","doi-asserted-by":"crossref","unstructured":"J. Cox, S. Ross and M. Runinstein,\nOption pricing: A simplified approach,\nJ. Financial Econ. 7 (1979), 229\u2013263.","DOI":"10.1016\/0304-405X(79)90015-1"},{"key":"2026043020441019009_j_mcma-2022-2122_ref_004","unstructured":"D. Duffie,\nDynamic Asset Pricing Theory,\nPrinceton University, Princeton, 2001."},{"key":"2026043020441019009_j_mcma-2022-2122_ref_005","doi-asserted-by":"crossref","unstructured":"N. Halidias,\nAn elementary approach to the option pricing problem,\nAsian Res. J. Math. 1 (2016), 1\u201318.","DOI":"10.9734\/ARJOM\/2016\/26251"},{"key":"2026043020441019009_j_mcma-2022-2122_ref_006","doi-asserted-by":"crossref","unstructured":"N. Halidias,\nOn the option pricing by the binomial model,\nAsian J. Math. Appl. 2022 (2022), Paper No. 9.","DOI":"10.20944\/preprints202107.0407.v1"},{"key":"2026043020441019009_j_mcma-2022-2122_ref_007","unstructured":"J. Hull,\nOptions, Futures and Other Derivatives,\nPrentice Hall, Upper Saddle River, 2010."},{"key":"2026043020441019009_j_mcma-2022-2122_ref_008","doi-asserted-by":"crossref","unstructured":"L. Jiang,\nMathematical Modeling and Methods of Option Pricing,\nWorld Scientific, Singapure, 2005.","DOI":"10.1142\/5855"},{"key":"2026043020441019009_j_mcma-2022-2122_ref_009","doi-asserted-by":"crossref","unstructured":"L. Jiang and M. Dai,\nConvergence of binomial tree methods for European\/American path-dependent options,\nSIAM J. Numer. Anal. 42 (2004), no. 3, 1094\u20131109.","DOI":"10.1137\/S0036142902414220"},{"key":"2026043020441019009_j_mcma-2022-2122_ref_010","doi-asserted-by":"crossref","unstructured":"I. Karatzas and S. Shreve,\nMethods of Mathematical Finance,\nSpringer, New York, 1998.","DOI":"10.1007\/b98840"},{"key":"2026043020441019009_j_mcma-2022-2122_ref_011","doi-asserted-by":"crossref","unstructured":"R. Korn and E. Korn,\nOption Pricing and Portfolio Optimization,\nAmerican Mathematical Society, Providence, 2000.","DOI":"10.1090\/gsm\/031"},{"key":"2026043020441019009_j_mcma-2022-2122_ref_012","doi-asserted-by":"crossref","unstructured":"M. Musiela and M. Rutkowski,\nMartingale Methods in Financial Modelling,\nSpringer, Berlin, 2005.","DOI":"10.1007\/b137866"},{"key":"2026043020441019009_j_mcma-2022-2122_ref_013","doi-asserted-by":"crossref","unstructured":"J. Nygaard Nielsen, H. Madsen and P. C. Young,\nParameter estimation in stochastic differential equations: An overview,\nAnnu. Rev. Control 24 (2000), 83\u201394.","DOI":"10.1016\/S1367-5788(00)90017-8"},{"key":"2026043020441019009_j_mcma-2022-2122_ref_014","doi-asserted-by":"crossref","unstructured":"A. Pascucci and W. Runggaldier,\nFinancial Mathematics,\nSpringer, Milan, 2012.","DOI":"10.1007\/978-88-470-2538-7"},{"key":"2026043020441019009_j_mcma-2022-2122_ref_015","doi-asserted-by":"crossref","unstructured":"N. Privault,\nStochastic Finance: An introduction with Market Examples,\nCRC, Boca Raton, 2014.","DOI":"10.1201\/b16359"},{"key":"2026043020441019009_j_mcma-2022-2122_ref_016","doi-asserted-by":"crossref","unstructured":"S. Shreve,\nStochastic Calculus for Finance I and II,\nSpringer, New York, 2004.","DOI":"10.1007\/978-1-4757-4296-1"},{"key":"2026043020441019009_j_mcma-2022-2122_ref_017","unstructured":"P. Wilmott,\nPaul Wilmott on Quantitative Finance,\nWiley, New York, 2007."}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/mcma-2022-2122\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/mcma-2022-2122\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T20:44:17Z","timestamp":1777581857000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/mcma-2022-2122\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,28]]},"references-count":17,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,9,28]]},"published-print":{"date-parts":[[2022,12,1]]}},"alternative-id":["10.1515\/mcma-2022-2122"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2022-2122","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"value":"0929-9629","type":"print"},{"value":"1569-3961","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,28]]}}}