{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T15:18:57Z","timestamp":1784128737689,"version":"3.55.0"},"reference-count":10,"publisher":"Walter de Gruyter GmbH","issue":"4","license":[{"start":{"date-parts":[[2025,11,10]],"date-time":"2025-11-10T00:00:00Z","timestamp":1762732800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In this note we will discuss and review some recent results\nconcerning well-known financial mathematical problems such as\nportfolio construction, dynamic trading, option pricing, etc. We\nwill use some Python codes concerning the above and we will\ncompare the results with the existing methods and techniques. We\npropose also a new type of multi-asset options; the options on\ncorrelation. Using this kind of options one can refine more\neffectively the profit function of his\/her portfolio when this\ncontain two or more assets.\nIt is mathematically certain that, in practice, someone will eventually apply the techniques described in this paper. This is because, regarding the portfolio construction problem, we allow the investor to employ any forecasting technique \u2013 e.g., statistical methods, machine learning, behavioral finance, intuition, etc. Subsequently, the investor can enhance both the return and safety of their portfolio by incorporating call and put options.\nIn contrast, for the derivative pricing problem, it is evident that there is no room for forecasts (see volatility for example), as pricing involves two counterparties \u2013 the seller and the buyer \u2013 making it, metaphorically, a dance for two. For this reason, the pricing methodology proposed in this paper is model-free, ensuring that the resulting prices are fully consistent with the market values of available contracts. Moreover, the investor decides at which price to buy or sell a contract based on practical, statically implementable hedging strategies that we propose in this work. That is, any pricing method should justify why an investor ought to buy or sell a derivative at the proposed price. In other words, the method must provide a clear, economically sound rationale-typically grounded in no-arbitrage principles, replication arguments, or explicit hedging strategies \u2013 that links the quoted price to actionable, implementable decisions for market participants.\nWhat remains to be explored are advanced forecasting techniques that account for events affecting the stocks of interest to the investor, as well as the documentation of hedging strategies for path-dependent options.<\/jats:p>","DOI":"10.1515\/mcma-2025-2020","type":"journal-article","created":{"date-parts":[[2025,11,10]],"date-time":"2025-11-10T23:37:31Z","timestamp":1762817851000},"page":"279-309","source":"Crossref","is-referenced-by-count":1,"title":["An overview of financial mathematics with Python codes"],"prefix":"10.1515","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8756-8229","authenticated-orcid":false,"given":"Nikolaos","family":"Halidias","sequence":"first","affiliation":[{"name":"Department of Statistics and Actuarial-Financial Mathematics , University of the Aegean , Karlovassi 83200, Samos , Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2025,11,10]]},"reference":[{"key":"2025121816432003619_j_mcma-2025-2020_ref_001","doi-asserted-by":"crossref","unstructured":"L.  Bachelier,\nTheorie de la speculation,\nAnn. Sci. \u00c9c. Norm. Sup\u00e9r. (3) 17 (1900), 21\u201386.","DOI":"10.24033\/asens.476"},{"key":"2025121816432003619_j_mcma-2025-2020_ref_002","doi-asserted-by":"crossref","unstructured":"F.  Black and M.  Scholes,\nThe pricing of options and corporate liabilities,\nJ. Political Econom. 81 (1973), 637\u2013659.","DOI":"10.1086\/260062"},{"key":"2025121816432003619_j_mcma-2025-2020_ref_003","doi-asserted-by":"crossref","unstructured":"C.  Bernard, O.  Bondarenko and S.  Vanduffel,\nA model-free approach to multivariate option pricing,\nRev. Derivatives Res. 24 (2021), 135\u2013155.","DOI":"10.1007\/s11147-020-09172-2"},{"key":"2025121816432003619_j_mcma-2025-2020_ref_004","doi-asserted-by":"crossref","unstructured":"J.  Cox, S.  Ross and M.  Rubinstein,\nOption pricing: A simplified approach,\nJ. Financial Econom. 7 (1979), 229\u2013264.","DOI":"10.1016\/0304-405X(79)90015-1"},{"key":"2025121816432003619_j_mcma-2025-2020_ref_005","doi-asserted-by":"crossref","unstructured":"N.  Halidias,\nA novel portfolio optimization method and its application to the hedging problem,\nMonte Carlo Methods Appl. 30 (2024), no. 3, 249\u2013267.","DOI":"10.1515\/mcma-2024-2009"},{"key":"2025121816432003619_j_mcma-2025-2020_ref_006","doi-asserted-by":"crossref","unstructured":"N.  Halidias,\nOn the practical point of view of option pricing,\nMonte Carlo Methods Appl. 28 (2022), no. 4, 307\u2013318.","DOI":"10.1515\/mcma-2022-2122"},{"key":"2025121816432003619_j_mcma-2025-2020_ref_007","doi-asserted-by":"crossref","unstructured":"N.  Halidias and I. S.  Stamatiou,\nStochastic Analysis: Financial Mathematics with Matlab,\nDe Gruyter, Berlin, 2025.","DOI":"10.1515\/9783111443737"},{"key":"2025121816432003619_j_mcma-2025-2020_ref_008","unstructured":"N.  Halidias,\nFinancial Engineering, ResearchGate 2025."},{"key":"2025121816432003619_j_mcma-2025-2020_ref_009","doi-asserted-by":"crossref","unstructured":"H.  Markowitz,\nPortfolio Selection,\nJ. Finance 7 (1952), 77\u201391.","DOI":"10.1111\/j.1540-6261.1952.tb01525.x"},{"key":"2025121816432003619_j_mcma-2025-2020_ref_010","doi-asserted-by":"crossref","unstructured":"A.  Neufeld, A.  Papapantoleon and Q.  Xiang,\nModel-free bounds for multi-asset options using option-implied information and their exact computation,\nManag. Sci. 69 (2023), no. 4, 2051\u20132068.","DOI":"10.1287\/mnsc.2022.4456"}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/mcma-2025-2020\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/mcma-2025-2020\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T16:52:46Z","timestamp":1766076766000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/mcma-2025-2020\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,10]]},"references-count":10,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,7,1]]},"published-print":{"date-parts":[[2025,12,1]]}},"alternative-id":["10.1515\/mcma-2025-2020"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2025-2020","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"value":"0929-9629","type":"print"},{"value":"1569-3961","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,10]]}}}