{"id":434024,"date":"2026-08-24T17:23:52","date_gmt":"2026-08-24T09:23:52","guid":{"rendered":"https:\/\/library.usj.edu.mo\/?post_type=tnc_col_19837_item&#038;p=434024"},"modified":"2026-08-24T18:33:16","modified_gmt":"2026-08-24T10:33:16","slug":"the-role-of-the-volatility-in-the-option-market","status":"publish","type":"tnc_col_19837_item","link":"https:\/\/library.usj.edu.mo\/zh\/scholarly-work-usj\/the-role-of-the-volatility-in-the-option-market\/","title":{"rendered":"THE ROLE OF THE VOLATILITY IN THE OPTION MARKET"},"content":{"rendered":"<p>WE REVIEW SOME GENERAL ASPECTS ABOUT THE BLACK\u2013SCHOLES EQUATION, WHICH IS USED FOR PREDICTING THE FAIR PRICE OF AN OPTION INSIDE THE STOCK MARKET. OUR ANALYSIS INCLUDES THE SYMMETRY PROPERTIES OF THE EQUATION AND ITS SOLUTIONS. WE USE THE HAMILTONIAN FORMULATION FOR THIS PURPOSE. TAKING INTO ACCOUNT THAT THE VOLATILITY INSIDE THE BLACK\u2013SCHOLES EQUATION IS A PARAMETER, WE THEN INTRODUCE THE MERTON\u2013GARMAN EQUATION, WHERE THE VOLATILITY IS STOCHASTIC, AND THEN IT CAN BE PERCEIVED AS A FIELD. WE THEN SHOW HOW THE BLACK\u2013SCHOLES EQUATION AND THE MERTON\u2013GARMAN ONE ARE LOCALLY EQUIVALENT BY IMPOSING A GAUGE SYMMETRY UNDER CHANGES IN THE PRICES OVER THE BLACK\u2013SCHOLES EQUATION. THIS DEMONSTRATES THAT THE STOCHASTIC VOLATILITY EMERGES NATURALLY FROM SYMMETRY ARGUMENTS. FINALLY, WE ANALYZE THE ROLE OF THE VOLATILITY ON THE DECISIONS TAKEN BY THE HOLDERS OF THE OPTIONS WHEN THEY USE THE SOLUTION OF THE BLACK\u2013SCHOLES EQUATION AS A TOOL FOR MAKING INVESTMENT DECISIONS.<\/p>","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","format":"standard","class_list":["post-434024","tnc_col_19837_item","type-tnc_col_19837_item","status-publish","format-standard","hentry","tnc_tax_19818-english","tnc_tax_19716-faculty-of-business-and-law","tnc_tax_19659-journal-article"],"taxonomy_info":[],"featured_image_src_large":false,"author_info":[],"comment_info":0,"featured_img":false,"coauthors":[],"author_meta":{"author_link":"https:\/\/library.usj.edu.mo\/zh\/author\/emilychan\/","display_name":"emily chan"},"relative_dates":{"created":"Posted 6 \u5929 ago","modified":"Updated 6 \u5929 ago"},"absolute_dates":{"created":"Posted on 24 8 \u6708, 2026","modified":"Updated on 24 8 \u6708, 2026"},"absolute_dates_time":{"created":"Posted on 24 8 \u6708, 2026 5:23 \u4e0b\u5348","modified":"Updated on 24 8 \u6708, 2026 6:33 \u4e0b\u5348"},"featured_img_caption":"","tax_additional":{"tnc_tax_19993":{"linked":[],"unlinked":[],"slug":"tnc_tax_19993","name":"SDGs"},"tnc_tax_19818":{"linked":["<a href=\"https:\/\/library.usj.edu.mo\/zh\/language\/english\/\" class=\"advgb-post-tax-term\">ENGLISH<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">ENGLISH<\/span>"],"slug":"tnc_tax_19818","name":"LANGUAGE"},"tnc_tax_19716":{"linked":["<a href=\"https:\/\/library.usj.edu.mo\/zh\/faculty-research-unit\/faculty-of-business-and-law\/\" class=\"advgb-post-tax-term\">FACULTY OF BUSINESS AND LAW<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">FACULTY OF BUSINESS AND LAW<\/span>"],"slug":"tnc_tax_19716","name":"FACULTY \/ RESEARCH UNIT"},"tnc_tax_19664":{"linked":[],"unlinked":[],"slug":"tnc_tax_19664","name":"SUBJECT"},"tnc_tax_19659":{"linked":["<a href=\"https:\/\/library.usj.edu.mo\/zh\/resource-type\/journal-article\/\" class=\"advgb-post-tax-term\">Journal Article<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">Journal Article<\/span>"],"slug":"tnc_tax_19659","name":"Document Type"}},"series_order":"","_links":{"self":[{"href":"https:\/\/library.usj.edu.mo\/zh\/wp-json\/wp\/v2\/tnc_col_19837_item\/434024","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/library.usj.edu.mo\/zh\/wp-json\/wp\/v2\/tnc_col_19837_item"}],"about":[{"href":"https:\/\/library.usj.edu.mo\/zh\/wp-json\/wp\/v2\/types\/tnc_col_19837_item"}],"replies":[{"embeddable":true,"href":"https:\/\/library.usj.edu.mo\/zh\/wp-json\/wp\/v2\/comments?post=434024"}],"version-history":[{"count":1,"href":"https:\/\/library.usj.edu.mo\/zh\/wp-json\/wp\/v2\/tnc_col_19837_item\/434024\/revisions"}],"predecessor-version":[{"id":436414,"href":"https:\/\/library.usj.edu.mo\/zh\/wp-json\/wp\/v2\/tnc_col_19837_item\/434024\/revisions\/436414"}],"wp:attachment":[{"href":"https:\/\/library.usj.edu.mo\/zh\/wp-json\/wp\/v2\/media?parent=434024"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}