{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/tighter-uniform-bounds-for-black-scholes","title":"Tighter 'uniform bounds for Black-Scholes implied volatility' and the applications to root-finding","arxiv_id":"2302.08758","date":"2023-02-17","proceeding":null,"authors":["Jaehyuk Choi","Jeonggyu Huh","Nan Su"],"abstract":"Using the option delta systematically, we derive tighter lower and upper bounds of the Black-Scholes implied volatility than those in Tehranchi [SIAM J. Financ. Math. 7 (2016), 893-916]. As an application, we propose a Newton-Raphson algorithm on the log price that converges rapidly for all price ranges when using a new lower bound as an initial guess. Our new algorithm is a better alternative to the widely used naive Newton-Raphson algorithm, whose convergence is slow for extreme option prices.","url_abs":"https://arxiv.org/abs/2302.08758v2","url_pdf":"https://arxiv.org/pdf/2302.08758v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"tighter-uniform-bounds-for-black-scholes","repo_url":"https://github.com/PyFE/PyfengForPapers","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"tighter-uniform-bounds-for-black-scholes","repo_url":"https://github.com/PyFE/PyFENG","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"math","task_name":"Math"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}