{"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/mass-at-zero-in-the-uncorrelated-sabr-model","title":"Mass at zero in the uncorrelated SABR model and implied volatility asymptotics","arxiv_id":"1502.03254","date":"2016-11-22","proceeding":null,"authors":[],"abstract":"We study the mass at the origin in the uncorrelated SABR stochastic\nvolatility model, and derive several tractable expressions, in particular when\ntime becomes small or large. As an application--in fact the original motivation\nfor this paper--we derive small-strike expansions for the implied volatility\nwhen the maturity becomes short or large. These formulae, by definition\narbitrage free, allow us to quantify the impact of the mass at zero on existing\nimplied volatility approximations, and in particular how correct/erroneous\nthese approximations become.","url_abs":"http://arxiv.org/abs/1502.03254v2","url_pdf":"http://arxiv.org/pdf/1502.03254v2.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":"mass-at-zero-in-the-uncorrelated-sabr-model","repo_url":"https://github.com/JackJacquier/SABR-Implied-Volatility","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}