{"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/a-note-on-the-option-price-and-mass-at-zero","title":"A note on the option price and 'Mass at zero in the uncorrelated SABR model and implied volatility asymptotics'","arxiv_id":"2011.00557","date":"2020-11-01","proceeding":null,"authors":["Jaehyuk Choi","Lixin Wu"],"abstract":"Gulisashvili et al. [Quant. Finance, 2018, 18(10), 1753-1765] provide a small-time asymptotics for the mass at zero under the uncorrelated stochastic-alpha-beta-rho (SABR) model by approximating the integrated variance with a moment-matched lognormal distribution. We improve the accuracy of the numerical integration by using the Gauss--Hermite quadrature. We further obtain the option price by integrating the constant elasticity of variance (CEV) option prices in the same manner without resorting to the small-strike volatility smile asymptotics of De Marco et al. [SIAM J. Financ. Math., 2017, 8(1), 709-737]. For the uncorrelated SABR model, the new option pricing method is accurate and arbitrage-free across all strike prices.","url_abs":"https://arxiv.org/abs/2011.00557v2","url_pdf":"https://arxiv.org/pdf/2011.00557v2.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":"a-note-on-the-option-price-and-mass-at-zero","repo_url":"https://github.com/PyFE/PyfengForPapers","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"a-note-on-the-option-price-and-mass-at-zero","repo_url":"https://github.com/PyFE/PyFENG","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"math","task_name":"Math"},{"task_slug":"numerical-integration","task_name":"Numerical Integration"}],"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}