{"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/hyperbolic-normal-stochastic-volatility-model","title":"Hyperbolic normal stochastic volatility model","arxiv_id":"1809.04035","date":"2018-09-11","proceeding":null,"authors":[],"abstract":"For option pricing models and heavy-tailed distributions, this study proposes\na continuous-time stochastic volatility model based on an arithmetic Brownian\nmotion: a one-parameter extension of the normal stochastic alpha-beta-rho\n(SABR) model. Using two generalized Bougerol's identities in the literature,\nthe study shows that our model has a closed-form Monte-Carlo simulation scheme\nand that the transition probability for one special case follows Johnson's\n$S_U$ distribution---a popular heavy-tailed distribution originally proposed\nwithout stochastic process. It is argued that the $S_U$ distribution serves as\nan analytically superior alternative to the normal SABR model because the two\ndistributions are empirically similar.","url_abs":"http://arxiv.org/abs/1809.04035v1","url_pdf":"http://arxiv.org/pdf/1809.04035v1.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":"hyperbolic-normal-stochastic-volatility-model","repo_url":"https://github.com/PyFE/PyfengForPapers","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"hyperbolic-normal-stochastic-volatility-model","repo_url":"https://github.com/PyFE/NSVh-R","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"model","task_name":"model"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}