{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:21:28Z","timestamp":1760149288399,"version":"build-2065373602"},"reference-count":7,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,7,29]],"date-time":"2023-07-29T00:00:00Z","timestamp":1690588800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministerio de Ciencia e Innovaci\u00f3n","award":["PID2020-118339GBI00"],"award-info":[{"award-number":["PID2020-118339GBI00"]}]},{"name":"Center for Advanced Research in Finance (CARF)","award":["PID2020-118339GBI00"],"award-info":[{"award-number":["PID2020-118339GBI00"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In the short time to maturity limit, it is proved that for the conditionally lognormal SABR model the zero vanna implied volatility is a lower bound for the volatility swap strike. The result is valid for all values of the correlation parameter and is a sharper lower bound than the at-the-money implied volatility for correlation less than or equal to zero.<\/jats:p>","DOI":"10.3390\/axioms12080749","type":"journal-article","created":{"date-parts":[[2023,7,31]],"date-time":"2023-07-31T03:30:02Z","timestamp":1690774202000},"page":"749","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Lower Bound for the Volatility Swap in the Lognormal SABR Model"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4234-0671","authenticated-orcid":false,"given":"Elisa","family":"Al\u00f2s","sequence":"first","affiliation":[{"name":"Barcelona Graduate School of Economics, Universitat Pompeu Fabra, 08005 Barcelona, Spain"}]},{"given":"Frido","family":"Rolloos","sequence":"additional","affiliation":[{"name":"Independent Researcher, 2500 The Hague, The Netherlands"}]},{"given":"Kenichiro","family":"Shiraya","sequence":"additional","affiliation":[{"name":"Graduate School of Economics, The University of Tokyo, Tokyo 113-0033, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Carr, P., and Lee, R. (2008, January 21). Robust replication of volatility derivatives. PRMIA award for Best Paper in Derivatives. Proceedings of the MFA 2008 Annual Meeting, New York, NY, USA.","DOI":"10.2139\/ssrn.1108429"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1080\/14697680500362452","article-title":"Valuation of volatility derivatives as an inverse problem","volume":"5","author":"Friz","year":"2005","journal-title":"Quant. Financ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1002\/wilm.10566","article-title":"Taylor-made volatility swaps","volume":"2017","author":"Rolloos","year":"2017","journal-title":"Wilmott"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1137\/20M134722X","article-title":"On the difference between the volatility swap strike and the zero vanna implied volatility","volume":"12","author":"Rolloos","year":"2021","journal-title":"Siam J. Financ. Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1111\/1467-9965.00057","article-title":"Long memory in continuous-time stochastic volatility models","volume":"8","author":"Comte","year":"1998","journal-title":"Math. Financ."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1080\/14697688.2017.1393551","article-title":"Volatility is rough","volume":"18","author":"Gatheral","year":"1998","journal-title":"Quant. Financ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1007\/s00780-019-00384-5","article-title":"Estimating the Hurst parameter from short term volatility swaps: A Malliavin calculus approach","volume":"23","author":"Shiraya","year":"2019","journal-title":"Financ. Stoch."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/8\/749\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:22:19Z","timestamp":1760127739000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/8\/749"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,29]]},"references-count":7,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["axioms12080749"],"URL":"https:\/\/doi.org\/10.3390\/axioms12080749","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2023,7,29]]}}}