{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:33:52Z","timestamp":1787319232553,"version":"build-2736575974"},"reference-count":33,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"name":"Centre for Doctoral Training in Financial Computing and Analytics"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Finan. Math."],"published-print":{"date-parts":[[2022,3]]},"abstract":"<jats:p>We develop a method to study the implied volatility of exotic underlyings, with special focus on volatility derivatives such as VIX options. Remarkably, our approach is flexible enough to be applied to any underlying, subject to mild technical conditions. Our method, built upon Malliavin calculus techniques, allows to transform any such underlying into the Black--Scholes model with a particular type of stochastic volatility. This, in turn, allows us to describe the properties of the at-the-money implied volatility (ATMI) in terms of the Malliavin derivatives of the transformed underlying process. Concretely, we study the short-time behavior of the ATMI level and skew. As an application, we describe the short-term behavior of the ATMI of VIX and realize variance options in terms of the Hurst parameter of the model, and most importantly, we describe the class of volatility processes that generate a positive skew for the VIX implied volatility. Several numerical examples are provided to support our theoretical results.<\/jats:p>","DOI":"10.1137\/19m1269981","type":"journal-article","created":{"date-parts":[[2022,1,10]],"date-time":"2022-01-10T10:17:02Z","timestamp":1641809822000},"page":"32-69","source":"Crossref","is-referenced-by-count":13,"title":["On Smile Properties of Volatility Derivatives: Understanding the VIX Skew"],"prefix":"10.1137","volume":"13","author":[{"given":"Elisa","family":"Al\u00f2s","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Garc\u00eda-Lorite","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aitor Muguruza","family":"Gonzalez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2022,1,10]]},"reference":[{"key":"atypb1","unstructured":"M. Abramowitz and I. A. Stegun,\n                      Handbook of Mathematical Functions\n                      , National Bureau of Standards, 1965."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-006-0013-5"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1239\/aap\/1208358890"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/16M1086315"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-007-0049-1"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-019-00384-5"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1080\/1350486X.2013.868631"},{"key":"atypb8","first-page":"93","author":"Barndorff-Nielsen O. E.","year":"2007","journal-title":"Berlin"},{"key":"atypb9","first-page":"1","volume":"16","author":"Bayer C.","year":"2015","journal-title":"Quant. Finance"},{"key":"atypb10","doi-asserted-by":"crossref","unstructured":"A. Barletta, E. Nicolato, and S. Pagliarani,\n                      The short-time behavior of VIX-implied volatilitiesin a multifactor stochastic volatility framework\n                      , Math. Finance, (2018), pp. 1-39.","DOI":"10.2139\/ssrn.2942262"},{"key":"atypb11","doi-asserted-by":"crossref","unstructured":"M. Bennedsen, A. Lunde, and M. S. Pakkanen,\n                      Decoupling the Short- and Long-Term Behavior of Stochastic Volatility\n                      ,https:\/\/arxiv.org\/abs\/1610.00332, 2017.","DOI":"10.2139\/ssrn.2846756"},{"key":"atypb12","first-page":"67","author":"Bergomi L.","year":"2005","journal-title":"Risk"},{"key":"atypb13","first-page":"90","author":"Bergomi L.","year":"2008","journal-title":"Risk"},{"key":"atypb14","first-page":"94","author":"Bergomi L.","year":"2009","journal-title":"Risk"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1080\/0740817X.2013.857063"},{"key":"atypb16","unstructured":"S. de Marco,\n                      VIX Derivatives in Rough Forward Variance Models\n                      , Presentation, Bachelier Congress, Dublin, 2018."},{"key":"atypb17","first-page":"451","volume":"4","author":"Fouque J. P.","year":"2004","journal-title":"Finance Stoch."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1080\/14697688.2017.1412493"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1080\/14697688.2017.1393551"},{"key":"atypb20","unstructured":"J. Gatheral,\n                      Consistent Modeling of SPX and VIX Options\n                      , Presentation Bachelier Congress, 2008."},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1080\/1350486X.2017.1333015"},{"key":"atypb22","unstructured":"J. Guyon,\n                      On the Joint Calibration of SPX and VIX Options\n                      , Presentation, Bachelier Congress, Dublin, 2018."},{"key":"atypb23","doi-asserted-by":"crossref","unstructured":"J. Guyon,\n                      The joint S&P 500\/VIX smile calibration puzzle solved\n                      , Risk, 2020.","DOI":"10.2139\/ssrn.3397382"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1080\/14697688.2020.1753885"},{"key":"atypb25","doi-asserted-by":"crossref","unstructured":"B. Horvath, A. Jacquier, and A. Muguruza\n                      Functional Central Limit Theorems for Rough Volatility\n                      ,https:\/\/arxiv.org\/abs\/1711.03078, 2017.","DOI":"10.2139\/ssrn.3078743"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1137\/18M1169242"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1080\/14697688.2017.1353127"},{"key":"atypb28","doi-asserted-by":"crossref","unstructured":"I. Karatzas and S. E. Shreve,\n                      Brownian Motion and Stochastic Calculus\n                      , Springer, Berlin, 1997.","DOI":"10.1007\/978-1-4612-0949-2"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1108\/JRF-06-2014-0090"},{"key":"atypb30","unstructured":"R. W. Lee,\n                      Implied Volatility: Statics, dynamics, and probabilistic interpretation\n                      , in Recent Advances in Applied Probability, R. Baeza-Yates, J. Glaz, H. Gzyl, J. H\u00fcsler, and J. L. Palacios, eds., Springer, Berlin, 2005."},{"key":"atypb31","unstructured":"D. Nualart,\n                      The Malliavin Calculus and Related Topics\n                      , Springer, Berlin, 2006."},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1080\/14697688.2013.814923"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.1996.tb00117.x"}],"container-title":["SIAM Journal on Financial Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1269981","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:46:43Z","timestamp":1787316403000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1269981"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,10]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,3]]}},"alternative-id":["10.1137\/19M1269981"],"URL":"https:\/\/doi.org\/10.1137\/19m1269981","relation":{},"ISSN":["1945-497X"],"issn-type":[{"value":"1945-497X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,10]]}}}