Alòs, ElisaGarcía-Lorite, DavidPravosud, Makar2024-02-192023Alòs E, García-Lorite D, Pravosud M. On the skew and curvature of the implied and local volatilities. Appl Math Finance. 2023;30(1):47-67. DOI: 10.1080/1350486X.2023.22614591350-486Xhttp://hdl.handle.net/10230/59131In this paper, we study the relationship between the short-end of the local and the implied volatility surfaces. Our results, based on Malliavin calculus techniques, recover the recent 1H+3/2 rule (where H denotes the Hurst parameter of the volatility process) for rough volatilities (see F. Bourgey, S. De Marco, P. Friz, and P. Pigato. 2022. “Local Volatility under Rough Volatility.” arXiv:2204.02376v1 [q-fin.MF] https://doi.org/10.48550/arXiv.2204.02376.), that states that the short-time skew slope of the at-the-money implied volatility is 1H+3/2 of the corresponding slope for local volatilities. Moreover, we see that the at-the-money short-end curvature of the implied volatility can be written in terms of the short-end skew and curvature of the local volatility and vice versa. Additionally, this relationship depends on H.application/pdfeng© This is an Accepted Manuscript of an article published by Taylor & Francis in Applied mathematical finance on 09 Oct 2023, available online: http://www.tandfonline.com/10.1080/1350486X.2023.2261459info:eu-repo/semantics/articlehttp://dx.doi.org/10.1080/1350486X.2023.2261459Stochastic volatilitylocal volatilityrough volatilityMalliavin calculusinfo:eu-repo/semantics/embargoedAccess