On the skew and curvature of the implied and local volatilities
In 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,...
| Autores: | , , |
|---|---|
| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2023 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10230/59131 |
| Acesso em linha: | http://hdl.handle.net/10230/59131 http://dx.doi.org/10.1080/1350486X.2023.2261459 |
| Access Level: | acceso abierto |
| Palavra-chave: | Stochastic volatility local volatility rough volatility Malliavin calculus |
| Resumo: | In 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. |
|---|