On smile properties of volatility derivatives: understanding the VIX skew
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 te...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | 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:10230/59132 |
| Acceso en línea: | http://hdl.handle.net/10230/59132 http://dx.doi.org/10.1137/19M1269981 |
| Access Level: | acceso abierto |
| Palabra clave: | variance options VIX implied volatility Malliavin calculus stochastic volatility models rough volatility fractional Brownian motion |
| Sumario: | 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. |
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