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EnglishIn a model driven by a multi-dimensional local diffusion, we study the behavior of implied volatility {\sigma} and its derivatives with respect to log-strike k and maturity T near expiry and at the money. We recover explicit limits of these derivatives for (T,k) approaching the origin within the parabolic region |x-k|^2 < {\lambda} T, with x denoting the spot log-price of the underlying asset and where {\lambda} is a positive and arbitrarily large constant. Such limits yield the exact Taylor formula for implied volatility within the parabola |x-k|^2 < {\lambda} T. In order to include important models of interest in mathematical finance, e.g. Heston, CEV, SABR, the analysis is carried out under the assumption that the infinitesimal generator of the diffusion is only locally elliptic.
| Titolo: | The exact Taylor formula of the implied volatility |
| Autori: | |
| Data di pubblicazione: | 2017 |
| Data ahead of print: | 25-mag-2017 |
| Stato di pubblicazione: | Pubblicato |
| Rivista: | |
| Abstract: | In a model driven by a multi-dimensional local diffusion, we study the behavior of implied volatility {\sigma} and its derivatives with respect to log-strike k and maturity T near expiry and at the money. We recover explicit limits of these derivatives for (T,k) approaching the origin within the parabolic region |x-k|^2 < {\lambda} T, with x denoting the spot log-price of the underlying asset and where {\lambda} is a positive and arbitrarily large constant. Such limits yield the exact Taylor formula for implied volatility within the parabola |x-k|^2 < {\lambda} T. In order to include important models of interest in mathematical finance, e.g. Heston, CEV, SABR, the analysis is carried out under the assumption that the infinitesimal generator of the diffusion is only locally elliptic. |
| Handle: | http://hdl.handle.net/11368/2903972 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00780-017-0330-x |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
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| Pagliariani_The exact Taylor formula of the implied volatility.pdf | Documento in Versione Editoriale | Digital Rights Management non definito | Administrator Richiedi una copia | |
| The exact Taylor formula of the implied volatility_postprint.pdf | postprint | Bozza finale post-referaggio (post-print) | Digital Rights Management non definito | Open Access Visualizza/Apri |
http://hdl.handle.net/11368/2903972
