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 30 Marzo, 2016  16:00 oclock
Sezione di Finanza Quantitativa

The Parabolic Taylor Formula of the Implied Volatility

 Stefano Pagliarani, Ecole Polytechnique, CMAP
 Aula Seminari III piano
Abstract

We are concerned with the study of the asymptotic behavior of the implied volatility (IV) and its derivatives with respect to strike and maturity. We consider a multivariate model driven by a stochastic process that, locally, is a diffusion in the sense of Stroock and Varadhan (1979) and Friedman (1975, 1976). Our main result is a rigorous derivation of the exact Taylor formula of the IV in a parabolic region close to expiry and at the money (ATM).