30 Marzo, 2016 16:00 in punto

Sezione di Finanza Quantitativa

The Parabolic Taylor Formula of the Implied Volatility

Stefano Pagliarani, Ecole Polytechnique, CMAP

Aula Seminari III piano

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).