Abstract
We calculate the American local volatility. New insights on the American vanilla, call and put options in this paper are presented. In particular, the sensitivities of these products to the local volatility surface are illustrated. The Automatic Algorithmic Differentiation (AAD) pseudo code is presented for the American options in line with the paper [CLP] and [AP]. We propose a generalisation formula for the American vanilla option in the presence of smile. A gradient descent algorithm is presented and applied to the calibration task. A deep analysis of the difference between market practitionners and the true solution is presented and exploited to generate good initial guess for the calibration algorithm.
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