Decoding the American Vanilla Prices

12 Pages Posted: 31 Oct 2013

Date Written: October 31, 2013

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.

Keywords: American options, local volatility, calibration, algorithmic differentiation, gradient descent, market practice

JEL Classification: G13, C0, C60

Suggested Citation

Reghai, Adil and Langnau, Alex and Ben Haj Yedder, Adel, Decoding the American Vanilla Prices (October 31, 2013). Available at SSRN: https://ssrn.com/abstract=2347910 or http://dx.doi.org/10.2139/ssrn.2347910

Adil Reghai (Contact Author)

ADIA ( email )

211 Corniche
Abu Dhabi
United Arab Emirates

Alex Langnau

Allianz Investment Management ( email )

Königinstrasse 28
Munich, 80802
Germany

Adel Ben Haj Yedder

Independent ( email )

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