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The Smile Calibration Problem Solved

17 Pages Posted: 15 Jul 2011  

Julien Guyon

Bloomberg L.P.; Columbia University - Department of Mathematics; New York University - Courant Institute of Mathematical Sciences

Pierre Henry-Labordere

Société Générale - Paris, France

Date Written: July 13, 2011

Abstract

Following previous work on calibration of multi-factor local stochastic volatility models to market smiles, we show how to calibrate exactly any such models. Our approach, based on McKean’s particle method, extends to hybrid models, for which we provide a Malliavin representation of the effective local volatility. We illustrate the efficiency of our algorithm on hybrid local stochastic volatility models.

Keywords: non linear SDEs, particle method, calibration, Malliavin calculus

JEL Classification: G13

Suggested Citation

Guyon, Julien and Henry-Labordere, Pierre, The Smile Calibration Problem Solved (July 13, 2011). Available at SSRN: https://ssrn.com/abstract=1885032 or http://dx.doi.org/10.2139/ssrn.1885032

Julien Guyon (Contact Author)

Bloomberg L.P. ( email )

731 Lexington Avenue
New York, NY 10022
United States

Columbia University - Department of Mathematics ( email )

3022 Broadway
New York, NY 10027
United States

New York University - Courant Institute of Mathematical Sciences ( email )

New York University
New York, NY 10012
United States

Pierre Henry-Labordere

Société Générale - Paris, France ( email )

Paris-La Défense, Paris 92987
France

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