The Smile Calibration Problem Solved

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