Being particular about calibration

Following previous work on the calibration of multi-factor local stochastic volatility models to market smiles, Julien Guyon and Pierre Henry-Labordère show how to calibrate exactly any such model. Their approach, based on McKean’s particle method, extends to hybrid models, where interest rates are also stochastic. They illustrate the efficiency of their algorithm on hybrid local stochastic volatility models

The calibration of stochastic volatility and hybrid models to market smiles is a longstanding problem in quantitative finance. Partial answers have been given, for low-dimensional factor models such as old-fashioned one-factor local stochastic volatility (LSV) models or a hybrid Dupire local volatility model with a one-factor interest rate model, this calibration can be achieved by solving a two-dimensional non-linear Fokker-Planck partial differential equation (PDE) (Lipton, 2002). For multi