This PhD focuses on the calibration of local and stochastic volatility models.
According to Gyongy's theorem, a local and stochastic volatility (LSV) model calibrated to the European call prices for all positive strikes and maturities leads to a stochastic differential equation (SDE) which is non-linear in the sense of McKean.
In the industry, probabilistic particle methods provide a practical and efficient calibration procedure of LSV models, provided that the range of the stochastic volatility process is not too large.
But so far, no existence or uniqueness result is available for the SDE describing the calibrated LSV model. The objective of this PhD is therefore to analyze this kind of equation and its simulation.
CERMICS, École Nationale des Ponts et Chaussées
6 et 8, av. Blaise Pascal
Cité Descartes - Champs-sur-Marne
77455 Marne-la-Vallée cedex 2