Nonlinear Option Pricing

Chapter 10

McKean Nonlinear Stochastic

Differential Equations

The advantage of being smart is that you can always make a fool,

while the opposite is quite impossible.

— Woody Allen

As will be explained in Chapters 11 and 12, the calibration of local stochastic

volatility models and local correlation models to market smiles leads to the

so-called McKean nonlinear stochastic differential equations (SDEs). In such

nonlinear SDEs, in contrast with classical Itˆo SDEs, the drift and volatil-

ity coefficients depend on the (unknown) marginal law of the process. The

Fokker-Planck equation associated to this SDE is therefore nonlinear, hence

the denomination. In