Nonlinear Option Pricing

Chapter 11

Calibration of Local Stochastic

Volatility Models to Market Smiles

You’re never fully dressed without a smile.

— Martin Charnin

The calibration of local stochastic volatility models to market smiles leads

to McKean nonlinear stochastic differential equations (SDEs), introduced in

Chapter 10. As shown in Section 10.1, the Fokker-Planck equations associated

to McKean SDEs are nonlinear. In this chapter, we review various methods

for solving such nonlinear PDEs. For one-factor stochastic volatility models,

we can rely on finite difference schemes. But, as PDEs suffer from the curse of

dimensionality, we must turn to probabilistic methods to handle ...