ABSTRACT
Many recent issues in option pricing, ranging from parameter uncertainty to illiquidity, from optimal exercise to calibration of local stochastic volatility models or local correlation models to market smiles, from transaction costs to credit valuation adjustment, are described by nonlinear PDEs. In this chapter, as an appetizer for the rest of the book, we present various practical examples of such nonlinear PDEs. Finite difference schemes are described in a one-dimensional setup. Probabilistic methods are required in the multidimensional setup and will be extensively covered in the following chapters.
