Finite difference methods for medium-and high-dimensional derivative pricing PDEs

Many models in financial mathematics and financial engineering, particularly in derivative pricing, can be formulated as partial differential equations (PDEs). Specifically, for the most commonly used continuous-time models of asset prices the value function of a derivative security, that is the option value as a function of the underlying asset price, is given by a PDE. This opens up the possibility to use accurate approximation schemes for PDEs for the numerical computation of derivative prices.