Random grids

In the context of a stochastic local volatility model, Jesper Andreasen and Brian Huge present a numerical solution scheme that achieves full consistency between calibration, finite difference solution and Monte Carlo simulation. The method is based on a fully implicit finite difference scheme for the model

Derivatives models are generally specified in continuous form as a stochastic differential equation (SDE), and implementation of a model will typically involve a number of different discrete approximations of the SDE. For example, an implementation of the Heston (1993) model might have calibration to European-style option prices via numerical inversion of discrete Fourier transforms, backward pricing of exotics handled in a Craig-Sneyd (1988) finite difference scheme, and Monte Carlo pricing