Numerical solution for derivative models using finite difference methods and how this can be used with Monte Carlo simulation
Derivative models often come in the form of stochastic differential equations. From these equations a partial differential equation (PDE) can be derived. By discretizing the PDE the numerical solution is obtained on a form where the value of the derivative can be seen as a probabilistic weighting of future values. These probabilities can be used to simulate trajectories of the under- lying assets.