ABSTRACT
For derivatives pricing, in a Markovian framework, the Feynman-Kac formula establishes a link between partial differential equations (PDEs) and stochastic processes. As we have seen finite difference schemes can be used to numerically solve PDEs/PIDEs. As the number of dimensions in Markovian frameworks grows, finite difference schemes become unworkable and unrealistic. Monte Carlo methods may be related to finite difference schemes for solving PDEs/PIDEs via the Feynman-Kac characterization. But unlike finite difference schemes that are limited to Markovian frameworks, Monte Carlo simulation is not and does not suffer from dimensionality issues.
