Exact scenario simulation for selected multi-dimensional stochastic processes

Abstract

Accurate scenario simulation methods for solutions of multi - dimensional stochastic differential equations find application in stochastic analysis, the statistics of stochastic processes and many other areas, for in- stance, in finance. Various discrete time simulation methods have been devel- oped over the years. However, the simulation of solutions of some stochastic differential equations can be problematic due to systematic errors and nu- merical instabilities. Therefore, it is valuable to identify multi-dimensional stochastic differential equations with solutions that can be simulated exactly. This avoids several of the theoretical and practical problems encountered by those simulation methods that use discrete time approximations. This paper provides a survey of methods for the exact simulation of paths of some multi- dimensional solutions of stochastic differential equations including Ornstein- Uhlenbeck, square root, squared Bessel, Wishart and Levy type processes.