Exact Simulation of Solutions of SDEs

Abstract

Accurate scenario simulation methods for solutions of multi-dimensional stochastic differential equations find applications in the statistics of stochastic processes and many applied areas, in particular in finance. They play a crucial role when used in standard models in various areas. These models often dominate the communication and thinking in a particular field of application, even though they may be too simple for advanced tasks. Various simulation techniques have been developed over the years. However, the simulation of solutions of some stochastic differential equations can still be problematic. 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 of those simulation methods that use discrete-time approximations. This chapter follows closely Platen & Rendek (2009a) and provides methods for the exact simulation of paths of multi-dimensional solutions of stochastic differential equations, including Ornstein-Uhlenbeck, square root, squared Bessel, Wishart and Levy type processes. Other papers that could be considered to be related with exact simulation include Lewis & Shedler (1979), Beskos & Roberts (2005), Broadie & Kaya (2006), Kahl & Jackel (2006), Smith (2007), Andersen (2008), Burq & Jones (2008) and Chen (2008).