Exact Scenario Simulation for Selected Multi-dimensional Stochastic Processes

Eckhard Platen () and Renata Rendek

No 259, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

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 instance, in finance. They have been playing a crucial role as standard models in various areas and dominate often the communication and thinking in a particular field of application, even that they may be too simple for more advanced tasks. Various discrete time simulation methods have been developed over the years. However, the simulation of solutions of some stochastic differential equations can be problematic due to systematic errors and numerical 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.

Keywords: exact scenario simulation; multi-dimensional stochastic differential equations; multi-dimensional Ornstein-Uhlenbeck process; multi-dimensional square root process; multi-dimensional squared Bessel process; Wishart process; multi-dimensional Levy process (search for similar items in EconPapers)
Pages: 29 pages
Date: 2009-10-01
New Economics Papers: this item is included in nep-cmp
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Citations: View citations in EconPapers (12)

Published as: Platen, E. and Rendek, R., 2009, "Exact Scenario Simulation for Selected Multi-dimensional Stochastic Processes", Communications on Stochastic Analysis, 3(3), 443-465.

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