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Exact Scenario Simulation for Selected Multi-dimensional Stochastic Processes

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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.

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  • Eckhard Platen & Renata Rendek, 2009. "Exact Scenario Simulation for Selected Multi-dimensional Stochastic Processes," Research Paper Series 259, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:259
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    Cited by:

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    2. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen & Erik Schlögl, 2009. "Alternative Defaultable Term Structure Models," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(1), pages 1-31, March.
    3. Ke Du, 2013. "Commodity Derivative Pricing Under the Benchmark Approach," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2, July-Dece.
    4. Eckhard Platen & Renata Rendek, 2009. "Simulation of Diversified Portfolios in a Continuous Financial Market," Research Paper Series 264, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Yaacov Kopeliovich & Michael Pokojovy, 2024. "On Merton's Optimal Portfolio Problem under Sporadic Bankruptcy," Papers 2403.15923, arXiv.org.
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    7. Ke Du, 2013. "Commodity Derivative Pricing Under the Benchmark Approach," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2013.
    8. Eckhard Platen & Renata Rendek, 2019. "Dynamics of a Well-Diversified Equity Index," Research Paper Series 398, Quantitative Finance Research Centre, University of Technology, Sydney.
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    11. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2013.

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