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Strong Predictor-Corrector Euler Methods for Stochastic Differential Equations

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Abstract

This paper introduces a new class of numerical schemes for the pathwise approximation of solutions of stochastic differential equations (SDEs). The proposed family of strong predictor-corrector Euler methods are designed to handle scenario simulation of solutions of SDEs. It has the potential to overcome some of the numerical instabilities that are often experienced when using the explicit Euler method. This is of importance, for instance, in finance where martingale dynamics arise for solutions of SDEs with multiplicative diffusion coefficients. Numerical experiments demonstrate the improved asymptotic stability properties of the new symmetric predictor-corrector Euler methods.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp222.pdf
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Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 222.

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Length: 23
Date of creation: 01 Jun 2008
Date of revision:
Handle: RePEc:uts:rpaper:222

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Keywords: Stochastic differential equations; simulation methods; strong predictor-corrector Euler methods; strong convergence; asymptotic stability;

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  1. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151.
  2. Yoshihiro Saito & Taketomo Mitsui, 1993. "Simulation of stochastic differential equations," Annals of the Institute of Statistical Mathematics, Springer, vol. 45(3), pages 419-432, September.
  3. Platen, Eckhard, 1995. "On weak implicit and predictor-corrector methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 69-76.
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Cited by:
  1. 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.
  2. Eckhard Platen & Lei Shi, 2008. "On the Numerical Stability of Simulation Methods for SDES," Research Paper Series 234, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Eckhard Platen & Renata Rendek, 2009. "Quasi-exact Approximation of Hidden Markov Chain Filters," Research Paper Series 258, Quantitative Finance Research Centre, University of Technology, Sydney.

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