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On the Efficiency of Simplified Weak Taylor Schemes for Monte Carlo Simulation in Finance

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Abstract

The purpose of this paper is to study the efficiency of simplified weak schemes for stochastic differential equations. We present a numerical comparison between weak Taylor schemes and their simplified versions. In the simplified schemes discrete random variables, instead of Gaussian ones, are generated to approximate multiple stochastic integrals. We show that an implementation of simplified schemes based on random bits generators significantly increases the computational speed. The efficiency of the proposed schemes is demonstrated.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp114.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 114.

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Date of creation: 01 Jan 2004
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Handle: RePEc:uts:rpaper:114

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Keywords: random bits generators; stochastic differential equations; simplified weak taylor schemes;

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References

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  1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-47.
  2. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
  3. Steve Heston & Guofu Zhou, 2000. "On the Rate of Convergence of Discrete-Time Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 53-75.
  4. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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Cited by:
  1. Nicola Bruti-Liberati & Eckhard Platen, 2006. "On Weak Predictor-Corrector Schemes for Jump-Diffusion Processes in Finance," Research Paper Series 179, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. Nicola Bruti-Liberati & Filippo Martini & Massimo Piccardi & Eckhard Platen, 2005. "A Hardware Generator of Multi-point Distributed Random Numbers for Monte Carlo Simulation," Research Paper Series 156, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Nicola Bruti-Liberati & Eckhard Platen, 2007. "Approximation of jump diffusions in finance and economics," Computational Economics, Society for Computational Economics, vol. 29(3), pages 283-312, May.

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