On the Efficiency of Simplified Weak Taylor Schemes for Monte Carlo Simulation in Finance
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.
|Date of creation:||01 Jan 2004|
|Date of revision:|
|Publication status:||Published as: Bruti Liberati, N. and PLaten, E., 2004, "On the Efficiency of Simplified Weak Taylor Schemes for Monte Carlo Simulation in Finance", In: Computational Science - ICCS 2004: Lecture Notes in Computer Science, 771-778.|
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- 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.
- 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.
- 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.
- 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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