Multilevel Dimension Reduction Monte-Carlo Simulation for High-Dimensional Stochastic Models in Finance

10 Pages Posted: 21 Jan 2015 Last revised: 13 Dec 2015

See all articles by Duy-Minh Dang

Duy-Minh Dang

University of Queensland - School of Mathematics and Physics

Qifan Xu

University of Queensland - Department of Mathematics

Shangzhe Wu

University of Queensland - Department of Mathematics

Date Written: January 18, 2015

Abstract

One-way coupling often occurs in multi-dimensional stochastic models in finance. In this paper, we develop a highly efficient Monte Carlo (MC) method for pricing European options under a N-dimensional one-way coupled model, where N is arbitrary. The method is based on a combination of (i) the powerful dimension and variance reduction technique, referred to as drMC, developed in Dang et. al (2014), that exploits this structure, and (ii) the highly effective multilevel MC (mlMC) approach developed by Giles (2008). By first applying Step (i), the dimension of the problem is reduced from N to 1, and as a result, Step (ii) is essentially an application of mlMC on a 1-dimensional problem. Numerical results show that, through a careful construction of the ml-dr estimator, improved efficiency expected from the Milstein timestepping with first order strong convergence can be achieved. Moreover, our numerical results show that the proposed ml-drMC method is significantly more efficient than the mlMC methods currently available for multi-dimensional stochastic problems.

Keywords: Monte Carlo, multilevel, conditional Monte Carlo, dimension reduction, variance reduction

JEL Classification: E40, E43, G12, G13, C61, C63

Suggested Citation

Dang, Duy-Minh and Xu, Qifan and Wu, Shangzhe, Multilevel Dimension Reduction Monte-Carlo Simulation for High-Dimensional Stochastic Models in Finance (January 18, 2015). Available at SSRN: https://ssrn.com/abstract=2553047 or http://dx.doi.org/10.2139/ssrn.2553047

Duy-Minh Dang (Contact Author)

University of Queensland - School of Mathematics and Physics ( email )

Priestly Building
St Lucia
Brisbane, Queesland 4067
Australia

HOME PAGE: http://people.smp.uq.edu.au/Duy-MinhDang/

Qifan Xu

University of Queensland - Department of Mathematics ( email )

Priestly Building
St Lucia
Brisbane, Queensland 4072
Australia

Shangzhe Wu

University of Queensland - Department of Mathematics ( email )

Priestly Building
St Lucia
Brisbane, Queensland 4072
Australia

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