Dimension and variance reduction for Monte Carlo methods for high-dimensional models in finance

Dang, Duy-Minh, Jackson, Kenneth R. and Mohammadi, Mohammadreza (2015) Dimension and variance reduction for Monte Carlo methods for high-dimensional models in finance. Applied Mathematical Finance, 22 6: 522-552. doi:10.1080/1350486X.2015.1110492

Author Dang, Duy-Minh
Jackson, Kenneth R.
Mohammadi, Mohammadreza
Title Dimension and variance reduction for Monte Carlo methods for high-dimensional models in finance
Journal name Applied Mathematical Finance   Check publisher's open access policy
ISSN 1350-486X
Publication date 2015
Sub-type Article (original research)
DOI 10.1080/1350486X.2015.1110492
Open Access Status Not Open Access
Volume 22
Issue 6
Start page 522
End page 552
Total pages 31
Place of publication Abingdon, Oxon, United Kingdom
Publisher Routledge
Collection year 2016
Language eng
Formatted abstract
One-way coupling often occurs in multi-dimensional models in finance. In this paper, we present a dimension reduction technique for Monte Carlo (MC) methods, referred to as drMC, that exploits this structure for pricing plain-vanilla European options under an N-dimensional one-way coupled model, where N is arbitrary. The dimension reduction also often produces a significant variance reduction.

The drMC method is a dimension reduction technique built upon (i) the conditional MC technique applied to one of the factors which does not depend on any other factors in the model, and (ii) the derivation of a closed-form solution to the conditional partial differential equation (PDE) that arises via Fourier transforms. In the drMC approach, the option price can be computed simply by taking the expectation of this closed-form solution. Hence, the approach results in a powerful dimension reduction from N to one, which often results in a significant variance reduction as well, since the variance associated with the other (N−1) factors in the original model are completely removed from the drMC simulation. Moreover, under the drMC framework, hedging parameters, or Greeks, can be computed in a much more efficient way than in traditional MC techniques. A variance reduction analysis of the method is presented and numerical results illustrating the method’s efficiency are provided.
Keyword Conditional Monte Carlo
Variance reduction
Dimension reduction
Fourier transform
Partial differential equations
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ
Additional Notes Published online 11 February 2016

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2016 Collection
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Created: Tue, 13 Oct 2015, 12:01:32 EST by Duy-minh Dang on behalf of Mathematics