# 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-MinhJackson, Kenneth R.Mohammadi, Mohammadreza Dimension and variance reduction for Monte Carlo methods for high-dimensional models in finance Applied Mathematical Finance   Check publisher's open access policy 1350-486X1466-4313 2015 Article (original research) 10.1080/1350486X.2015.1110492 Not Open Access 22 6 522 552 31 Abingdon, Oxon, United Kingdom Routledge 2016 eng 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. Conditional Monte CarloVariance reductionDimension reductionCross-currencyFourier transformPartial differential equations C1 Provisional Code UQ Published online 11 February 2016

 Document type: Journal Article Article (original research) School of Mathematics and Physics Official 2016 Collection

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