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Regression-Based Variance Reduction Approach for Strong Approximation Schemes

  • Denis BelomestnyEmail author
  • Stefan Häfner
  • Mikhail Urusov
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 208)

Abstract

In this paper, we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the terminal functionals. In this way, the complexity order of the standard Monte Carlo algorithm (\(\varepsilon ^{-3}\)) can be reduced down to \(\varepsilon ^{-2}\sqrt{\left| \log (\varepsilon )\right| }\) in case of the Euler scheme with \(\varepsilon \) being the precision to be achieved. These theoretical results are illustrated by several numerical examples.

Keywords

Monte Carlo methods Regression methods Control variates Stochastic differential equations Strong schemes 

Notes

Acknowledgements

Stefan Häfner thanks the Faculty of Mathematics of the University of Duisburg-Essen, where this work was carried out.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Denis Belomestny
    • 1
    • 2
    Email author
  • Stefan Häfner
    • 3
  • Mikhail Urusov
    • 1
  1. 1.Duisburg-Essen UniversityEssenGermany
  2. 2.National Research University Higher School of EconomicsMoscowRussia
  3. 3.PricewaterhouseCoopers GmbHFrankfurtGermany

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