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Dimension- and Time-Adaptive Multilevel Monte Carlo Methods

  • Thomas Gerstner
  • Stefan Heinz
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 88)

Abstract

We use the multilevel Monte Carlo method to estimate option prices in computational finance and combine this method with two adaptive algorithms. In the first algorithm we consider time discretization and sample size as two separate dimensions and use dimension-adaptive refinement to optimize the error with respect to these dimensions in relation to the computational costs. The second algorithm uses locally adaptive timestepping and is constructed especially for non-Lipschitz payoff functions whose weak and strong order of convergence is reduced when the Euler-Maruyama method is used to discretize the underlying SDE. The numerical results show that for barrier and double barrier options the convergence order for smooth payoffs can be recovered in these cases.

Keywords

Root Mean Square Error Stochastic Differential Equation Payoff Function Barrier Option Discount Payoff 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institut für MathematikJohann Wolfgang Goethe-UniversitätFrankfurt am MainGermany

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