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.
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Gerstner, T., Heinz, S. (2012). Dimension- and Time-Adaptive Multilevel Monte Carlo Methods. In: Garcke, J., Griebel, M. (eds) Sparse Grids and Applications. Lecture Notes in Computational Science and Engineering, vol 88. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31703-3_5
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DOI: https://doi.org/10.1007/978-3-642-31703-3_5
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