Brownian meanders, importance sampling and unbiased simulation of diffusion extremes

Brownian meanders, importance sampling and unbiased simulation of diffusion extremes

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Article ID: iaor20127765
Volume: 40
Issue: 6
Start Page Number: 554
End Page Number: 563
Publication Date: Nov 2012
Journal: Operations Research Letters
Authors: ,
Keywords: simulation
Abstract:

Computing expected values of functions involving extreme values of diffusion processes can find many applications in financial engineering. Conventional discretization simulation schemes often converge slowly. We propose a Wiener‐measure‐decomposition based approach to construct unbiased Monte Carlo estimators. Combined with the importance sampling technique and the Williams path decomposition of Brownian motion, this approach transforms simulating extreme values of a general diffusion process to simulating two Brownian meanders. Numerical experiments show this estimator performs efficiently for diffusions with and without boundaries.

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