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epsilon-Strong simulation of the Brownian path

Beskos, A; Peluchetti, S; Roberts, G; (2012) epsilon-Strong simulation of the Brownian path. Bernoulli , 18 (4) pp. 1223-1248. 10.3150/11-BEJ383. Green open access

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Abstract

We present an iterative sampling method which delivers upper and lower bounding processes for the Brownian path. We develop such processes with particular emphasis on being able to unbiasedly simulate them on a personal computer. The dominating processes converge almost surely in the supremum and L1L1 norms. In particular, the rate of converge in L1L1 is of the order O(K−1/2)O(K−1/2), KK denoting the computing cost. The a.s. enfolding of the Brownian path can be exploited in Monte Carlo applications involving Brownian paths whence our algorithm (termed the εε-strong algorithm) can deliver unbiased Monte Carlo estimators over path expectations, overcoming discretisation errors characterising standard approaches. We will show analytical results from applications of the εε-strong algorithm for estimating expectations arising in option pricing. We will also illustrate that individual steps of the algorithm can be of separate interest, giving new simulation methods for interesting Brownian distributions.

Type: Article
Title: epsilon-Strong simulation of the Brownian path
Open access status: An open access version is available from UCL Discovery
DOI: 10.3150/11-BEJ383
Publisher version: https://doi.org/10.3150/11-BEJ383
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Brownian bridge, intersection layer, iterative algorithm, option pricing, pathwise convergence, unbiased sampling
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/1325568
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