Beskos, Alexandros, Peluchetti, Stefano and Roberts, Gareth O. (2012) ε-Strong simulation of the Brownian path. Bernoulli, Volume 18 (Number 4). pp. 1223-1248. doi:10.3150/11-BEJ383

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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 L 1 norms. In particular, the rate of converge in L 1 is of the order O(K −1/2 ) , K 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 ε -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 ε -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.

Item Type:	Journal Article
Divisions:	Faculty of Science > Statistics
Journal or Publication Title:	Bernoulli
Publisher:	Int Statistical Institute
ISSN:	1350-7265
Official Date:	12 November 2012
Dates:	Date Event 12 November 2012 Published
Volume:	Volume 18
Number:	Number 4
Page Range:	pp. 1223-1248
DOI:	10.3150/11-BEJ383
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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