Statistical Romberg extrapolation: A new variance reduction method and applications to option pricing

Simple item page
dc.creatorKebaier, Ahmed
dc.date2006-02-23
dc.date.accessioned2026-07-07T07:03:43Z
dc.date.available2026-07-07T07:03:43Z
dc.descriptionWe study the approximation of $\mathbb{E}f(X_T)$ by a Monte Carlo algorithm, where $X$ is the solution of a stochastic differential equation and $f$ is a given function. We introduce a new variance reduction method, which can be viewed as a statistical analogue of Romberg extrapolation method. Namely, we use two Euler schemes with steps $δ$ and $δ^β,0<β<1$. This leads to an algorithm which, for a given level of the statistical error, has a complexity significantly lower than the complexity of the standard Monte Carlo method. We analyze the asymptotic error of this algorithm in the context of general (possibly degenerate) diffusions. In order to find the optimal $β$ (which turns out to be $β=1/2$), we establish a central limit type theorem, based on a result of Jacod and Protter for the asymptotic distribution of the error in the Euler scheme. We test our method on various examples. In particular, we adapt it to Asian options. In this setting, we have a CLT and, as a by-product, an explicit expansion of the discretization error.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051605000000511 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0602529
dc.identifierhttp://arxiv.org/abs/math/0602529
dc.identifierAnnals of Applied Probability 2005, Vol. 15, No. 4, 2681-2705
dc.identifierdoi:10.1214/105051605000000511
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/109082
dc.subjectProbability
dc.subject65C05, 60F05 (Primary) 62P05 (Secondary)
dc.titleStatistical Romberg extrapolation: A new variance reduction method and applications to option pricing
dc.typetext

Files

Collections

arXiv