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Article Dans Une Revue The Annals of Applied Probability Année : 2005

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

Résumé

We study the approximation of Ef(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 delta and delta(beta), 0 < beta < 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 beta (which turns out to be beta = 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.

Dates et versions

hal-00693106 , version 1 (01-05-2012)

Identifiants

Citer

Ahmed Kebaier. Statistical Romberg extrapolation: A new variance reduction method and applications to option pricing. The Annals of Applied Probability, 2005, 15 (4), pp.2681--2705. ⟨10.1214/105051605000000511⟩. ⟨hal-00693106⟩
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