Multi-step Richardson-Romberg Extrapolation: Remarks on Variance Control and Complexity

Pagès Gilles ()
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Pagès Gilles: Email: gpa@ccr.jussieu.fr

Monte Carlo Methods and Applications, 2007, vol. 13, issue 1, 37-70

Abstract: We propose a multi-step Richardson-Romberg extrapolation method for the computation of expectations Ef(XT ) of a diffusion (Xt)t∈[0,T] when the weak time discretization error induced by the Euler scheme admits an expansion at an order R ≥ 2. The complexity of the estimator grows as R2 (instead of 2R in the classical method) and its variance is asymptotically controlled by considering some consistent Brownian increments in the underlying Euler schemes. Some Monte Carlo simulations were carried with path-dependent options (lookback, barrier) which support the conjecture that their weak time discretization error also admits an expansion (in a different scale). Then an appropriate Richardson-Romberg extrapolation seems to outperform the Euler scheme with Brownian bridge.

Keywords: SDE; Euler-Maruyama scheme; Romberg extrapolation; Vandermonde determinant; lookback option; barrier option . (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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DOI: 10.1515/MCMA.2007.003

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