Gilles Pags
Multi-step Richardson-Romberg Extrapolation: Remarks on Variance Control and Complexity
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 R
2 (instead of 2
R
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.
Monte Carlo Methods and Applications, Walter de Gruyter
Print ISSN: 0929-9629
Volume: 13, 04/2007
Pages: 37 - 70
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