A variance reduction technique using a quantized Brownian motion as a control variate

Antoine Lejay (1, 2) , Victor Reutenauer (3)

1 IECN - Institut Élie Cartan de Nancy
2 TOSCA - Simuler et calibrer des modèles stochastiques
3 FIM - Service Interest Rates and Hybrid Quantitative Research

This article presents a new variance reduction technique for diffusion processes where a control variate is constructed using a quantization of the coefficients of the Karhunen-Loève decomposition of the underlying Brownian motion. This method may be indeed used for other Gaussian processes.

Mots clés: Variance reduction; Control variate; Least squares method; Monte Carlo simulation for diffusion processes; Karhunen-Loève decomposition

Domaines: Probabilités [math.PR]

Antoine Lejay, Victor Reutenauer. A variance reduction technique using a quantized Brownian motion as a control variate. The Journal of Computational Finance, 2012, 16 (2), pp.61-84. ⟨inria-00393749v3⟩