A multilevel approach to control variates

ABSTRACT We present a new variance reduction technique that naturally applies to the pricing of financial derivatives by Monte Carlo simulation. Inspired by multigrid methods for solving partial differential equations, the technique is based on control variates derived from a sequence of approximations that converge pathwise to a limiting model. It applies to a large class of problems, and is easy to implement. Theory and computational results show this method can substantially reduce computational time relative to crude Monte Carlo estimation and is competitive with other variance reduction techniques under Monte Carlo sampling.