Monte Carlo integration, quadratic resampling, and asset pricing Original Research Article

We present a new error reduction technique for Monte-Carlo valuation of multidimensional integrals. The method, called Quadratic Resampling, consists in applying a linear transform over a sequence of random samples. This linear transform is computed from a comparative analysis of the theoretical and empirical second order moments. The resulting linearly transformed quadrature scheme is shown to be exact for any polynomial integrand of degree two. Quadratic resampling can be efficiently combined with classical variance reduction methods such as importance sampling to further improve the accuracy of the estimate. We have applied this method for pricing a class of financial assets called European assets. Our numerical experiments show that the method is practical for computing integrals with up to one hundred dimensions. We also describe an implementation of the method on a massively parallel supercomputer, yielding two orders of magnitude of performance improvement over the same implementation on a desktop workstation.