ABSTRACT

The quasi-Monte Carlo method for financial valuation and other integration problems has error bounds of size O((log N)^k N^-1), or even O((log N)^k N^-3/2), which suggests significantly better performance than the error size O(N^-1/2) for standard Monte Carlo. But in high-dimensional problems, this benefit might not appear at feasible sample sizes. Substantial improvements from quasi-Monte Carlo integration have, however, been reported for problems such as the valuation of mortgage-backed securities, in dimensions as high as 360. The authors believe that this is due to a lower effective dimension of the integrand in those cases. This paper defines the effective dimension and shows in examples how the effective dimension may be reduced by using a Brownian bridge representation.