Valuation of mortgage-backed securities using Brownian bridges to reduce effective dimension

The quasi-Monte Carlo method for nancial 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 signiicantly better performance than the error size O(N ?1=2) for standard Monte Carlo. But in high dimensional problems this beneet 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. We believe that this is due to a lower eeective dimension of the integrand in those cases. This paper deenes the eeective dimension and shows in examples how the eeective dimension may be reduced by using a Brownian bridge representation.