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

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. We 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. 1 Introduction Simulation is often the only effective numerical method for the accurate valuation of securities whose value depends on the whole trajectory of interest Mathematics Departmen. . .