Acceleration of quasi-Monte Carlo approximations

In this paper, a new method is presented for numerically approximating integrals using quasi-Monte Carlo sequences. By applying a least-squares smoothing procedure to the sequences, a faster rate of convergence is achieved thus reducing the number of nodes required for the same degree of accuracy.

This acceleration method is applied to four particular integrals in a variety of dimensions. The first integral is a smooth exponential function and the second has a discontinuous integrand. The last two integrals deal with specific problems in mathematical finance. One computes the price for a European call option, while the other finds the present value of a mortgage-backed security over thirty years.