Notes on the application of randomized quasi-Monte Carlo methods to financial engineering problems

An outstanding performance of randomized quasi-Monte Carlo methods for multidimensional integration problems in finance are widely appreciated. Many financial option pricing problems use quasirandom (vector) sequences to generate sample paths of the underlying asset price by summing up the transformed (usually by inverse normal distribution) components of each vector. In this paper we consider the distribution of the summation of the transformed components of each vector in the randomized quasirandom sequence. Numerical experiments for financial option pricing problems are shown to compare randomized quasirandom sequence and another Monte Carlo method. In Sec. 2 we introduce several notions used in the rest part of the paper. Sec. 3 gives the investigation on the distribution of the sum of point coordinates in scrambled nets. We present several numerical experimental results in Sec. 5. In the final section we summarize our result.