Comparison of Sobol' sequences in financial applications

TL;DR

This paper compares different high-dimensional Sobol' sequences and a modified Niederreiter sequence in financial models to evaluate their effectiveness in quasi-Monte Carlo methods.

Contribution

It provides a comparative analysis of various Sobol' sequence implementations and introduces a modified Niederreiter sequence for financial applications.

Findings

Different Sobol' sequences show varying performance in financial models

The modified Niederreiter sequence performs competitively with Sobol' sequences

Insights into the suitability of sequences for high-dimensional financial simulations

Abstract

Sobol' sequences are widely used for quasi-Monte Carlo methods that arise in financial applications. Sobol' sequences have parameter values called direction numbers, which are freely chosen by the user, so there are several implementations of Sobol' sequence generators. The aim of this paper is to provide a comparative study of (non-commercial) high-dimensional Sobol' sequences by calculating financial models. Additionally, we implement the Niederreiter sequence (in base 2) with a slight modification, that is, we reorder the rows of the generating matrices, and analyze and compare it with the Sobol' sequences.