13.7.1 Low Discrepancy Sequences

Low Discrepancy Sequences, also called quasi-random numbers, are a recent substitute to the traditional random numbers used by all compilers (usually called pseudo-random numbers). They were introduced in the '50s and '60s by mathematicians like Halton, Sobol, and Niederreiter. The theory and implementation of low discrepancy sequences have enjoyed tremendous progress in the past 10 years, and they are now becoming increasingly popular in the area of financial mathematics.

The main objective of low discrepancy sequences is to reduce the error of Monte Carlo methods. Because the error in Monte Carlo methods decreases with the number of scenarios, we can also state that Monte Carlo with LDS needs fewer scenarios than traditional Monte Carlo to obtain the same result. Therefore, Monte Carlo with LDS should be faster than traditional Monte Carlo.