QuantLib 1.33 provides an implementation of Owen scrambling for Sobol sequences following Burley’s paper [1]. Compared to unscrambled sequences it provides faster convergence and removal of artifacts. We test the properties by performing the integration
from [2] for dimensions d from 100 to 5000 using sequences of length 30031, see section 6.3 and Figure 9 in [2]. The following graph shows the order of the absolute integration error
for an unscrambled sequence using Kuo direction numbers vs. the Burley scrambled version. To use the sequence generator in OpenSourceRiskEngine select the sequence type “Burley2020SobolBrownianBridge” as in this example.
References:
[1] Brent Burley: Practical Hash-based Owen Scrambling, Journal of Computer Graphics Techniques, Vol. 9, No. 4, 2020
[2] Sobol, Asotsky, Kreinin, Kucherenko: Construction and Comparison of High-Dimensional Sobol’ Generators