A Computational Study on Sobol’ Sequences
Chapter from the book:
Tahtalı,
Y.
&
Demir,
İ.
&
Bayyurt,
L.
(eds.)
2025.
Current Approaches in Applied Statistics I.
Synopsis
This study presents a computational comparison between Quasi-Monte Carlo (QMC) methods based on Sobol’ sequences and traditional Monte Carlo (MC) methods using the Mersenne Twister (MT) generator. While Sobol’ sequences are widely recognized for outperforming MT in terms of convergence, our results reveal notable deficiencies when applied to high-dimensional Geometric Asian option pricing. To investigate this behavior, we conduct moment and correlation analyses, identifying a bias in the incremental construction of Sobol’ paths—a bias that is absent in MT and can be alleviated through skipping initial points, scrambling, or Brownian Bridge (BB) techniques. All simulations are implemented in Python, with additional acceleration achieved through Graphics Processing Unit (GPU)-based parallel computing environments.
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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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Copyright (c) 2025 Yalçın Tahtalı- İbrahim Demir- Lütfi Bayyurt; Ahmet Arvas- Mercan Hatipoğlu- Bahri Tokmak- Ömer Ugur- Berra Kocakoç- Gülistan Erdal- Beyhan Doğan- Dursun Yılmaz- Cem Gül- Bilge Gözener- Mehmet Can Kaya- Dursun Yılmaz- Feridun Taşdan- Rukiye Dağalp- Melike Tekin- Gülistan Erdal- Mustafa Talip Koyuncu- Burak Demir- Muhammet Fatih Aslan- Akif Durdu- Nurgül Okur- Tuğçe Yıldırım Dal- Uğur Ayık- Hasan Hüseyin Gül