A Computational Study on Sobol' Sequences
VI. International Applied Statistics Congress (UYIK – 2025), Ankara, Türkiye, 14 - 16 Mayıs 2025, ss.15-48, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Doi Numarası: 10.58830/ozgur.pub862.c3485
- Basıldığı Şehir: Ankara
- Basıldığı Ülke: Türkiye
- Sayfa Sayıları: ss.15-48
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
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.