High-Performance Simulation of Generalized Tempered Stable Random Variates: Exact and Numerical Methods for Heavy-Tailed Data
Bibliographic record
Abstract
The Generalized Tempered Stable (GTS) distribution extends classical stable laws through exponential tempering, preserving the power-law behavior while ensuring finite moments. This makes it especially suitable for modeling heavy-tailed financial data. However, the lack of closed-form densities poses significant challenges for simulation. This study provides a comprehensive and systematic comparison of GTS simulation methods, including rejection-based algorithms, series representations, and an enhanced Fast Fractional Fourier Transform (FRFT)-based inversion method. Through extensive numerical experiments on major financial assets (Bitcoin, Ethereum, the S&P 500, and the SPY ETF), this study demonstrates that the FRFT method outperforms others in terms of accuracy and ability to capture tail behavior, as validated by goodness-of-fit tests. Our results provide practitioners with robust and efficient simulation tools for applications in risk management, derivative pricing, and statistical modeling.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".