High-Performance Simulation of Generalized Tempered Stable Random Variates: Exact and Numerical Methods for Heavy-Tailed Data

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.