Exact Simulation for General Tempered Stable Random Variates: Review and Empirical Analysis

This study develops and implements exact sampling methods for the Generalized Tempered Stable (GTS) distribution. The seven-parameter model lacks a closed-form Probability Density Function (PDF), making direct sampling challenging. The exact sampling methods are applied to empirical financial data, including daily returns of Bitcoin and the S&P 500 Index. To assess the adequacy of the GTS model, we use quantile-quantile (Q-Q) plots, which reveal that the stability index parameters significantly impact sampling performance. Specifically, when the stability indexes are low, the SSR and Double Rejection methods demonstrate diminished accuracy. Our findings highlight the crucial role of the stability index parameters in the effectiveness of GTS sampling algorithms, offering valuable insights into their practical application for modeling financial returns.