Simulation of Generalized Tempered Stable (GTS) Random Variates via Series Representations: A Case Study of Bitcoin and Ethereum

Abstract

The paper presents two series representations of a L{\'e}vy process for the Generalized Tempered Stable (GTS) distribution: a series representation generated by the inverse tail integral and a short noise representation. Both series representations are used to simulate the daily returns of Bitcoin and Ethereum. The Q-Q plot analysis shows smooth linear patterns, indicating strong agreement between the empirical and theoretical GTS distributions.