Exact discrete sampling of finite variation tempered stable Ornstein–Uhlenbeck processes

Abstract

Exact yet simple simulation algorithms are developed for a wide class of Orn- stein-Uhlenbeck processes with tempered stable stationary distribution of finite varia- tion with the help of their exact transition probability between consecutive time points. Random elements involved can be divided into independent tempered stable and com- pound Poisson distributions, each of which can be simulated in the exact sense through acceptance-rejection sampling, respectively, with stable and gamma proposal distribu- tions. We discuss various alternative simulation methods within our algorithms on the ba- sis of acceptance rate in acceptance-rejection sampling for both high- and low-frequency sampling. Numerical results illustrate their advantage relative to the existing approxima- tive simulation method based on infinite shot noise series representation.