Exact Simulation of Finite Variation Tempered Stable Ornstein-Uhlenbeck Processes

MI: Global COE Program Education-and-Research Hub for Mathematics-for-IndustryグローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」We develop an exact yet simple simulation algorithm for a wide class of Ornstein-Uhlenbeck processes with a tempered stable stationary distribution of finite variation. We derive the exact transition probability of tempered stable Ornstein-Uhlenbeck processes between consecutive times due to the homogeneous Markovian autoregressive structure. Random element involved can be divided into independent tempered stable and compound Poisson distributions, each of which can be generated in the exact sense with acceptance-rejection methods, respectively, with stable and gamma proposal distributions. Our algorithm proves useful for the simulations of bilateral tempered stable Ornstein-Uhlenbeck processes and normal tempered stable processes. The effectiveness of the proposed algorithm is discussed relative to the existing approximative method based on infinite series representation of sample paths