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

Kawai Reiichiro () and Masuda Hiroki ()
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Kawai Reiichiro: Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK.
Masuda Hiroki: Institute of Mathematics for Industry, Kyushu University, Fukuoka 819-0395, Japan.

Monte Carlo Methods and Applications, 2011, vol. 17, issue 3, 279-300

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

Keywords: Acceptance-rejection sampling; high-frequency sampling; Lévy process; Ornstein–Uhlenbeck process; subordinator; transition probability; tempered stable process (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1515/mcma.2011.012

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