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

Author

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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.)

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.

Suggested Citation

  • Kawai Reiichiro & Masuda Hiroki, 2011. "Exact discrete sampling of finite variation tempered stable Ornstein–Uhlenbeck processes," Monte Carlo Methods and Applications, De Gruyter, vol. 17(3), pages 279-300, January.
    • Handle: RePEc:bpj:mcmeap:v:17:y:2011:i:3:p:279-300:n:4
    DOI: 10.1515/mcma.2011.012
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    References listed on IDEAS

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    1. Shibin Zhang & Xinsheng Zhang, 2008. "Exact Simulation of IG-OU Processes," Methodology and Computing in Applied Probability, Springer, vol. 10(3), pages 337-355, September.
    2. Fred Espen Benth & Martin Groth & Rodwell Kufakunesu, 2007. "Valuing Volatility and Variance Swaps for a Non-Gaussian Ornstein-Uhlenbeck Stochastic Volatility Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(4), pages 347-363.
    3. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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