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Transition Law-based Simulation of Generalized Inverse Gaussian Ornstein–Uhlenbeck Processes

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  • Shibin Zhang

    (Shanghai Maritime University)

Abstract

In this paper, a stochastic integral of Ornstein–Uhlenbeck type is represented to be the sum of three independent random variables—one follows a distribution whose density is a deconvolution of the densities of two generalized inverse Gaussian distributions, and the two others all have compound Poisson distributions. Based on the representation of the stochastic integral, a simulation procedure for obtaining discretely observed values of Ornstein–Uhlenbeck processes with given generalized inverse Gaussian distribution is provided. For some subclasses of the generalized inverse Gaussian Ornstein–Uhlenbeck process, the innovations can be sampled exactly. The performance of the simulation method is evidenced by some empirical results.

Suggested Citation

  • Shibin Zhang, 2011. "Transition Law-based Simulation of Generalized Inverse Gaussian Ornstein–Uhlenbeck Processes," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 619-656, September.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:3:d:10.1007_s11009-010-9179-6
    DOI: 10.1007/s11009-010-9179-6
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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.
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    4. Taufer, Emanuele & Leonenko, Nikolai, 2009. "Simulation of Lvy-driven Ornstein-Uhlenbeck processes with given marginal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2427-2437, April.
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    6. Ole E. Barndorff‐Nielsen & Neil Shephard, 2003. "Integrated OU Processes and Non‐Gaussian OU‐based Stochastic Volatility Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 277-295, June.
    7. Fotopoulos, Stergios B. & Jandhyala, Venkata K., 2004. "Bessel inequalities with applications to conditional log returns under GIG scale mixtures of normal vectors," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 117-125, January.
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    Cited by:

    1. Kevin W. Lu, 2022. "Calibration for multivariate Lévy-driven Ornstein-Uhlenbeck processes with applications to weak subordination," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 365-396, July.

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