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Sequential Maximum Likelihood Estimation for the Hyperbolic Diffusion Process

Author

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  • Nenghui Kuang

    (Hunan University of Science and Technology
    Wuhan University)

  • Huantian Xie

    (Wuhan University
    Linyi University)

Abstract

This paper investigates the properties of a sequential maximum likelihood estimator (SMLE) of the unknown parameter for the hyperbolic diffusion process. We derive the explicit formulas for the sequential estimator and its mean squared error (MSE). The estimator is proved to be closed, unbiased, normally distributed and strongly consistent. Finally a simulation study is presented to illustrate the efficiency of the estimator.

Suggested Citation

  • Nenghui Kuang & Huantian Xie, 2015. "Sequential Maximum Likelihood Estimation for the Hyperbolic Diffusion Process," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 373-381, June.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:2:d:10.1007_s11009-013-9362-7
    DOI: 10.1007/s11009-013-9362-7
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    References listed on IDEAS

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    1. Bo Martin Bibby & Michael SÛrensen, 1996. "A hyperbolic diffusion model for stock prices (*)," Finance and Stochastics, Springer, vol. 1(1), pages 25-41.
    2. Y. K. Tse & Xibin Zhang & Jun Yu, 2004. "Estimation of hyperbolic diffusion using the Markov chain Monte Carlo method," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 158-169.
    3. Tina Hviid Rydberg, 1999. "Generalized Hyperbolic Diffusion Processes with Applications in Finance," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 183-201, April.
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    Cited by:

    1. Huantian Xie & Nenghui Kuang, 2021. "Sequential Maximum Likelihood Estimation for the Squared Radial Ornstein-Uhlenbeck Process," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1409-1417, December.

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