IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v17y2015i2d10.1007_s11009-013-9362-7.html
   My bibliography  Save this article

Sequential Maximum Likelihood Estimation for the Hyperbolic Diffusion Process

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-013-9362-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-013-9362-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. David R. Ba~nos & Salvador Ortiz-Latorre & Oriol Zamora Font, 2022. "Change of measure in a Heston-Hawkes stochastic volatility model," Papers 2210.15343, arXiv.org.
    3. Danijel Grahovac & Nenad Suvak, 2015. "Heavy-tailed modeling of CROBEX," Financial Theory and Practice, Institute of Public Finance, vol. 39(4), pages 411-430.
    4. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    5. Grigelionis, Bronius, 2003. "On point measures of [var epsilon]-upcrossings for stationary diffusions," Statistics & Probability Letters, Elsevier, vol. 61(4), pages 403-410, February.
    6. Wael Bahsoun & Pawel Góra & Silvia Mayoral & Manuel Morales, 2006. "Random Dynamics and Finance: Constructing Implied Binomial Trees from a Predetermined Stationary Den," Faculty Working Papers 13/06, School of Economics and Business Administration, University of Navarra.
    7. Song Li & Mervyn J. Silvapulle & Param Silvapulle & Xibin Zhang, 2015. "Bayesian Approaches to Nonparametric Estimation of Densities on the Unit Interval," Econometric Reviews, Taylor & Francis Journals, vol. 34(3), pages 394-412, March.
    8. Zhang, Xibin & King, Maxwell L., 2008. "Box-Cox stochastic volatility models with heavy-tails and correlated errors," Journal of Empirical Finance, Elsevier, vol. 15(3), pages 549-566, June.
    9. Malmsten, Hans & Teräsvirta, Timo, 2004. "Stylized Facts of Financial Time Series and Three Popular Models of Volatility," SSE/EFI Working Paper Series in Economics and Finance 563, Stockholm School of Economics, revised 03 Sep 2004.
    10. Han Shang, 2014. "Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density," Computational Statistics, Springer, vol. 29(3), pages 829-848, June.
    11. Ahmed Nafidi & Abdenbi El Azri & Ramón Gutiérrez-Sánchez, 2023. "A Stochastic Schumacher Diffusion Process: Probability Characteristics Computation and Statistical Analysis," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-15, June.
    12. Li Lin, 2024. "Quantum Probability Theoretic Asset Return Modeling: A Novel Schr\"odinger-Like Trading Equation and Multimodal Distribution," Papers 2401.05823, arXiv.org.
    13. Leonenko, N.N. & Petherick, S. & Sikorskii, A., 2012. "A normal inverse Gaussian model for a risky asset with dependence," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 109-115.
    14. Barbachan, José Santiago Fajardo, 2003. "Optimal Consumption and Investment with Lévy Processes," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 57(4), October.
    15. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2011. "Bayesian estimation of bandwidths for a nonparametric regression model with a flexible error density," Monash Econometrics and Business Statistics Working Papers 10/11, Monash University, Department of Econometrics and Business Statistics.
    16. Nakajima, Jouchi & Omori, Yasuhiro, 2012. "Stochastic volatility model with leverage and asymmetrically heavy-tailed error using GH skew Student’s t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3690-3704.
    17. Denitsa Stefanova, 2012. "Stock Market Asymmetries: A Copula Diffusion," Tinbergen Institute Discussion Papers 12-125/IV/DSF45, Tinbergen Institute.
    18. Luo, Min & Kontosakos, Vasileios E. & Pantelous, Athanasios A. & Zhou, Jian, 2019. "Cryptocurrencies: Dust in the wind?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1063-1079.
    19. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2016. "Bayesian Bandwidth Selection for a Nonparametric Regression Model with Mixed Types of Regressors," Econometrics, MDPI, vol. 4(2), pages 1-27, April.
    20. Meade, Nigel, 2010. "Oil prices -- Brownian motion or mean reversion? A study using a one year ahead density forecast criterion," Energy Economics, Elsevier, vol. 32(6), pages 1485-1498, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:17:y:2015:i:2:d:10.1007_s11009-013-9362-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.