IDEAS home Printed from https://ideas.repec.org/a/oup/jfinec/v4y2006i4p617-635.html
   My bibliography  Save this article

Sample and Implied Volatility in GARCH Models

Author

Listed:
  • Lajos Horváth
  • Piotr Kokoszka
  • Ricardas Zitikis

Abstract

The unconditional variance of various GARCH-type models is a function h(theta) of the parameter vector theta which is estimated by theta. For most models used in practice, closed-form expressions of h(.) have been found. On the contrary, the unconditional variance can be estimated by the sample variance sigma^2. This article establishes the asymptotic distributions of the differences sigma^2 - h(theta) and &sigma^2 - h(theta) for broad classes of GARCH-type models. Even though both limit distributions are normal, the asymptotic variances are not equal. Potential practical consequences of these results are discussed. Copyright 2006, Oxford University Press.

Suggested Citation

  • Lajos Horváth & Piotr Kokoszka & Ricardas Zitikis, 2006. "Sample and Implied Volatility in GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 4(4), pages 617-635.
    • Handle: RePEc:oup:jfinec:v:4:y:2006:i:4:p:617-635
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/jjfinec/nbl002
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

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

    Citations

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


    Cited by:

    1. Christian Francq & Lajos Horváth, 2011. "Merits and Drawbacks of Variance Targeting in GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 9(4), pages 619-656.
    2. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2016. "Copula--based Specification of vector MEMs," Papers 1604.01338, arXiv.org.
    3. Hotta, Luiz & Trucíos, Carlos, 2015. "Robust bootstrap forecast densities for GARCH models: returns, volatilities and value-at-risk," DES - Working Papers. Statistics and Econometrics. WS ws1523, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Stanislav Khrapov, 2011. "Pricing Central Tendency in Volatility," Working Papers w0168, New Economic School (NES).
    5. Mao, Xiuping & Czellar, Veronika & Ruiz, Esther & Veiga, Helena, 2020. "Asymmetric stochastic volatility models: Properties and particle filter-based simulated maximum likelihood estimation," Econometrics and Statistics, Elsevier, vol. 13(C), pages 84-105.
    6. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2017. "Copula–Based vMEM Specifications versus Alternatives: The Case of Trading Activity," Econometrics, MDPI, vol. 5(2), pages 1-24, April.
    7. Jiang, Feiyu & Li, Dong & Zhu, Ke, 2021. "Adaptive inference for a semiparametric generalized autoregressive conditional heteroskedasticity model," Journal of Econometrics, Elsevier, vol. 224(2), pages 306-329.
    8. Antonis Demos, 2023. "Statistical Properties of Two Asymmetric Stochastic Volatility in Mean Models," DEOS Working Papers 2303, Athens University of Economics and Business.

    More about this item

    Statistics

    Access and download statistics

    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:oup:jfinec:v:4:y:2006:i:4:p:617-635. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Oxford University Press (email available below). General contact details of provider: https://edirc.repec.org/data/sofieea.html .

    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.