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Sample and Implied Volatility in GARCH Models

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  • 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, Society for Financial Econometrics, vol. 4(4), pages 617-635.
  • Handle: RePEc:oup:jfinec:v:4:y:2006:i:4:p:617-635
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    Cited by:

    1. Christian Francq & Lajos Horváth, 2011. "Merits and Drawbacks of Variance Targeting in GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(4), pages 619-656.
    2. repec:gam:jecnmx:v:5:y:2017:i:2:p:16-:d:95642 is not listed on IDEAS
    3. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2016. "Copula--based Specification of vector MEMs," Papers 1604.01338, arXiv.org.
    4. Hotta, Luiz & Trucíos, Carlos & Ruiz, Esther, 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.
    5. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2017. "Copula-based vMEM Specifications versus Alternatives: The Case of Trading Activity," Econometrics Working Papers Archive 2017_02, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    6. Stanislav Khrapov, 2011. "Pricing Central Tendency in Volatility," Working Papers w0168, Center for Economic and Financial Research (CEFIR).

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