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BL-GARCH models and asymmetries in volatility

Author

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  • Giuseppe Storti

    (Università di Salerno)

  • Cosimo Vitale

    (Università di Salerno)

Abstract

In this paper the class of Bilinear GARCH (BL-GARCH) models is proposed. BL-GARCH models allow to capture asymmetries in the conditional variance of financial and economic time series by means of interactions between past shocks and volatilities. The availability of likelihood based inference is an attractive feature of BL-GARCH models. Under the assumption of conditional normality, the log-likelihood function can be maximized by means of an EM type algorithm. The main reason for using the EM algorithm is that it allows to obtain parameter estimates which naturally guarantee the positive definiteness of the conditional variance with no need for additional parameter constraints. We also derive a robust LM test statistic which can be used for model identification. Finally, the effectiveness of BL-GARCH models in capturing asymmetric volatility patterns in financial time series is assessed by means of an application to a time series of daily returns on the NASDAQ Composite stock market index.

Suggested Citation

  • Giuseppe Storti & Cosimo Vitale, 2003. "BL-GARCH models and asymmetries in volatility," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 12(1), pages 19-39, February.
    • Handle: RePEc:spr:stmapp:v:12:y:2003:i:1:d:10.1007_bf02511581
    DOI: 10.1007/BF02511581
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    References listed on IDEAS

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    Cited by:

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    2. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    3. Abdou Kâ Diongue & Dominique Guegan & Rodney C. Wolff, 2010. "BL-GARCH model with elliptical distributed innovations," Post-Print halshs-00368340, HAL.
    4. Dominique Guegan & Jing Zhang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," PSE-Ecole d'économie de Paris (Postprint) halshs-00368336, HAL.
    5. Abdou Kâ Diongue & Dominique Guegan & Rodney C. Wolff, 2008. "Exact Maximum Likelihood estimation for the BL-GARCH model under elliptical distributed innovations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00270719, HAL.
    6. Chuffart Thomas & Flachaire Emmanuel & Péguin-Feissolle Anne, 2018. "Testing for misspecification in the short-run component of GARCH-type models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(5), pages 1-17, December.
    7. Haas, Markus, 2009. "Persistence in volatility, conditional kurtosis, and the Taylor property in absolute value GARCH processes," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1674-1683, August.
    8. Choi, M.S. & Park, J.A. & Hwang, S.Y., 2012. "Asymmetric GARCH processes featuring both threshold effect and bilinear structure," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 419-426.
    9. Dominique Guegan & Jing Zhang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," Post-Print halshs-00368336, HAL.
    10. Dominique Guegan & Jing Zhang, 2007. "Pricing bivariate option under GARCH-GH model with dynamic copula : application for Chinese market," Post-Print halshs-00188248, HAL.
    11. Tan, Shay-Kee & Chan, Jennifer So-Kuen & Ng, Kok-Haur, 2020. "On the speculative nature of cryptocurrencies: A study on Garman and Klass volatility measure," Finance Research Letters, Elsevier, vol. 32(C).
    12. Giuseppe Storti & Cosimo Vitale, 2003. "Likelihood inference in BL-GARCH models," Computational Statistics, Springer, vol. 18(3), pages 387-400, September.

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