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Analytic Approximations to GARCH Aggregated Returns Distributions with Applications to VaR and ETL

Author

Listed:
  • Carol Alexander

    (ICMA Centre, Henley Business School, University of Reading)

  • Emese Lazar

    (ICMA Centre, Henley Business School, University of Reading)

  • Silvia Stanescu

    (Kent Business School, University of Kent)

Abstract
It is widely accepted that some of the most accurate predictions of aggregated asset returns are based on an appropriately specified GARCH process. As the forecast horizon is greater than the frequency of the GARCH model, such predictions either require time-consuming simulations or they can be approximated using a recent development in the GARCH literature, viz. analytic conditional moment formulae for GARCH aggregated returns. We demonstrate that this methodology yields robust and rapid calculations of the Value-at-Risk (VaR) generated by a GARCH process. Our extensive empirical study applies Edgeworth and Cornish-Fisher expansions and Johnson SU distributions, combined with normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets; it validates the accuracy of the analytic approximations to GARCH aggregated returns and derives GARCH VaR estimates that are shown to be highly accurate over multiple horizons and significance levels.

Suggested Citation

  • Carol Alexander & Emese Lazar & Silvia Stanescu, 2011. "Analytic Approximations to GARCH Aggregated Returns Distributions with Applications to VaR and ETL," ICMA Centre Discussion Papers in Finance icma-dp2011-08, Henley Business School, University of Reading.
    • Handle: RePEc:rdg:icmadp:icma-dp2011-08
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    File URL: http://www.icmacentre.ac.uk/files/discussion-papers/DP2011-08.pdf
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    References listed on IDEAS

    as
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