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Forecasting VaR using analytic higher moments for GARCH processes

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  • Alexander, Carol
  • Lazar, Emese
  • Stanescu, Silvia

Abstract

It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency of the GARCH model, such predictions have typically required time-consuming simulations of the aggregated returns distributions. This paper shows that fast, quasi-analytic GARCH VaR calculations can be based on new formulae for the first four moments of aggregated GARCH returns. Our extensive empirical study compares the Cornish–Fisher expansion with the Johnson SU distribution for fitting distributions to analytic moments of normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets, for the purpose of deriving accurate GARCH VaR forecasts over multiple horizons and significance levels.

Suggested Citation

  • Alexander, Carol & Lazar, Emese & Stanescu, Silvia, 2013. "Forecasting VaR using analytic higher moments for GARCH processes," International Review of Financial Analysis, Elsevier, vol. 30(C), pages 36-45.
    • Handle: RePEc:eee:finana:v:30:y:2013:i:c:p:36-45
    DOI: 10.1016/j.irfa.2013.05.006
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    More about this item

    Keywords

    GARCH; Higher conditional moments; Approximate predictive distributions; Value-at-Risk; S&P 500; Treasury bill rate; Euro–US dollar exchange rate;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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