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Value at Risk (VaR) and the alpha-stable distribution

Author

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  • John C. Frain

    (Department of Economics, Trinity College Dublin)

Abstract

Volatility in financial markets is a matter of considerable concern to financial institutions and their supervisors. Already it is clear that this volatility has had an adverse effect on the real economy. Many measures of risk that are used today do not take full account of the kind of extreme changes in asset prices that have been observed. This paper finds that the Value at Risk measure of risk can be improved by the use of an alpha-stable distribution in place of more conventional measures. The paper describes the use of this measure and implements it for six total returns equity portfolios. We find that alpha-stable based measures are feasible and are better than conventional measures. They are a useful tool for the risk manager and the financial regulator.

Suggested Citation

  • John C. Frain, 2008. "Value at Risk (VaR) and the alpha-stable distribution," Trinity Economics Papers tep0308, Trinity College Dublin, Department of Economics, revised May 2008.
    • Handle: RePEc:tcd:tcduee:tep0308
    as

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    File URL: http://www.tcd.ie/Economics/TEP/2008/TEP0308.pdf
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    References listed on IDEAS

    as
    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401, December.
    2. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    3. Frain, John & Meegan, Conor, 1996. "Market Risk: An introduction to the concept & analytics of Value-at-risk," Research Technical Papers 7/RT/96, Central Bank of Ireland.
    4. Nancy Masschelein, 2007. "Monitoring pro-cyclicality under the capital requirements directive : preliminary concepts for developing a framework," Working Paper Document 120, National Bank of Belgium.
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    Cited by:

    1. Carlo Marinelli & Stefano D'Addona & Svetlozar T. Rachev, 2012. "Multivariate Heavy-Tailed Models For Value-At-Risk Estimation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 1-32.

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    More about this item

    Keywords

    alpha stable distribution; Value at Risk; VaR;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • G18 - Financial Economics - - General Financial Markets - - - Government Policy and Regulation
    • G19 - Financial Economics - - General Financial Markets - - - Other
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation
    • G29 - Financial Economics - - Financial Institutions and Services - - - Other

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