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Comparing VaR Approximation Methods Which Use the First Four Moments as Inputs

Author

Listed:
  • Donald Lien

    (UTSA)

  • Christopher Stroud
  • Keying Ye

Abstract

This paper compares four methods used to approximate value at risk (VaR) from the _rst four moments of a probability distribution: Cornish-Fisher (1938), Edgeworth (1907), Gram-Charlier (1902), and Johnson distributions (1949). We apply a procedure described by Chernozhukov et al. (2010) called the increasing rearrangement to the Cornish-Fisher, Edgeworth, and Gram-Charlier methods. Using the increasing rear- rangement yields a single VaR approximation for any possible combination of skewness and kurtosis, and facilitates comparison of all four methods across the entire skewness- kurtosis space. Simulation results suggest that with enough data, the Johnson family yields the most accurate approximation on average.

Suggested Citation

  • Donald Lien & Christopher Stroud & Keying Ye, 2013. "Comparing VaR Approximation Methods Which Use the First Four Moments as Inputs," Working Papers 0220mss, College of Business, University of Texas at San Antonio.
    • Handle: RePEc:tsa:wpaper:0220mss
    as

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    File URL: http://interim.business.utsa.edu/wps/mss/0050MSS-202-2013.pdf
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    References listed on IDEAS

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    1. Victor Chernozhukov & Iván Fernández-Val & Alfred Galichon, 2010. "Rearranging Edgeworth–Cornish–Fisher expansions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 419-435, February.
    2. Das, Sanjiv Ranjan & Sundaram, Rangarajan K., 1999. "Of Smiles and Smirks: A Term Structure Perspective," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(2), pages 211-239, June.
    3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    4. I. D. Hill & R. Hill & R. L. Holder, 1976. "Fitting Johnson Curves by Moments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(2), pages 180-189, June.
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    Cited by:

    1. Stéphane Hamayon & Florence Legros & Pradat Yannick, 2016. "Non gaussian returns: which impact on default options retirement plans? [Distribution non gaussienne des rendements : quel impact sur les options par défaut des plans d'épargne retraite ?]," Working Papers hal-03003588, HAL.

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    Keywords

    VaR Approximation;

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