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On a Class of Alpha-stable Distributions and Its Applications in Estimating Market Risk

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  • Daniel Traian Pele
  • Vasile Nicolae Stanciulescu

Abstract

This paper uses a straightforward application of alpha-stable distributions for Romanian Stock Market, showing how a relatively simple implementation in the real world of a complex mathematical tool can be much more reliable in risk management than the classical Gaussian or log-normal distributions. In this paper we use a SAS macro for estimating the parameters of an alpha-stable distribution, using the time-series regression method from Kogon and Williams (1998). Using the Fast Fourier Transform, we estimate the probability density function, the cumulative distribution function and consequently, the VaR (99.5%) and TVaR (99%). For numerical illustration we are using daily logreturns of the BET Index; the measures of market risk, estimated on rolling windows using alpha-stable distributions and Gaussian distribution, are then compared to the actual logreturns of the BET Index. Numerical experiments show that using alpha-stable distributions for estimating VaR and TVaR can be a better alternative for managing the risk of financial assets.

Suggested Citation

  • Daniel Traian Pele & Vasile Nicolae Stanciulescu, 2015. "On a Class of Alpha-stable Distributions and Its Applications in Estimating Market Risk," The Review of Finance and Banking, Academia de Studii Economice din Bucuresti, Romania / Facultatea de Finante, Asigurari, Banci si Burse de Valori / Catedra de Finante, vol. 7(2), pages 007-015, December.
  • Handle: RePEc:rfb:journl:v:07:y:2015:i:2:p:007-015
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    References listed on IDEAS

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    1. Weron, Rafal, 1996. "Correction to: "On the Chambers–Mallows–Stuck Method for Simulating Skewed Stable Random Variables"," MPRA Paper 20761, University Library of Munich, Germany, revised 2010.
    2. Szymon Borak & Wolfgang Härdle & Rafal Weron, 2005. "Stable Distributions," SFB 649 Discussion Papers SFB649DP2005-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Szymon Borak & Rafal Weron, 2010. "STABLEREGKW: MATLAB function to estimate stable distribution parameters using the regression method of Kogon and Williams," Statistical Software Components M429004, Boston College Department of Economics.
    4. Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
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