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

Listed author(s):
  • Daniel Traian Pele
  • Vasile Nicolae Stanciulescu
Registered author(s):

    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.

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    File URL: http://www.rfb.ase.ro/articole/ART1_7_2.pdf
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    Article provided by Academia de Studii Economice din Bucuresti, Romania / Facultatea de Finante, Asigurari, Banci si Burse de Valori / Catedra de Finante in its journal The Review of Finance and Banking.

    Volume (Year): 07 (2015)
    Issue (Month): 2 (December)
    Pages: 007-015

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    Handle: RePEc:rfb:journl:v:07:y:2015:i:2:p:007-015
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    1. Rafal Weron, 1996. "Correction to: "On the Chambers-Mallows-Stuck Method for Simulating Skewed Stable Random Variables"," HSC Research Reports HSC/96/01, Hugo Steinhaus Center, Wroclaw University of Technology.
    2. Szymon Borak & Wolfgang Härdle & Rafal Weron, 2005. "Stable Distributions," SFB 649 Discussion Papers SFB649DP2005-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. 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.
    4. 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.
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