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

*Daniel Traian Pele* and
*Vasile Nicolae Stanciulescu*

*The Review of Finance and Banking*, 2015, vol. 07, issue 2, 007-015

**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.

**Date:** 2015

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**Persistent link:** https://EconPapers.repec.org/RePEc:rfb:journl:v:07:y:2015:i:2:p:007-015

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