Abstract
In this paper, we analyze the role of the heavy tail and skewed distribution in market risk estimation (Value at Risk (VaR)). In particular, we are interested in knowing if in the framework of the conditional extreme value theory, the estimation of the volatility model below heavy tail and skewed distribution contributes to improve the VaR estimation respect to these obtained from a symmetric distribution. The study has been carried out for six individual assets belonging to the digital sector: ADP, Amazon, Cerner, Apple, Microsoft and Telefonica. The analysis period runs from January 1st, 2008 to the end of December 2013. Although the evidence found is a little bit weak, the results obtained seem to indicate that the heavy tail and skewed distribution outperforms the symmetric distribution both in terms of accuracy VaR estimations as in terms of firm’s loss function. Furthermore, the market risk capital requirements fixed on the base of the VaR estimations are also lowest below a skewed distribution.
Highlights
A context of risk is one in which we do not know with certainty the consequences associated with a decision
As we will see later, below the conditional extreme value theory, the value at risk of a portfolio at (1 − α)% confidence level is calculated as the product of the conditional standard deviation of the return portfolio by the α quantile of Pareto generalize distribution (PGD)
The conditional standard deviation of the return portfolio is estimated by assuming a symmetric distribution for the financial return
Summary
A context of risk is one in which we do not know with certainty the consequences associated with a decision. The size of the actual losses is much higher than that predicted by a normal distribution Taking this into account, the research in the framework of parametric method has focus on investigating other density functions which capture the skew and kurtosis of financial returns. The research in the framework of parametric method has focus on investigating other density functions which capture the skew and kurtosis of financial returns In this line, Abad, Benito, López-Martín and Sánchez (2016), Chen, Gerlach, Lin and Lee (2012), Polansky and Stoja (2010), Bali and Theodossiou (2008), Ausin and Galeano (2007), Zhang and Cheng (2005) among others, show that, in the context of parametric method, assuming fat tail and skewness distributions improve the performance of this model in VaR estimation.
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