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Tail Point Density Estimation Using Probabilistic Fuzzy Systems

Value at Risk (VaR) is a popular measure for quantifying the market risk that a financial institution faces into a single number. Due to the complexity of financial markets, the risks associated with a portfolio may vary over time. For accurate VaR estimation, it is necessary to have flexible methods that adapt to the underlying data distribution. In this paper, we consider VaR estimation by using probabilistic fuzzy systems (PFS). Contrary to previous publications, our focus is on the modeling of the tail points of the distribution of returns. We study two approaches to designing probabilistic fuzzy VaR models that take into account the extreme values of the data and compare their performance with the performance of a GARCH model. It is found that the VaR estimation process is simplified and improved by our proposed method. Keywords— Density estimation, extreme values, fuzzy histograms, probabilistic fuzzy systems, value-at-risk.