Probabilistic fuzzy systems in value-at-risk estimation

Value-at-risk (VaR) is a popular measure for quantifying the market risk that a financial institution faces into a single number. Owing to the complexity of financial markets, the risks associated with a portfolio varies over time. Consequently, advanced methods of VaR estimation use parametric conditional models of portfolio volatility (e.g. generalized autoregressive heteroscedasticity (GARCH) models) to adapt risk estimation to changing market conditions. However, more flexible semi-parametric methods that adapt to the highly flexible underlying data distribution are better suited for accurate VaR estimation. In this paper, we consider VaR estimation by using probabilistic fuzzy systems (PFSs). A PFS is a semi-parametric method that combines a linguistic description of the system behaviour with statistical properties of the data. Therefore, they provide the potential to adapt estimations of probability density to the linguistic framework of the modeller. We study two approaches to designing probabilistic fuzzy VaR models and compare their performances with the performance of a GARCH model. It is found that statistical back testing always accepts PFS models after tuning, whereas GARCH models may be rejected.

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