Value-at-risk estimation by using probabilistic fuzzy systems

Value at Risk (VaR) measures the worst expected loss of a portfolio over a given horizon at a given confidence level. It summarises the financial risk a company faces into one single number. Recent methods of VaR estimation use parametric conditional models of portfolio volatility to adapt risk estimation to changing market conditions. However, more flexible methods that adapt to the underlying data distribution would be better suited for VaR estimation. In this paper, we consider VaR estimation by using probabilistic fuzzy systems, a semi-parametric method, which combines a linguistic description of the system behaviour with statistical properties of data. The performance of the proposed model is compared to the performance of a GARCH model for VaR estimation. It is found that statistical back testing always accepts PFS models after tuning, while GARCH models may be rejected.