Value-at-Risk Estimation with Fuzzy Histograms

Value at risk (VaR) is a measure for senior management that summarises the financial risk a company faces into one single number. In this paper, we consider the use of fuzzy histograms for quantifying the value-at-risk of a portfolio. It is shown that the use of fuzzy histograms provides a good method of value-at-risk estimation for a portfolio of stocks. The conditional parameters of the model are obtained through minimisation of a test statistic for a VaR back testing method. Evolutionary optimisation is used for this purpose. It is found that statistical back testing always accepts fuzzy histogram models, while the popular GARCH models may be rejected.