A fuzzy-G.M.D.H. approach to V.a.R.

(Series editor: TAYLOR J.G.)

Value at Risk (V.a.R.) is used to measure the possible losses of a stock, of a derivative, of a portfolio and so on. Different approaches were proposed to determine such a value, based on the past history, or on stochastic simulation, or on estimation of the theoretical distributions. We propose a method that empirically reconstructs the conditional distribution of the analyzed financial returns using two soft-computing techniques based, respectively, on fuzzy estimation and on a polynomial neural network. At first, a non-parametric density estimation is proposed, using a fuzzy similarity measure between k-patterns, that are sequence of k consecutive values sampled from the considered time series, extending the Nadaraya-Watson approach. Subsequently, the Group Method of Data Handling neural network is used to compute a polynomial approximation of the unknown relationship between the data. The two-phases algorithm was finally applied to a real financial time series, and the results are used to create a V.a.R. predictor.