Reconstruction of Attractors for Options Implied Volatility with Using Fuzzy Clustering Method

On the bases of dynamic system theory and fuzzy clustering methods for attractors of options implied volatility on market indexes S & P 500, NASDAQ 100, S & P 100 was researched. Results of researches stay that entropy of implied volatility fuzzy clustering equal from 0.6477 to 0.7986. Implied volatility attractor structure for market indexes are presented with two main components with rest dispersion in interval from 88.82 % to 57.59 %. On the bases of reconstruction of options attractor implied volatility method the prognoses method for dynamic of options implied volatility was formulated.