Reflexivity in modern financial markets. The case of Volatility Indices

in this study, we attempt to investigate the presence of reflexivity in financial markets. In particular, starting from the definition of reflexivity (this theory rejects the basic assumption of the classical theory that the market totally and instantaneously absorbs the information flow expressing an equilibrium price of each asset class in the continuous), the purpose of the present work is to analyze the volatility of stock market indices identifying the statistical features of Reflexivity theory. We introduce a multi-step statistical model able to recognize stressed market periods and identify breakout points and short-term trend and reversal signals. Our conclusions are oriented towards confirmation of reflexivity theory in the historical time series of listed Volatility indices.