Turbulence on financial markets and multiplicative cascade model of volatility

In this paper, we develop a volatility model on multiple time horizons taking into account a distribution of frequencies of price oscillations. The main point of the model lies in the ability to analyze and exploit the «carrier frequencies» of market prices to gain more precise estimate of the current volatility. Our focus is on the determination of market structure, implied in price dynamics and assuming different market agents, which work on different time-scales. Finally, in order to examine proposed model, we compare volatility estimations calculated for S&P 500 index with VIX index, as the main objective indicator of market volatility. Comparison of historical volatility, MCM model and the proposed model showed the advantage of the last one in terms of mean absolute percentage error.