Coarse-graining and self-similarity of price fluctuations

We propose a new approach for analyzing price fluctuations in their strongly correlated regime ranging from minutes to months. This is done by employing a self-similarity assumption for the magnitude of coarse-grained price fluctuation or volatility. The existence of a Cramér function, the characteristic function for self-similarity, is confirmed by analyzing real price data from a stock market. We also discuss the close interrelation among our approach, the scaling-ofmoments method and the multifractal approach for price fluctuations. Scaling and self-similarity play an important role not only in physics but also in various socio-economic systems including market fluctuations, internet traffic, growth rates of firms and social networks. If phenomenological theory is shown to be applicable to observations, it would guide one to meaningful models and possibly to universal and specific description of such systems without any apparent “Hamiltonian”.