A dynamical model of the capital markets

A dynamical theory of the capital markets is proposed based on a continuous-time model and a basic differential equation that governs the price differential, derived by analogy from hydrodynamic flow. A critical number M determines the onset of turbulent behavior of volatility. Scaling laws are formulated for the time-series spectra of volatility distributions, which show intermittency associated with a fractal behavior of the distribution functions. This model may help in an understanding of volatility risk and the relationship between short- and long-term trading in the financial markets.