Economy – Quantitative Finance – Statistical Finance
Scientific paper
2008-04-27
Economy
Quantitative Finance
Statistical Finance
34 pages, 22 figures; added Langeven equations
Scientific paper
We propose coalescent mechanism of economic grow because of redistribution of external resources. It leads to Zipf distribution of firms over their sizes, turning to stretched exponent because of size-dependent effects, and predicts exponential distribution of income between individuals. We also present new approach to describe fluctuations on the market, based on separation of hot (short-time) and cold (long-time) degrees of freedoms, which predicts tent-like distribution of fluctuations with stable tail exponent mu=3 (mu=2 for news). The theory predicts observable asymmetry of the distribution, and its size dependence. In the case of financial markets the theory explains first time market mill patterns, conditional distribution, D-smile, z-shaped response, conditional double dynamics, the skewness and so on. We derive the set of Langeven equations, which predicts logarithmic dependence of price shift on trading volume and volatility patterns after jumps. We calculate parameters of price distributions, correlation functions and Hurst exponents at different time scales. At large times the price experiences fractional Brownian motion with chaotically switching of long-time persistent and anti-persistent behavior, and we calculate corresponding probabilities, response functions, and risks.
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