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Abstract: We propose coalescent mechanism of economic grow because of redistribution ofexternal resources. It leads to Zipf distribution of firms over their sizes,turning to stretched exponent because of size-dependent effects, and predictsexponential distribution of income between individuals. We also present newapproach to describe fluctuations on the market, based on separation of hotshort-time and cold long-time degrees of freedoms, which predicts tent-likedistribution of fluctuations with stable tail exponent mu=3 mu=2 for news.The theory predicts observable asymmetry of the distribution, and its sizedependence. In the case of financial markets the theory explains first timemarket mill patterns, conditional distribution, D-smile, z-shaped response,conditional double dynamics, the skewness and so on. We derive the set ofLangeven equations, which predicts logarithmic dependence of price shift ontrading volume and volatility patterns after jumps. We calculate parameters ofprice distributions, correlation functions and Hurst exponents at differenttime scales. At large times the price experiences fractional Brownian motionwith chaotically switching of long-time persistent and anti-persistentbehavior, and we calculate corresponding probabilities, response functions, andrisks.



Author: S.V. Panyukov

Source: https://arxiv.org/







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