We address microscopic, agent based, and macroscopic, stochastic, modeling of the financial markets combining it with exogenous noise. The interplay between the endogenous dynamics of agents and exogenous noise is the primary mechanism responsible for the observed statistical properties of high volatility return intervals. By exogenous noise we mean information flow or/and order flow fluctuations. This approach is based on the methods of stochastic and agent-based modeling to deal with social systems composed of heterogeneous agents and can be considered as alternative to the Efficient Market Hypothesis. Behavioral finance is frequently seen as an alternative view to the financial market efficiency as it relates the large price fluctuations to the animal spirits; human brain bugs and herding tendencies, see recent books by Prof. R.J. Shiller and Prof. A. Scheinkman. We do consider human conformity, from the statistical point of view equivalent to the herding, to develop agent based model of the financial markets, which in interaction with exogenous noise reproduces the main most general statistical properties of the real markets. Namely we follow a basic idea, from the statistical physics, that individual intricacies of each trader are not so statistically important. The traders can be assumed boundedly rational, as their rationality is just too heterogeneous to be considered as statisticaly meaningful for the macroscopic outcome of financial market. Thus we consider the global herding interaction of agents, quantified by A. Kirman’s transition rates in one step Markov chain, to be an essential ingredient in the consentaneous agent based and stochastic modeling. This leads us to the financial market model with bursting endogenous fluctuations, which statistically match empirical data of various markets, various assets and can produce the large price movements on a longer time scales than it is allowed by the financial market efficiency hypothesis. Together with first and second order statistics of volatility quantified as an absolute return we concentrate on empirical data of high volatility return intervals and reproduce it’s statistical properties with the same model applicable to various markets, various assets and time scales of return definition ranging from one minute to one month. The ability to reproduce so many stylized facts with the same model really builds bridges between agent based and stochastic modeling.

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1. The first passage time statistics as empirical test of observed long-range memory in the financial markets