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Consentaneous Agent-Based and Stochastic Model of the Financial Markets

V. Gontis, A. Kononovicius

posted on 27 July 2014

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We are looking for the agent-based treatment of the financial markets considering necessity to build bridges between microscopic, agent based, and macroscopic, phenomenological modeling. The acknowledgment that agent-based modeling framework, which may provide qualitative and quantitative understanding of the financial markets, is very ambiguous emphasizes the exceptional value of well defined analytically tractable agent systems. Herding as one of the behavior peculiarities considered in the behavioral finance is the main property of the agent interactions we deal with in this contribution. Looking for the consentaneous agent-based and macroscopic approach we combine two origins of the noise: exogenous one, related to the information flow, and endogenous one, arising form the complex stochastic dynamics of agents. As a result we propose a three state agent-based herding model of the financial markets. From this agent-based model we derive a set of stochastic differential equations, which describes underlying macroscopic dynamics of agent population and log price in the financial markets. The obtained solution is then subjected to the exogenous noise, which shapes instantaneous return fluctuations. We test both Gaussian and q-Gaussian noise as a source of the short term fluctuations. The resulting model of the return in the financial markets with the same set of parameters reproduces empirical probability and spectral densities of absolute return observed in New York, Warsaw and NASDAQ OMX Vilnius Stock Exchanges. Our result confirms the prevalent idea in behavioral finance that herding interactions may be dominant over agent rationality and contribute towards bubble formation.


This text follows up our recent article „Consentaneous Agent-Based and Stochastic Model of the Financial Markets“ published in open access interdisciplinary journal PLoS ONE [1]. This article is a result of the ongoing research at the Institute of Theoretical Physics and Astronomy of Vilnius University implementing the ideas of econophysics. Though our research is mostly related to the modelling of return statistics in financial markets implementing ideas from statistical physics, the concepts behind this work and conclusions are related to the much more extensive interdisciplinary understanding of the social and physical sciences. The desire to extend conventional boundaries and achieve more understanding between researchers of physical and social sciences is a strong motivation for us to deal with econophysics.

The price is a key concept in economics as it enables general quantitative description in economy and theoretical economics. Market price plays a central role as it is assumed to precisely reflect the real exchange values. Therefore a belief that market price is the most objective one lies in the background of mainstream economics, based on the rational expectation and efficient market concepts. These concepts lie in the background of huge financial industry (stock exchange, other securities, derivatives, currency exchange, etc.), making a vast impact on the overall health of the global economy. However, periodically emerging local and global economic crises give rise to the alternative views opposing mainstream concepts of economics. More in: