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 . 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.<!--break-->
Econophysics much more often than econometrics criticizes mainstream theory of economics. The observed fluctuations of the market price are larger than it should be accordingto the equilibrium view of the efficient market theory. Alternative views arise even in circles of the economists as behavioral finance and economics receive much more attention. Nobel Prize winner of 2013 professor of Yale University Robert Shiller is an outstanding representative of the behavioral alternative. The decision to award a Nobel price of economics to the most outstanding advocate of efficient market theory prof. E.F. Fama and representative of the alternative view serves as a proof that economics with its concepts is in the crossroad. From our point of view behavioral finance criticism towards econometrics and mathematical finance serves as an obstacle to positively evaluate contribution of econophysics. Nevertheless, the understanding that unstable financial and economic processes have to be considered on the bases of statistical physics is taking place .
From the point of view of representatives of behavioral economics and finance the behavior of agents acting in the market is much more like the behavior of realistic personalities with inherent intellectual and psychological bugs than like the behavior of extraordinarily capable individuals with ability to evaluate and account for all of the surrounding circumstances and information. For example, they pay much more attention to the tendency of imitation than to the individual capabilities of agents to make independent decisions. In our work we aim to demonstrate that it is possible to build a consentaneous model of financial markets, where choice of agents between three different trading strategies is based only on the transition probabilities between these choices. From the mathematical point of view these transition probabilities between two of the choices are the same as proposed by Alan Kirman to describe the herding interactions of agents . This way we propose an adaption of the herding model to the financial markets, which can be solved by using method from statistical physics to shape macroscopic description of financial markets by the set of two stochastic differential equations. The main objective of this model is to reproduce general statistical properties of price movements observed in the real stock exchanges from Vilnius to New York.
The detailed simulation of market return statistics, reproducing power law probability density functions, power spectral densities and autocorrelations of absolute return as well as reproducing very details of these statistics, shows that herding of market participants is the most general property dominating their very heterogeneous and less meaningful rationality. We think that rationality is so heterogeneous and so ambiguous, that in the final macroscopic view of the whole agent society only the most general statistically meaningful property – herding –is observed. Rationality as very diverse can be neglected in a same way that physicists neglect trajectories of separate particles in thermodynamic consideration.
Our proposed structure of agent groups is based on a conventional choice considering three opportunities : 1) intrinsic (fundamental) value oriented market traders – fundamentalists, which buy stocks, when market price is lower than fundamental value and sell when market price is higher than fundamental value; 2) speculative traders, who forecast price movement and believe that market price will go up – optimists and 3) speculative traders, who believe that market price will go down, pessimists. Permanent dynamical change of traders’ choices impacts the demand and supply ratio and so forms a long term dynamics of market price. In order to make such agent population dynamics comparable with real financial markets we had to combine it with permanent exogenous impact – external information flow or order flow noise. These are all necessary assumptions to reproduce main general properties of market price dynamics, observed for all markets and all stocks. Though the model proposed has few independent parameters, the same choice of parameter values is appropriate for all markets and all stocks is the main it‘s advantage.
Proposed model provides evidence that price dynamics can be reproduced by the memory-less Markov transitions of traders between possible choices of behavior. From our point of view the proposed model suggests new interpretation of market price, which may exhibit very large deviations from fundamental value. In this new interpretation market price highlights herding based drifts of agent-based societies, neglecting intrinsic (fundamental) understanding of value and surrendering to the imitational waves of collective wandering. Such wandering can be supported by the public tales about unexpected economic opportunities, emerging in the context of new financial, technological, social and political tendencies. As the proposed model is based on the agent opinion dynamics, we ask a question – whether the market price is economic or sociological category? Answering the question we would prefer to assume that fundamental value is more likely to be economic concept and market price is more likely to be sociological concept. To make practical distinction between different market price constituents might be a hard task, nevertheless, the new market price interpretation can be helpful looking for the opportunities to diminish observed huge market price movements, responsible for the local or global economic crises.
From our point of view, the herding as a statistically dominating behavioral property of agents can be used for the stabilization of undesirable market price fluctuations. It appears that only a small number of agents trading exceptionally based only on fundamental values is required to make a considerable influence on other market participants leading to the much more stable movement of the market price . Certainly, it is obvious that for the implementation of such mechanism a new and more comprehensive understanding of fundamental price is needed. It should help to define a new reference point in economics instead of the currently used market price.
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