Consentaneous Agent-Based and Stochastic Model of the Financial Markets

Abstract

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.

Agent-based models in financial market studies

“…It is well described in the work of Gontis and Kononovicius [34], which relates microscopic ABM to macroscopic phenomenological modeling, combining exogenous noise with the stochastic dynamics of agents by defining joint endogenous and exogenous volatilities. They uncover the origin of power-law (i.e., scaling behavior) in both developed and emerging markets.…”

Economics and Finance: q-Statistical Stylized Features Galore

“…Illustrations in artificial systems include signal and image processing [97,98] and (asymptotically) scale-free networks [99][100][101]. In the realm of social systems, from now on, we focus on economics and financial theory [102][103][104][105][106][107][108][109][110][111][112][113][114][115][116][117][118].…”

Study of market model describing the contrary behaviors of informed and uninformed agents: Being minority and being majority

“…In the minority side of in-agents In the majority side of un-agents markets, such as peak-fat-tail non-normal behavior, long range correlation, and volatility clustering [1][2][3]. Unlike in many physical systems, we have no direct way to gain insights into the nature of microscopic interactions in financial markets, thus our understanding on their underlying mechanism remains rather limited and ambiguous.…”