Emergence of Power-Law and Two-Phase Behavior in Financial Market Fluctuations

Abstract

In this paper, we provide an insight into the emergence of power-law and two-phase behavior in the financial market fluctuations by defining an analytical model for time evolution of stock share prices. The defined model can exhibit bimodal behavior in the supply-demand structure of the market. Moreover, it differs from existing Ising-type models. It turns out that the constructed model is a solution of a thermodynamic limit of a Gibbs probability measure when the number of investors and the number of stock shares approaches the infinity. The energy functional of the Gibbs probability measure is derived from the Nash equilibrium of the underlying game.

Scaling properties of extreme price fluctuations in Bitcoin markets

“…The observed bubbles testify to the level of feedback and herding effects in these markets. In addition, if we think of the power-law behavior as a consequence of investors poor estimation of the true asset value [11] -it is only logical that the observed tails are heavier, since the intrinsic value for cryptocurrencies is especially hard to determine. However, a more detailed study of the behavioral issues in these markets is necessary to reach definite conclusions.…”

“…The emergence of power-law behavior in price fluctuations is argued to be a consequence of underlying complex mechanisms, such as feedback effects and correlations in financial markets [6,7,9,10]. Some theories associate this phenomenon with market impact and the distribution of large investors [4,5], while other studies model the power-law behavior as a consequence of investors' poor estimation of the true value of a company and limited information [11]. While there are various models which can generate adequate statistical properties of stock prices [12], the reported universal scaling behavior in price fluctuations is yet to be comprehensively studied across various financial markets [13,14,15].…”

Physics and financial economics (1776–2014): puzzles, Ising and agent-based models

“…For instance, bailing out the first few defaulting firms does not solve the problem, but does have the effect of alleviating considerably the global shock, as measured by the fraction of firms that are not defaulting as a consequence. Kostanjcar and Jeren (2013) defined a generalized Ising model of financial markets with a kind of minority-game payoff structure and strategies that depend on order sizes. Because their agents focus on the change of their wealth, they find that the macroscopic dynamics of the aggregated set of orders (reflected into the market returns) remains stochastic even in the thermodynamic limit of a very large number of agents.…”

Crypto Wash Trading

“…One explanation for the power-law tails in financial data is the trading behavior of large investors who try to avoid large price impacts in the markets (Gabaix, Gopikrishnan, Plerou, and Stanley, 2003a). Other studies attribute them to the investors' limited information on the value of assets (Kostanjčar and Jeren, 2013;Nirei, Stachurski, and Watanabe, 2020) and herding (Nirei, Stachurski, and Watanabe, 2020). Specifically, for trade volume, several previous studies (Maslov and Mills, 2001;Gabaix et al, 2006;Plerou and Stanley, 2007) found that in stock markets, trading volume distribution follows the power law with exponent α ≅ .…”