Ising model of financial markets with many assets

Financial price dynamics and phase transitions in the stock markets

“…In ref. [ 5 , 8 , 10 , 12 , 13 , 16 , 17 , 23 , 24 , 29 ], the spin can simulate the investor or the trader. The stock market consists of N traders and each of them can share one of two investment attitudes, buyer or seller.…”

“…Zhang described interacting micromechanism for the formation of the price and various properties of logarithmic returns for the financial model were investigated by some statistical analyses [ 29 ]. Some novel mathematical methods are also utilized in explaining and analyzing the stock market, such as the minimal spanning tree [ 21 , 27 , 28 ] and cross-correlation matrix [ 8 , 10 , 15 , 21 , 24 , 27 , 29 , 30 ]. Moreover, the Ising model allows the identification of phase transitions as a simplified model of reality, and phase transitions are also observed in financial research [ 14 , 21 , 26 , 27 ].…”

“…Nowadays, as a famous statistical physics system, the Ising model can also be adopted to explain and model the interaction mechanism of financial market [2][3][4][5][6][8][9][10][12][13][14]16,18,[22][23][24]26,[28][29][30]. The Ising model is popularly applied in the stock market [2][3][4][5][6][8][9][10][12][13][14][15][16][17][18][20][21][22][23][24][26][27][28][29][30] and also be used in the study of financial crash [12][13][14]26]. For example, Borysov analyzed the historical behavior of the parameters inferred using exact and approximate learning algorithms within Boltzmann learning framework.…”

Agent-based model generating stylized facts of fixed income markets

“…A market model characterized by the interactions of fundamentalist and chartist traders through the price-vector of dimension higher than two is provided in Xu et al (2014). Other models introducing heterogeneous agents investing in a multi-asset market can be found in Borghesi and Bouchaud (2007), Chiarella et al (2007), Fedyk et al (2013) and Eckrot et al (2016). More recent articles revealing a renewed interest in agent-based modelling are proposed by Gualdi et al (2015), Baghestanian et al (2015), Bouchaud (2013) and Hommes and LeBaron (2018).…”

Measuring critical transitions in financial markets

“…We start with the assumption, that only a few big market participants are responsible for the major changes in share prices 25 , 26 and we assume that these investors are not noise traders 27 but follow the principle of risk reduction by diversification 28 – 30 and belong to the group of fundamental traders 31 . The general idea of a diversified portfolio is that it is more robust against turbulences since not all selected assets are influenced by the news regarding one particular sector 1 , 32 . However, determining the correlation between assets faces the problem that time-series in financial markets react on exogenous news and are therefore not stable 33 – 36 as commonly assumed 1 , 37 .…”