This review deals with several microscopic (``agent-based'') models of financial markets which have been studied by economists and physicists over the last decade: Kim-Markowitz, Levy-Levy-Solomon, Cont-Bouchaud, Solomon-Weisbuch, Lux-Marchesi, Donangelo-Sneppen and Solomon-Levy-Huang. After an overview of simulation approaches in financial economics, we first give a summary of the Donangelo-Sneppen model of monetary exchange and compare it with related models in economics literature. Our selective review then outlines the main ingredients of some influential early models of multi-agent dynamics in financial markets (Kim-Markowitz, Levy-Levy-Solomon). As will be seen, these contributions draw their inspiration from the complex appearance of investors' interactions in real-life markets. Their main aim is to reproduce (and, thereby, provide possible explanations) for the spectacular bubbles and crashes seen in certain historical episodes, but they lack (like almost all the work before 1998 or so) a perspective in terms of the universal statistical features of financial time series.
Artificial stock market simulation based on agent is an important means to study financial market. Based on the assumption that the investors are composed of a main fund, small trend and contrarian investors characterized by four parameters, we simulate and research a kind of financial phenomenon with the characteristics of pyramid schemes. Our simulation results and theoretical analysis reveal the relationships between the rate of return of the main fund and the proportion of the trend investors in all small investors, the small investors' parameters of taking profit and stopping loss, the or…
We present a simple order book mechanism that regulates an artificial financial market with self-organized criticality dynamics and fat tails of returns distribution. The model shows the role played by individual imitation in determining trading decisions, while fruitfully replicates typical aggregate market behavior as the "self-fulfilling prophecy". We also address the role of random traders as a possible decentralized solution to dampen market fluctuations.
We introduce a new Self-Organized Criticality (SOC) model for simulating price evolution in an artificial financial market, based on a multilayer network of traders. The model also implements, in a quite realistic way with respect to previous studies, the order book dy- namics, by considering two assets with variable fundamental prices. Fat tails in the probability distributions of normalized returns are observed, together with other features of real financial markets.
The financial market is nonpredictable, as according to the Bachelier, the mathematical expectation of the speculator is zero. Nevertheless, we observe in the price fluctuations the two distinct scales, short and long time. Behaviour of a market in long terms, such as year intervals, is different from that in short terms. A diffusion equation with a time dependent diffusion coefficient that describes the fluctuations of the financial market, is subject to a two-scale homogenisation, and long term characteristics of the market such as mean behaviour of price and variance, are obtained. We indic…
We introduce solvable stochastic dealer models, which can reproduce basic empirical laws of financial markets such as the power law of price change. Starting from the simplest model that is almost equivalent to a Poisson random noise generator, the model becomes fairly realistic by adding only two effects, the self-modulation of transaction intervals and a forecasting tendency, which uses a moving average of the latest market price changes. Based on the present microscopic model of markets, we find a quantitative relation with market potential forces, which has recently been discovered in the …
We present an analysis of the price impact associated with trades effected by different financial firms. Using data from the Spanish Stock Market, we find a high degree of heterogeneity across different market members, both in the instantaneous impact functions and in the time-dependent market response to trades by individual members. This heterogeneity is statistically incompatible with the existence of market-wide universal impact dynamics which apply uniformly to all trades and suggests that rather, market dynamics emerge from the complex interaction of different behaviors of market partici…
We propose a Markov jump process with the three-state herding interaction. We see our approach as an agent-based model for the financial markets. Under certain assumptions this agent-based model can be related to the stochastic description exhibiting sophisticated statistical features. Along with power-law probability density function of the absolute returns we are able to reproduce the fractured power spectral density, which is observed in the high-frequency financial market data. Given example of consistent agent-based and stochastic modeling will provide background for the further developme…
Anchoring is a term used in psychology to describe the common human tendency to rely too heavily (anchor) on one piece of information when making decisions. A trading algorithm inspired by biological motors, introduced by L. Gil\cite{Gil}, is suggested as a testing ground for anchoring in financial markets. An exact solution of the algorithm is presented for arbitrary price distributions. Furthermore the algorithm is extended to cover the case of a market neutral portfolio, revealing additional evidence that anchoring is involved in the decision making of market participants. The exposure of a…
We consider models of financial markets in which all parties involved find incentives to participate. Strategies are evaluated directly by their virtual wealths. By tuning the price sensitivity and market impact, a phase diagram with several attractor behaviors resembling those of real markets emerge, reflecting the roles played by the arbitrageurs and trendsetters, and including a phase with irregular price trends and positive sums. The positive-sumness of the players' wealths provides participation incentives for them. Evolution and the bid-ask spread provide mechanisms for the gain in wealt…
A financial market is a system resulting from the complex interaction between participants in a closed economy. We propose a minimal microscopic model of the financial market economy based on the real economy's symmetry constraint and minimality requirement. We solve the proposed model analytically in the mean-field regime, which shows that various kinds of universal power-law-like behaviors in the financial market may depend on one another, just like the critical exponents in physics. We then discuss the parameters in the proposed model, and we show that each parameter in our model can be rel…
We apply the theory of continuous time random walks to study some aspects of the extreme value problem applied to financial time series. We focus our attention on extreme times, specifically the mean exit time and the mean first-passage time. We set the general equations for these extremes and evaluate the mean exit time for actual data.
In this paper the diffusion entropy technique is applied to investigate the scaling behavior of financial markets. The scaling behaviors of four representative stock markets, Dow Jones Industrial Average, Standard&Poor 500, Heng Seng Index, and Shang Hai Stock Synthetic Index, are almost the same; with the scale-invariance exponents all in the interval $[0.92, 0.95]$. These results provide a strong evidence of the existence of long-rang correlation in financial time series, thus several variance-based methods are restricted for detecting the scale-invariance properties of financial markets. In…
We investigate the financial network in the Korean stock exchange (KSE) market, using both numerical simulations and scaling arguments. We estimate the cross-correlation on the stock price exchanges of all companies listed on the the Korean stock exchange market, where all companies are fully connected via weighted links, by introducing a weighted random graph. The degree distribution and the edge density are discussed numerically from the market graph, and the statistical analysis for the degree distribution of vertices is particularly found to approximately follow the power law.
We survey systemic risks to financial markets and present a high-level description of an algorithm that measures systemic risk in terms of coupled networks.
Motivated by recent financial crises significant research efforts have been put into studying contagion effects and herding behaviour in financial markets. Much less has been said about influence of financial news on financial markets. We propose a novel measure of collective behaviour in financial news on the Web, News Cohesiveness Index (NCI), and show that it can be used as a systemic risk indicator. We evaluate the NCI on financial documents from large Web news sources on a daily basis from October 2011 to July 2013 and analyse the interplay between financial markets and financially relate…
Persistence is studied in a financial context by mapping the time evolution of the values of the shares quoted on the London Financial Times Stock Exchange 100 index (FTSE 100) onto Ising spins. By following the time dependence of the spins, we find evidence for power law decay of the proportion of shares that remain either above or below their ` starting\rq values. As a result, we estimate a persistence exponent for the underlying financial market to be $θ_f\sim 0.5$.
We study the effect of globalization on the Korean market, one of the emerging markets. Some characteristics of the Korean market are different from those of the mature market according to the latest market data, and this is due to the influence of foreign markets or investors. We concentrate on the market network structures over the past two decades with knowledge of the history of the market, and determine the globalization effect and market integration as a function of time.
We proposed a model of interacting market agents based on the Ising spin model. The agents can take three actions: "buy," "sell," or "stay inactive." We defined a price evolution in terms of the system magnetization. The model reproduces main stylized facts of real markets such as: fat-tailed distribution of returns and volatility clustering.
In recent years there has been a closer interrelationship between several scientific areas trying to obtain a more realistic and rich explanation of the natural and social phenomena. Among these it should be emphasized the increasing interrelationship between physics and financial theory. In this field the analysis of uncertainty, which is crucial in financial analysis, can be made using measures of physics statistics and information theory, namely the Shannon entropy. One advantage of this approach is that the entropy is a more general measure than the variance, since it accounts for higher o…
Geography effect is investigated for the Chinese stock market including the Shanghai and Shenzhen stock markets, based on the daily data of individual stocks. The Shanghai city and the Guangdong province can be identified in the stock geographical sector. By investigating a geographical correlation on a geographical parameter, the stock location is found to have an impact on the financial dynamics, except for the financial crisis time of the Shenzhen market. Stock distance effect is further studied, with a crossover behavior observed for the stock distance distribution. The probability of the …
We adapt continuous time random walk (CTRW) formalism to describe asset price evolution and discuss some of the problems that can be treated using this approach. We basically focus on two aspects: (i) the derivation of the price distribution from high-frequency data, and (ii) the inverse problem, obtaining information on the market microstructure as reflected by high-frequency data knowing only the daily volatility. We apply the formalism to financial data to show that the CTRW offers alternative tools to deal with several complex issues of financial markets.
With the random matrix theory, we study the spatial structure of the Chinese stock market, American stock market and global market indices. After taking into account the signs of the components in the eigenvectors of the cross-correlation matrix, we detect the subsector structure of the financial systems. The positive and negative subsectors are anti-correlated each other in the corresponding eigenmode. The subsector structure is strong in the Chinese stock market, while somewhat weaker in the American stock market and global market indices. Characteristics of the subsector structures in diffe…
We analyze the probability density function (PDF) of waiting times between financial loss exceedances. The empirical PDFs are fitted with the self-excited Hawkes conditional Poisson process with a long power law memory kernel. The Hawkes process is the simplest extension of the Poisson process that takes into account how past events influence the occurrence of future events. By analyzing the empirical data for 15 different financial assets, we show that the formalism of the Hawkes process used for earthquakes can successfully model the PDF of interevent times between successive market losses.
We investigate the large-volatility dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dynamic relaxation both before and after large volatilities is characterized by a power law, and the exponents $p_\pm$ usually vary with the strength of the large volatilities. The large-volatility dynamics is time-reversal symmetric at the time scale in minutes, while asymmetric at the daily time scale. Careful analysis reveals that the time-reversal asymmetry is mainly induced by exogenous events. It is also the exogenous events which driv…
It is widely accepted that there is strong persistence in the volatility of financial time series. The origin of the observed persistence, or long-range memory, is still an open problem as the observed phenomenon could be a spurious effect. Earlier we have proposed the consentaneous model of the financial markets based on the non-linear stochastic differential equations. The consentaneous model successfully reproduces empirical probability and power spectral densities of volatility. This approach is qualitatively different from models built using fractional Brownian motion. In this contributio…
The persistence phenomenon is studied in the Japanese financial market by using a novel mapping of the time evolution of the values of shares quoted on the Nikkei Index onto Ising spins. The method is applied to historical end of day data from the Japanese stock market during 2002. By studying the time dependence of the spins, we find clear evidence for a double-power law decay of the proportion of shares that remain either above or below ` starting\rq\ values chosen at random. The results are consistent with a recent analysis of the data from the London FTSE100 market. The slopes of the power…
We analyze the data of the Italian and U.S. futures on the stock markets and we test the validity of the Continuous Time Random Walk assumption for the survival probability of the returns time series via a renewal aging experiment. We also study the survival probability of returns sign and apply a coarse graining procedure to reveal the renewal aspects of the process underlying its dynamics.
We discuss the theoretical machinery involved in predicting financial market movements using an artificial market model which has been trained on real financial data. This approach to market prediction - in particular, forecasting financial time-series by training a third-party or 'black box' game on the financial data itself -- was discussed by Johnson et al. in cond-mat/0105303 and cond-mat/0105258 and was based on some encouraging preliminary investigations of the dollar-yen exchange rate, various individual stocks, and stock market indices. However, the initial attempts lacked a clear form…
Financial market prediction on the basis of online sentiment tracking has drawn a lot of attention recently. However, most results in this emerging domain rely on a unique, particular combination of data sets and sentiment tracking tools. This makes it difficult to disambiguate measurement and instrument effects from factors that are actually involved in the apparent relation between online sentiment and market values. In this paper, we survey a range of online data sets (Twitter feeds, news headlines, and volumes of Google search queries) and sentiment tracking methods (Twitter Investor Senti…
In this article we use the Mean-Variance Model in order to measure the current market state. In our study we take the approach of detecting the overall alignment of portfolios in the spin picture. The projection to the ground-states enables us to use physical observables in order to describe the current state of the explored market. The defined magnetization of portfolios shows cursor effects, which we use to detect turmoils.
The two phase behavior in financial markets actually means the bifurcation phenomenon, which represents the change of the conditional probability from an unimodal to a bimodal distribution. In this paper, the bifurcation phenomenon in Hang-Seng index is carefully investigated. It is observed that the bifurcation phenomenon in financial index is not universal, but specific under certain conditions. The phenomenon just emerges when the power-law exponent of absolute increment distribution is between 1 and 2 with appropriate period. Simulations on a randomly generated time series suggest the bifu…
This paper investigates the relationship between the spread of the COVID-19 pandemic, the state of community activity, and the financial index performance across 20 countries. First, we analyze which countries behaved similarly in 2020 with respect to one of three multivariate time series: daily COVID-19 cases, Apple mobility data and national equity index price. Next, we study the trajectories of all three of these attributes in conjunction to determine which exhibited greater similarity. Finally, we investigate whether country financial indices or mobility data responded quicker to surges in…
