Related papers: From Minority Game to Black & Scholes pricing
We discuss a simple model based on the Minority Game which reproduces the main stylized facts of anomalous fluctuations in finance. We present the analytic solution of the model in the thermodynamic limit and show that stylized facts arise…
We study analytically and numerically Minority Games in which agents may invest in different assets (or markets), considering both the canonical and the grand-canonical versions. We find that the likelihood of agents trading in a given…
Price dynamics is analyzed in terms of a model which includes the possibility of effective forces due to trend followers or trend adverse strategies. The method is tested on the data of a minority-majority model and indeed it is capable of…
The minority game (MG) model introduced recently provides promising insights into the understanding of the evolution of prices, indices and rates in the financial markets. In this paper we perform a time series analysis of the model…
The Minority Game is a generic model of competing adaptive agents, which is often believed to be a model of financial markets. We discuss to which extend this is a reasonable statement, and present minimal modifications that make this model…
The Black-Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time-to-maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power…
The dynamics of minority games with agents trading on different time scales is studied via dynamical mean-field theory. We analyze the case where the agents' decision-making process is deterministic and its stochastic generalization with…
In this paper, we present a simple stock market model (the market game) which incorporates, as ab initio dynamics delayed majority dynamics, according to which agents (with heterogeneous strategies and price expectations) are rewarded if…
We discuss in detail the derivation of stochastic differential equations for the continuum time limit of the Minority Game. We show that all properties of the Minority Game can be understood by a careful theoretical analysis of such…
The Minority Game is a simple model for the collective behavior of agents in an idealized situation where they have to compete through adaptation for a finite resource. This review summarizes the statistical mechanics community efforts to…
We address the question of market efficiency using the Minority Game (MG) model. First we show that removing unrealistic features of the MG leads to models which reproduce a scaling behavior close to what is observed in real markets. In…
We consider a version of large population games whose agents compete for resources using strategies with adaptable preferences. Diversity among the agents reduces their maladpative behavior. We find interesting scaling relations with…
We review the recent approaches to modelling financial markets based on multi-agent systems. After a brief summary of the basic stylised facts observed in real-market time-series we discuss some simple agent-based systems which are…
We study the continuous time dynamics of the Thermal Minority Game. We find that the dynamical equations of the model reduce to a set of stochastic differential equations for an interacting disordered system with non-trivial random…
We study the dynamics of a version of the batch minority game, with random external information and with different types of inhomogeneous decision noise (additive and multiplicative), using generating functional techniques \`{a} la De…
The Minority Game (MG), the Majority Game (MAJG) and the Dollar Game ($G) are important and closely-related versions of market-entry games designed to model different features of real-world financial markets. In a variant of these games,…
A brief review is given of the minority game, an idealized model stimulated by a market of speculative agents, and its complex many-body behaviour. Particular consideration is given to analytic results for the model rather than discussions…
We use the cavity method from statistical physics for analyzing the transient and stationary dynamics of a minority game that is played by agents performing market arbitrage. On the level of linear response the method allows to include the…
In this paper it was developed a modification of the known multiagent model Minority Game, designed to simulate the behavior of traders in financial markets and the resulting price dynamics on the abstract resource. The model was…
We use the expectation of the range of an arithmetic Brownian motion and the method of moments on the daily high, low, opening and closing prices to estimate the volatility of the stock price. The daily price jump at the opening is…