Modelling adaptive complex behaviour with an application to the stock markets dynamics

In this paper we review a simple agent-based model of adaptive complex behaviour that shows how the interaction of different agent's profit-oriented decisions leads to a wide spectra of organizational possibilities. We comment on some potential applications of this model to the social and life sciences, and later focus on the modelling of the stock market dynamics. We show how some ~f the features of stock price series, and in particular extreme events such as speculative bubbles and crashes, can be obtained when certain conditions are satisfied by most of the investors' preferences

Financial time series obtained by agent-based simulation

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2015, Director: Josep Fortiana GregoriEconomic news often talks about growths and drops of indexes and individual stocks, but many people (including me before I did this work) do not understand neither how the stock market works nor what causes its price fluctuations. Stock markets are complex systems. In empirical sciences, a common strategy used to study a real system consists in making simplified models that keep their main features, and analyze them in order to understand further the system dynamics. There is a type of models known as agent-based models that are used to simulate complex systems by creating software objects (called agents) whose behavior have global consequences for the system. This concept allows modelers to connect the micro-level of individuals with the macroscopic patterns, what is essential to understand systems interactions. One example of agent-based environment and programming language is NetLogo, created by Uri Wilensky in 1999. Since individual investors’ decisions control the dynamics of stock markets, it seems reasonable to treat the stock market as if it is a dynamic system of interacting agents, that will represent investors. The collective behavior of these investors, each of which acts independently, produces prive movements. Based on Silva’s (2014) Collective behavior in the Stock Market model, we have designed and implemented a model for the evolution of a very simple market, with a single asset price, using the NetLogo environment. On the other hand, companies’ share prices form time series. Statistics supplies powerful tools and methods to understand the processes behind time series, make a model of them and, furthermore, forecast future values based on the current data. Hence, financial time series analysis plays an important role in investments strategies and other economical applications. We are going to describe the main methods and models used for this kind of series, but there is so much bibliography on the statistical treatment of financial series; see, for example, Tsay (2005)

Consentaneous agent-based and stochastic model of the financial markets

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.Comment: 17 pages, 6 figures, Gontis V, Kononovicius A (2014) Consentaneous Agent-Based and Stochastic Model of the Financial Markets. PLoS ONE 9(7): e102201. doi: 10.1371/journal.pone.010220

Price Variations in a Stock Market With Many Agents

Large variations in stock prices happen with sufficient frequency to raise doubts about existing models, which all fail to account for non-Gaussian statistics. We construct simple models of a stock market, and argue that the large variations may be due to a crowd effect, where agents imitate each other's behavior. The variations over different time scales can be related to each other in a systematic way, similar to the Levy stable distribution proposed by Mandelbrot to describe real market indices. In the simplest, least realistic case, exact results for the statistics of the variations are derived by mapping onto a model of diffusing and annihilating particles, which has been solved by quantum field theory methods. When the agents imitate each other and respond to recent market volatility, different scaling behavior is obtained. In this case the statistics of price variations is consistent with empirical observations. The interplay between ``rational'' traders whose behavior is derived from fundamental analysis of the stock, including dividends, and ``noise traders'', whose behavior is governed solely by studying the market dynamics, is investigated. When the relative number of rational traders is small, ``bubbles'' often occur, where the market price moves outside the range justified by fundamental market analysis. When the number of rational traders is larger, the market price is generally locked within the price range they define.Comment: 39 pages (Latex) + 20 Figures and missing Figure 1 (sorry), submitted to J. Math. Eco