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Register a new userMinimal Agent Based Model for Financial Markets I: Origin and Self-Organization of Stylized Facts
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We introduce a minimal Agent Based Model for financial markets to understand the nature and Self-Organization of the Stylized Facts. The model is minimal in the sense that we try to identify the essential ingredients to reproduce the main most important deviations of price time series from a Random Walk behavior. We focus on four essential ingredients: fundamentalist agents which tend to stabilize the market; chartist agents which induce destabilization; analysis of price behavior for the two strategies; herding behavior which governs the possibility of changing strategy. Bubbles and crashes correspond to situations dominated by chartists, while fundamentalists provide a long time stability (on average). The Stylized Facts are shown to correspond to an intermittent behavior which occurs only for a finite value of the number of agents N. Therefore they correspond to finite size effect which, however, can occur at different time scales. We propose a new mechanism for the Self-Organization of this state which is linked to the existence of a threshold for the agents to be active or not active. The feedback between price fluctuations and number of active agents represent a crucial element for this state of Self-Organized-Intermittency. The model can be easily generalized to consider more realistic variants.
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We introduce a minimal Agent Based Model with two classes of agents, fundamentalists (stabilizing) and chartists (destabilizing) and we focus on the essential features which can generate the stylized facts. This leads to a detailed understanding of the origin of fat tails and volatility clustering and we propose a mechanism for the self-organization of the market dynamics in the quasi-critical state. The stylized facts are shown to correspond to finite size effects which, however, can be active at different time scales. This implies that universality cannot be expected in describing these properties in terms of effective critical exponents. The introduction of a threshold in the agents action (small price fluctuations lead to no-action) triggers the self-organization towards the quasi-critical state. Non-stationarity in the number of active agents and in their action plays a fundamental role. The model can be easily generalized to more realistic variants in a systematic way.
We present a detailed study of the statistical properties of an Agent Based Model and of its generalization to the multiplicative dynamics. The aim of the model is to consider the minimal elements for the understanding of the origin of the Stylized Facts and their Self-Organization. The key elements are fundamentalist agents, chartist agents, herding dynamics and price behavior. The first two elements correspond to the competition between stability and instability tendencies in the market. The herding behavior governs the possibility of the agents to change strategy and it is a crucial element of this class of models. The linear approximation permits a simple interpretation of the model dynamics and, for many properties, it is possible to derive analytical results. The generalized non linear dynamics results to be extremely more sensible to the parameter space and much more difficult to analyze and control. The main results for the nature and Self-Organization of the Stylized Facts are, however, very similar in the two cases. The main peculiarity of the non linear dynamics is an enhancement of the fluctuations and a more marked evidence of the Stylized Facts. We will also discuss some modifications of the model to introduce more realistic elements with respect to the real markets.
In this work we afford the statistical characterization of a linear Stochastic Volatility Model featuring Inverse Gamma stationary distribution for the instantaneous volatility. We detail the derivation of the moments of the return distribution, revealing the role of the Inverse Gamma law in the emergence of fat tails, and of the relevant correlation functions. We also propose a systematic methodology for estimating the parameters, and we describe the empirical analysis of the Standard & Poor 500 index daily returns, confirming the ability of the model to capture many of the established stylized fact as well as the scaling properties of empirical distributions over different time horizons.
We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and {it vanishes} around the current price. This result is generic, and only relies on mild assumptions about the order flow and on the fact that prices are (to a first approximation) diffusive. This naturally accounts for two striking stylized facts: first, large metaorders have to be fragmented in order to be digested by the liquidity funnel, leading to long-memory in the sign of the order flow. Second, the anomalously small local liquidity induces a breakdown of linear response and a diverging impact of small orders, explaining the square-root impact law, for which we provide additional empirical support. Finally, we test our arguments quantitatively using a numerical model of order flow based on the same minimal ingredients.
We present a detailed analysis of the self-organization phenomenon in which the stylized facts originate from finite size effects with respect to the number of agents considered and disappear in the limit of an infinite population. By introducing the possibility that agents can enter or leave the market depending on the behavior of the price, it is possible to show that the system self-organizes in a regime with a finite number of agents which corresponds to the stylized facts. The mechanism to enter or leave the market is based on the idea that a too stable market is unappealing for traders while the presence of price movements attracts agents to enter and speculate on the market. We show that this mechanism is also compatible with the idea that agents are scared by a noisy and risky market at shorter time scales. We also show that the mechanism for self-organization is robust with respect to variations of the exit/entry rules and that the attempt to trigger the system to self-organize in a region without stylized facts leads to an unrealistic dynamics. We study the self-organization in a specific agent based model but we believe that the basic ideas should be of general validity.
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