Complexity in financial market. Modeling psychological behavior in agent-based models and order book models

The fundamental idea developed throughout this work is the introduction of new metrics in Social Sciences (Economics, Finance, opinion dynamics, etc). The concept of metric, that is the concept of measure, is usually neglected by mainstream theories of Economics and Finance. Financial Markets are the natural starting point of such an approach to Social Sciences because a systematic approach can be undertaken and the methods of Physics has shown to be very effective. In fact since a decade there exists a very huge amount of high frequency data from stock exchanges which permit to perform experimental procedures as in Natural Sciences. Financial markets appear as a perfect playground where models can be tested and where repeatability of empirical evidences are well-established features differently from, for instance, Macro-Economy and Micro-Economy. Thus Finance has been the first point of contact for the interdisciplinary application of methods and tools deriving from Physics and it has been also the starting point of this work. We investigated the origin of the so-called Stylized Facts of financial markets (i.e. the statistical properties of financial time series) in the framework of agent-based models. We found that Stylized Facts can be interpreted as a finite size effect in terms of the number of effectively independent agents (i.e. strategy) which results to be a key variable to understand the self-organization of financial markets. As a second issue we focused our attention on the order book dynamics both from a theoretical and a data oriented point of view. We developed a zero intelligence model in order to investigate the role of vanishing liquidity in the price response to incoming orders. Within the framework of this model we have analyzed the effect of the introduction of strategies pointing out that simple strategic behaviors can explain bursts of intermittency and long memory effects. On the other hand we quantitatively showed that there exists a feedback effect in markets called self-fulfilling prophecy which is the mechanism through which technical trading can exist and work. This feature is a very interesting quantitative evidence of a self-reinforcement of agents’ belief. Last but not least nowadays we live in a computerized and networked society where many of our actions leave a digital trace and affect other people’s actions. This has lead to the emergence of a new data-driven research field. In this work we highlighted how non financial data can be used to track financial activity, in detail we investigate query log volumes, i.e. the volumes of searches for a specific query done by users in a search engine, as a proxy for trading volumes and we find that users’ activity on Yahoo! search engine anticipates trading volume by one-two days. Differently from Finance, Economics is far from being an ideal candidate to export the methodology of Natural Sciences because of the lack of empirical data since controlled (and repeatable) experiments are totally artificial while real experiments are almost incontrollable and non repeatable due to a high degree of non stationarity of economical systems. However, the application of method deriving from complexity to the Economics of Growth is one of the more important achievement of the work here developed. The basic idea is to study the network defined by international trade flows and introduce a (non-monetary) metric to measure the complexity and the competitiveness of countries’ productive system. In addition we are able to define a metric for products’ quality which overcomes traditional economic measure for the quality of products given in terms of hours of qualified labour needed to produce a good. The method developed provides some impressive results in predicting economical growth of countries and offers many opportunities of improvements and generalizations

How the Taxonomy of Products Drives the Economic Development of Countries

We introduce an algorithm able to reconstruct the relevant network structure on which the time evolution of country-product bipartite networks takes place. The significant links are obtained by selecting the largest values of the projected matrix. We first perform a number of tests of this filtering procedure on synthetic cases and a toy model. Then we analyze the bipartite network constituted by countries and exported products, using two databases for a total of almost 50 years. It is then possible to build a hierarchically directed network, in which the taxonomy of products emerges in a natural way. We study the influence of the structure of this taxonomy network on countries' development; in particular, guided by an example taken from the industrialization of South Korea, we link the structure of the taxonomy network to the empirical temporal connections between product activations, finding that the most relevant edges for countries' development are the ones suggested by our network. These results suggest paths in the product space which are easier to achieve, and so can drive countries' policies in the industrialization process.Comment: 16 pages, 8 figure

The complex dynamics of products and its asymptotic properties

We analyse global export data within the Economic Complexity framework. We couple the new economic dimension Complexity, which captures how sophisticated products are, with an index called logPRODY, a measure of the income of the respective exporters. Products' aggregate motion is treated as a 2-dimensional dynamical system in the Complexity-logPRODY plane. We find that this motion can be explained by a quantitative model involving the competition on the markets, that can be mapped as a scalar field on the Complexity-logPRODY plane and acts in a way akin to a potential. This explains the movement of products towards areas of the plane in which the competition is higher. We analyse market composition in more detail, finding that for most products it tends, over time, to a characteristic configuration, which depends on the Complexity of the products. This market configuration, which we called asymptotic, is characterized by higher levels of competition.Comment: 20 pages, 5 figures, supporting information. This paper was published on PLOS One on May 17, 201

Critical Overview of Agent-Based Models for Economics

We present an overview of some representative Agent-Based Models in Economics. We discuss why and how agent-based models represent an important step in order to explain the dynamics and the statistical properties of financial markets beyond the Classical Theory of Economics. We perform a schematic analysis of several models with respect to some specific key categories such as agents' strategies, price evolution, number of agents, etc. In the conclusive part of this review we address some open questions and future perspectives and highlight the conceptual importance of some usually neglected topics, such as non-stationarity and the self-organization of financial markets.Comment: 51 pages, 9 figures, Proceedings of the School of Physics "E. Fermi", course CLXXVI, 2010, Varenn

Capitolo 9. Appunti lessicali sul Misogallo romano (n. 407)

The paper deals with some lexical issues raised by one of the Romanesco poems (n. 407) included in the so-called Misogallo romano (late 18th century). In particular, the work tries to explain four rather puzzling words: 1) pilacche, which possibly has to be considered a copying mistake for pilucche ‘wigs’; 2) Mambrucche (in the syntagma aria de Mambrucche), to be linked to the French song Malbrough s’en va-t-en guerre; 3) tricche tracche, whose meaning could be just, as usually in Romanesco, ‘a kind of instrument used in the Holy Week’; 4) policche (in the phrase fà policche), still obscure, for which it is nonetheless possible - among other proposals - to establish a comparison with similar words occurring in the dialects of Todi and Subiaco

Minimal Agent Based Model for Financial Markets II: Statistical Properties of the Linear and Multiplicative Dynamics

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

Minimal Agent Based Model for Financial Markets I: Origin and Self-Organization of Stylized Facts

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