A Statistical Physics approach to financial bubbles: Ising-like modeling of social imitation in an Agent-based multi-asset market

From the seventeenth-century Dutch Tulip Bubble and the eighteenth-century South Sea Bubble to the more recent Dotcom Bubble and U.S. Housing Bubble, the economic history has been characterized by bubbles and crashes, booms, and crises of all sorts. To fully understand the financial markets, it is crucial to embrace the fact that the world economy is a constantly evolving multi-agent complex system, that can be studied using the tools of complex systems theory. Among them, the Agent-Based Models (ABMs) are powerful tools to investigate the dynamics of complex systems, and the Statistical Physics has a history of success in modeling systems with a large number of components (in this case the traders) whose collective interactions lead to the emergence of highly not trivial collective phenomena (the bubbles). The present thesis proposes an extension of an ABM, first introduced by Kaizoji et al. (2015) which is able to reproduce faster-than-exponential bubbles growth together with the "stylized facts" of the financial market. The original model is constituted by two classes of investors: the fundamentalist traders, rational risk-averse traders, and the noise traders guided instead by social imitation and trend following. The traders invest in two assets, one risk-free asset, and one risky asset. The price dynamics is generated imposing the market clearing conditions according to Walras' theory of general equilibrium. After a review of the original model, we introduce an extension to a multi-asset framework composed of one risk-free asset and many risky assets. First, we address the extension of the fundamentalist traders’ class. We then move to the market-clearing conditions, which involves the solution of a complex non-linear system that is addressed with numerical techniques. The remaining and largest part of the work deals with the extension of the noise traders class. The fundamental feature characterizing it is its Ising-like structure which models the competition between the ordering force of social imitation and the disordering impact of idiosyncratic opinion, hence we largely resort to statistical physics to consider its generalization. We propose four statistical models, deriving the stochastic dynamics characterizing each of them, and discussing their strengths and weaknesses. We consider a Potts model, an O(n) model, a vectorial extension of the BEG model, and an n-state extension of the BEG model. All the models share the same underlying mechanism triggering the bubbles. When the herding propensity parameter exceeds a certain critical threshold, the noise traders class undergo a phase transition from the disordered state dominated by the idiosyncratic opinion to the ordered state where the class polarizes towards specific investment preferences. This interaction-driven collective behavior leads to the emergence of the bubbles. A thorough analysis of the phase transition is carried out. In the last part of the work, we deepen the analysis of the ABM with the O(n) model for the noise traders class. We focus on it due to both the validity of the resulting price time series and the high controllability of its behavior. We first check the model’s ability to reproduce the "stylized facts" of financial markets. Then the ABM is applied to understand the mechanism behind the time synchronization of bubbles among the assets. Finally, the dynamic of the returns is compared to the one predicted by the Capital Asset Pricing Model.