Equilibrium model of fundamentalist and noise traders in a multi-asset framework

Kaizoji et al. (2015) formulated an artificial market model which is able to reproduce financial bubbles with faster-than-exponential growth. Given the importance of bubbles and crashes in the financial market, research in the direction of the understanding the mechanisms underlying such phenomena is more and more relevant. The present thesis moves in this direction proposing an enlargement of the original market model to the multi-asset framework. After a brief introduction of the original market model formulation, we aim at the comprehension of the reasons of the build-up of bubbles in the price trend and how they are related to the interplay between fundamentalists and noise traders. The former are rational traders whereas the latter are irrational traders influenced by social imitation and trend following. In particular, we deepen the insight into the category of noise traders and the Ising-like structure of their class. It is, indeed, the presence of an underlying phase transition from a disordered regime where the idiosyncratic opinion is determinant to the ordered phase where a manifested collective behavior of noise agents takes over that trigger the bubbles. Starting from a good comprehension of the original model, we move towards the enlargement of the original model to the case of multiple assets. In particular, our interest focuses on the case of two risky assets and one risk-free asset. We derive the new equations for the wealth dynamics, for the fundamentalists strategy and a complete new setup for the noise traders class. This latter is organized to be adherent to the original Ising-like scheme. For this reason, the class is divided into two sub-classes of traders that can trade only one type of risky asset and the risk-free asset. Each noise trader invests all his fortune in only one endowment. Thus, allowing the transitions between the two sub-classes, we can ensure the diversification of the noise traders portfolio at the aggregate level. In the typical time series, bubbles and crashes are still present and the extended model is also able to reproduce some 'stylized facts' of the financial market as far as regards the distributions of the returns. The theoretical insights into the model have been conducted in two different directions: the comprehension of the theoretical foundations at the origin of the bubbles and on the correlations between the two assets. In particular, we study the relationship between the correlation imposed a priori between the assets and the realised correlations found in the time series.