The Backbone Of The Financial Interaction Network Using A Maximum Entropy Distribution

We modeled the stocks of the financial system as a set of many interacting like spins derived from binary daily returns. From the empirical observation of these returns, we used a Boltzmann machine to infer a distribution of states equivalent to a maximum entropy distribution. This model describes the interaction couplings between each stock pair in the system, which can be considered a complete network with N(N-1)/2 couplings. We then engage in a coupling removal process to find a critical graph that can describe the observed states of the system with the minimum number of edges. We interpret the critical graph as the backbone of the system, and it allows us to evaluate the importance of markets in their relation to others in the system. We also found that the structure of this critical graph is highly variable over time and appears to be dependent on the level of entropy of the system.