Thermodynamical Modeling Stability of Financial Network Based on Their Structure on Fractal and Rule Driven Spin Lattice

Abstract

The stability and order of globalised financial network is crucial for economic health. Prediction of instabilities, or defaults of such macroscopic system based on many microscopic states of individual behaviour of assets, institutions, clients, and traders is a challenging problem. Is it possible to estimate a failure of financial institution on a large scale, or domain? Many approaches in financial mathematics were used for this and usually without quantitative success. They are struggling with complexity and NP difficulty given by complex relations in financial network. Such a network can contain some recurrent patterns and can be described like fractal or other patterns in structure. In this article, we are modelling the financial network as a thermodynamical rule-driven board, fractal spin lattice to describe equilibrial behaviour and analyse phase transitions and other thermodynamis quantities describing macroscopic behaviour of such structure system with recurrent patterns. Assets and liabilities of financial institutions and companies are represented with spin binary variables. Spin interactions are interpreted as mutual trading among assets and liabilities. The thermal coefficient introduces assets and liabilities fluctuations. Below phase transition temperature are large-scale clusters of assets formed and are dominant. Assets cluster size can be an order parameter. After phase transition, when fluctuations of prices increase, actors on the market are disturbed with increasing fluctuation and are not correlated on larger network distances into the communication, which suppresses long-range correlations. Crash of such a system can be represented with change of lattice order parameter, when system temperature jumps up over critical value and long range domain structure of assets is broken, which usually means that financial institutions fail to meet interest or payment obligations.