An Evolutionary Quantum Game Model of Financial Market Dynamics - Theory and Evidence

Carlos Pedro Goncalves
Carlos Goncalves

The development of models that generate multifractal patterns in a bottom-up fashion is necessary, both for financial theorists and financial agents. The presence of multifractal patterns makes the markets more risky than predicted by standard financial models, which means that financial agents need to have models that are able to provide for guiding tools in asset and risk management.

Within standard financial theory the multifractal behavior remains unexplained. The development of a model capable of explaining the presence of multifractal signatures in the markets would be a first step towards a financial theory of market dynamics. However, such a model, and such a theory cannot be found in the framework of standard finance.

It has become necessary to review the microscopic assumptions that form the basis for classical finance, where, by microscopic assumptions, we mean the individual agent’s behavior and the interaction rules between agents.

Mathematical physics, and econophysics have provided for competing fields of research where it is possible to study market dynamics from the perspective of microscopic modelling. Spin glasses provide for the oldest examples of the application of physical models to solve unexplained empirical facts in market dynamics. One of the early applications of these models dates back to Vaga’s (1990) coherent market hypothesis, that tried to relate market dynamics to different phases, in an analogy with the different phases of a spin glass.

Although spin glasses have been an example of a simple and effective modelling tool to build microscopic theories of market dynamics, one still lacked a robust model capable of generating self-organized multifractality, until a recent work by Sornette and Zhou (Sornette and Zhou, 2005; Zhou and Sornette 2005, 2007), in which multifractal structure is diagnosed, not only by the standard convexity of the structure functions’ exponents, but also by a continuous spectrum of power law response functions to endogenous shocks.