Modeling the financial market with labyrinth chaos

Abstract

In the present study, a deterministic model is introduced to explain the stylized facts of financial data. The adaptation introduced by the labyrinth chaos model can reproduce phenomena such as heavy tails observed in financial returns, volatility clustering and jumps. The model is based on the assumption that many unstable stationary states arise from the interaction or feedback between financial prices. Model tests are performed, and the results show that the model generates series that reject a normal distribution of the returns and which can be represented by the GARCH model. An analysis applying symbolic dynamics shows similar behaviors in a system with three stock indices, three currency relations and three prices generated by the introduced model. We observe sequences that have not been produced by any of the three systems, suggesting that in a three-dimensional space, the paths traveled by the real series and those of the model may not be completely random.