Abstract
In this paper, we detected the fractal/multifractal and asymmetric properties in a simple financial market model which is an analog of the Ising model. We introduced the virtual market with heterogeneous agents characterized by agents with bounded rationality, by which we mean that agents only have local information, and a market maker who is responsible for market liquidity. To investigate the heterogeneity and psychological factors in real financial market, we designed the parameters of individual expectations of agents to this model. Applying fractal/multifractal and Zipf techniques, we conducted many simulations under different scenarios and then analyzed the generated time series of this virtual market. We acquired some nontrivial findings: first, the virtual price returns generated by our model display fractal and multifractal features; secondly, we found that the price have the asymmetric behaviors; finally, our findings have qualitative similarities with many empirical results, which imply that although our toy model is seemingly simple, it can generate complex dynamics and thus can be a useful tool to investigate complex market behaviors and phenomena.
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