Coexisting Attractors in a Heterogeneous Agent Model in Discrete Time

In this paper, the discrete-time version of a continuous-time model with fundamentalists and momentum traders is presented. Our aim consists of studying the impact of cross-sectional momentum traders on the dynamics of the model. To this end, the continuous-time deterministic skeleton of the benchmark model is transformed using sophisticated discretization techniques. It is worth noting that the model does not always maintain the same characteristics after moving from continuous to discrete time. In spite of this, our discrete-time system preserves the dynamic properties of the continuous-time original model. Moreover, heterogeneity introduces an important non-linearity into the market dynamics, causing our deterministic financial model to generate erratic time series similar to the patterns observed in real markets. In particular, we show that the time series originated by the perturbed deterministic system capture some of the main stylized facts of the U.S. financial market. Converting the benchmark model from continuous time to discrete time allows the use of financial data available in discrete time.