The dynamics of financial markets are highly complex. Mainstream asset pricing models often are inaccurate and fail to account for the role human psychological tendencies play in determining stock price. In order to simulate this, we will implement the microsimulation models through a variation of the Ehrenfest urn model to thoroughly understand their modeling principles. We will then perform parameter study of 𝛼 and 𝛽 to compare the relevant characteristics of the simulation results after tuning the parameters. Following this, we will predict the outcome of each implemented case in order to present a general understanding of the origins of the stylized facts. Mainly, the collective behavior of the interacting elements under the influence of massive external factors with a focus on sensitivity based on behavior of other traders in the market.
Within our model, we defined two parameters, 𝜶 and 𝜷, to represent market preference. We denote 𝜶 to be the parameter controlling the ‘bull’ preference. This means when increasing 𝜶 in our Urn model, the market as a whole will increase its preference to act as a ‘bull’ (i.e demand more of the asset in question). We denote 𝜷 to be the bear preference. This means when we increase 𝜷, the market as a whole will prefer to act as a ‘bear’ (i.e. supply more of the asset in question).