The aim of the paper was to present a theoretical explanation of the effect of the mimetic contagion on the dynamics of the market price of a financial asset. It explains the birth, the life and the explosion of a "contagion" bubble as well as the "contagion" volatility of the price. The paper has two characteristics.
First, about the agents' economic behaviour. Market traders know they have an incomplete information set. Any investor set his bid and/or ask prices according to an additive learning process: (i) he adjusts his prices to his present value calculated from his incomplete information set, this is "limited" rational behaviour; (ii) to capture some information held by the other investors, he also adjusts his prices to average prices of his nearest buyers and sellers, this is a mimetic contagion. Stock price movement is then socially transmitted.
Second, about the mathematical treatment. the issue is to deduce the evolution of the stock price. One also must take into account that a transaction between a buyer and a seller is only realized when agents agree on the price. The paper presents an unusual stochastic treatment based on the equations of the market price are deduced.
The present paper investigates the simple case of a deterministic contagion. The main results are:
If there is no contagion and if agents make strong-form rational expectations, the dynamics of the moments of the market price correspond to the fundamental value. If agents make weak-form rational expectations the market price dynamics diverge from the fundamental price, although he is still rational in a weak sense. The moments of market price are independently determined and the representative agent hypothesis is correct.
If there is contagion and if agents make weak-form rational expectations, mimetic contagion, through correlations of the agents' behaviours, intervenes as an origin of a "contagion" speculative bubble and there is some volatility. Mean and variance of the market price are simultaneously determined. It is not possible to rigorously explain the market price dynamics with only one-agent statistical properties and the representative agent hypothesis is not valid.
More generally speaking, for the given period for which the modeller wants to describe the price evolution, as soon as the agents have incomplete information set and/or correlated behaviours, then the dynamics of the moments of the market price are driven away from the fundamental ones.
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