Bullish-Bearish strategies of trading: A non-linear equilibrium.

Abstract

In this paper, we study a financial market where risk neutral traders are endowed with a signal which is perfectly revealing of the direction (but not the exact amount) of the liquidation value of a normally distributed risky asset. This type of information is known as bullish or bearish. When the signal is positive (negative) the traders buy (sell) the asset. This type of information is different with the type of information which is classically considered in the literature where informed traders are endowed with a perfect or a noisy signal. In this model, since the optimal trading strategy is not linear, the pricing schedule is also a non-linear function of the volumes. The main results are the following i) the price function is a non-linear Sigmo¨ıd-shaped function. ii) A monopolistic bullish-bearish type trader makes nearly thirty six percent of the profits she would have made with a perfect signal in a linear model `a la Kyle (1985). iii) In the presence of competition, the market reveals his private information quicker than in a noisy informed strategic oligopoly. Moreover, liquidity is no longer a monotonic increasing function of the number of competitors