Before revision:  In particular, the price set by the market makers is the solution to a non-standard `quadratic' backward stochastic differential equation  .
After revision:  In particular, the price set by the market makers is the solution to a non-standard `quadratic' backward stochastic differential equation . The main result of the paper is the existence of a Markovian solution to this forward-backward system on an arbitrary time interval, which is obtained via a fixed-point argument on the space of absolutely continuous distribution functions. Moreover, the equilibrium obtained in this paper is able to explain several stylized facts which are not captured by the current asymmetric information models .