KYLE–BACK’S MODEL WITH A RANDOM HORIZON

Abstract

The continuous-time version of Kyle [(1985) Continuous auctions and insider trading, Econometrica 53 (6), 1315–1335.] developed by Back [(1992) Insider trading in continuous time, The Review of Financial Studies 5 (3), 387–409.] is studied here. In Back’s model, there is asymmetric information in the market in the sense that there is an insider having information on the real value of the asset. We extend this model by assuming that the fundamental value evolves with time and that it is announced at a future random time. First, we consider the case when the release time of information is predictable to the insider and then when it is not. The goal of the paper is to study the structure of equilibrium, which is described by the optimal insider strategy and the competitive market prices given by the market makers. We provide necessary and sufficient conditions for the optimal insider strategy under general dynamics for the asset demands. Moreover, we study the behavior of the price pressure and the market efficiency. In particular, we find that when the random time is not predictable, there can be equilibrium without market efficiency. Furthermore, for the two cases of release time and for classes of pricing rules, we provide a characterization of the equilibrium.