High Frequency Modelling in Kyle-Back Model

We consider a special version of the Kyle-Back model where not only the insider receives a private signal that converges to the true value of the asset, but also there is another public signal also converging to the true value of the asset that is shared with the market makers.

We are going to show that the expectation of the true value of the asset given the insider’s information is given by a linear combination of both the public and private signals and it is a martingale the insider’s filtration. Furthermore, we will show some discussions on the behaviour of the market makers and what is expected from the equilibrium(a) of the model. Hopefully, it will be possible discuss the empirical consequences of this model and what can be expected from real data.