Directional high frequency trading in the Kyle-Back model

In traditional Kyle-Back models, the only source of information is a static or dynamic signal about the price of a risky asset received by the insider. We consider a more realistic version of the Kyle-Back model with a private and a public signal. The insider builds a linear combination of the public and private signals to make their valuation about the risky asset. The market maker uses the public signal and the total demand to set a linear pricing rule that is a martingale on their filtration. We show that any optimal strategy in equilibrium is such that the mispricing, the difference between the price process and the insider’s valuation, converges to zero almost surely in the insider’s probability measure. We introduce a particular linear admissible trading strategy to show the existence of equilibrium in the economy. Moreover, we use numerical analysis to show that the insider’s ex-ante expected profit relies on the public signal and how this setting is able to explain a high-frequency trading pattern at the end of the trading period.