Insider Trading with Temporary Price Impact

TL;DR

This paper develops a model of insider trading with temporary price impact, analyzing equilibrium strategies and prices in both single auction and continuous time settings, highlighting the effects of transaction costs.

Contribution

It introduces a novel equilibrium framework incorporating transaction costs and derives explicit strategies and prices, extending previous models to include market frictions.

Findings

Equilibrium characterized by polynomial root in single auction model.

In continuous time, optimal strategies are solutions to coupled differential equations.

Transaction costs create an information gap, reducing price informativeness.

Abstract

We model an informed agent with information about the future value of an asset trying to maximize profits when subjected to a transaction cost as well as a market maker tasked with setting fair transaction prices. In a single auction model, equilibrium is characterized by the unique root of a particular polynomial. Analysis of this polynomial with small levels of risk-aversion and transaction costs reveal a dimensionless parameter which captures several orders of asymptotic accuracy of the equilibrium behaviour. In a continuous time analogue of the single auction model, incorporation of a transaction costs allows the informed agent's optimal trading strategy to be obtained in feedback form. Linear equilibrium is characterized by the unique solution to a system of two ordinary differential equations, of which one is forward in time and one is backward. When transaction costs are in effect, the price set by the market maker in equilibrium is not fully revealing of the informed agent's private signal, leaving an information gap at the end of the trading interval. When considering vanishing transaction costs, the equilibrium trading strategy and pricing rules converge to their frictionless counterparts.