How Temporary Trading Costs Shape Insider Trading Equilibrium

Summary

This document studies how temporary transaction costs affect an informed trader who knows an asset’s future value and a market maker who sets prices. It analyzes both a single-auction model and a continuous-time version, with the trader choosing trades to maximize profit while accounting for costs and, in some cases, risk aversion.

For the auction model, equilibrium is characterized as the unique root of a polynomial; asymptotic analysis identifies a dimensionless parameter that approximates behavior across small risk-aversion and cost levels. In continuous time, the optimal strategy is expressed in feedback form, and linear equilibrium depends on a coupled pair of forward and backward ordinary differential equations. Costs leave prices less informative about the private signal by the end of trading. As costs vanish, the strategy and pricing rules approach their frictionless counterparts. The document summarizes theoretical results but gives no empirical validation or implementation details.

Key ideas

• Temporary transaction costs alter the informed trader’s optimal strategy and market-maker pricing.
• The single-auction equilibrium can be characterized by a unique polynomial root.
• Small costs and risk aversion yield an asymptotic approximation governed by a dimensionless parameter.
• The continuous-time linear equilibrium is determined by coupled forward and backward differential equations.
• With transaction costs, prices do not fully reveal the trader’s signal by the end of the trading interval.

Tags

# Insider Trading with Temporary Price Impact


# Insider Trading with Temporary Price Impact









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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.