Transient Market Impact from a Directional Trader–Arbitrageur Game

Summary

The document offers a theoretical explanation for transient market impact, the temporary price response to trading that empirical research has observed. It models a directional trader and an arbitrageur interacting in a Nash equilibrium, even though the underlying impact in the game is fixed and permanent. The trader's behavior and the market's reaction to order flow can imply an apparent decay in impact.

Two approaches are proposed for deriving the decay kernel used by the Transient Impact Model. One uses the relationship between past order flow and future price changes; the other solves an inverse optimal execution problem. The first approach yields a unique implied kernel, while the second admits infinitely many solutions and can always infer a linear kernel. The document outlines theoretical derivations rather than empirical validation, and the description does not provide assumptions, calibration details, or evidence that the implied kernels fit particular markets.

Key ideas

• A Nash equilibrium between a directional trader and an arbitrageur can imply transient impact despite permanent impact in the game.
• The implied decay can be inferred from the trader's trading profile and price response to order flow.
• One derivation relates past order flow to future price changes and produces a unique kernel.
• An inverse optimal execution approach has infinitely many solutions and can always infer a linear kernel.
• The document describes a theoretical mechanism without empirical validation details.

Tags

# Transient impact from the Nash equilibrium of a permanent market impact game


# Transient impact from the Nash equilibrium of a permanent market impact game









A large body of empirical literature has shown that market impact of financial prices is transient. However, from a theoretical standpoint, the origin of this temporary nature is still unclear. We show that an implied transient impact arises from the Nash equilibrium between a directional trader and one arbitrageur in a market impact game with fixed and permanent impact. The implied impact is the one that can be empirically inferred from the directional trader's trading profile and price reaction to order flow. Specifically, we propose two approaches to derive the functional form of the decay kernel of the Transient Impact Model, one of the most popular empirical models for transient impact, from the behaviour of the directional trader at the Nash equilibrium. The first is based on the relationship between past order flow and future price change, while in the second we solve an inverse optimal execution problem. We show that in the first approach the implied kernel is unique, while in the second case infinite solutions exist and a linear kernel can always be inferred.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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