A Model of Market Making and Price Impact

TL;DR

This paper models market making as a dynamic auction using stochastic differential games, revealing how quoting strategies produce a price impact similar to the Almgren-Chriss model, crucial for market liquidity and profitability.

Contribution

It introduces a novel stochastic differential game framework to derive the emergence of price impact from market maker strategies, linking it to profit mechanisms.

Findings

Price impact function matches Almgren-Chriss form

Market makers' strategies generate profit through price impact

Price impact is essential for market liquidity

Abstract

Traders constantly consider the price impact associated with changing their positions. This paper seeks to understand how price impact emerges from the quoting strategies of market makers. To this end, market making is modeled as a dynamic auction using the mathematical framework of Stochastic Differential Games. In Nash Equilibrium, the market makers' quoting strategies generate a price impact function that is of the same form as the celebrated Almgren-Chriss model. The key insight is that price impact is the mechanism through which market makers earn profits while matching their books. As such, price impact is an essential feature of markets where flow is intermediated by market makers.