Liquidity in competitive dealer markets

Abstract

We study a continuous‐time version of the intermediation model of Grossman and Miller. To wit, we solve for the competitive equilibrium prices at which liquidity takers' demands are absorbed by dealers with quadratic inventory costs, who can in turn gradually transfer these positions to an exogenous open market with finite liquidity. This endogenously leads to transient price impact in the dealer market. Smooth, diffusive, and discrete trades all incur finite but nontrivial liquidity costs, and can arise naturally from the liquidity takers' optimization.

An Equilibrium Model for the Cross-Section of Liquidity Premia

“…Here, the transaction cost matrix Λ is symmetric and positive definite, 5 and we focus on admissible trading strategies that are absolutely continuous with rate φ ∈ H 4 (R K ). 6 Remark 4.1. As in [19, Section 3.2], the deadweight transaction costs can be seen as a compensation paid to liquidity providers who intermediate between the agents we model in the present paper.…”

“…We write Λ 1/2 for the unique symmetric and positive definite square root of Λ, and note that Λ and Λ 1/2 both are invertible. 6 The corresponding positions then also automatically belong to H 4 (R K ) as in the frictionless case, so that the frictional goal functional is well defined for expected returns process µ ∈ H 2 (R K ) and volatility matrix σ ∈ H 4 (R K×D ).…”

“…A matrix version of the variation of constants formula in turn allows to derive bounds on the unique local solution of this equation. This in turn finally 7 If one penalizes squared inventories rather than the corresponding fluctuations (which depend on the endogenous volatility), then the FBSDE system becomes linear and can be analyzed in very general settings, in particular, for arbitrary numbers of agents, compare [6,33].…”

Reinforcement Learning for Market Making in a Multi-agent Dealer Market

“…Most previous work focuses on market making in limit order book markets where all agents submit their orders to a central matching facility and can observe all outstanding orders and executed transactions in the market. In contrast, there has been relatively little work focused on dealer markets (Guéant (2017), Bank, Ekren, and Muhle-Karbe (2018), Ghoshal and Roberts (2016))where the agents interact directly with each other and only observe the trades they are involved in. Our multi-agent simulation realistically replicates the partial observability conditions of a dealer market allowing us to study the challenges it poses for reinforcement learning algorithms.…”

“…In this section, we will define a more realistic, adaptive pricing and hedging policy for the market maker agent. The pricing/hedging algorithms used in this section are inspired by standard meanvariance trade-off formulations used in the mathematical finance literature for pricing and hedging, cf Almgren and Chriss (2001), Bank, Ekren, and Muhle-Karbe (2018), further tailored to suit our framework.…”