Optimal make take fees in a multi market maker environment

Abstract

Following the recent literature on make take fees policies, we consider an exchange wishing to set a suitable contract with several market makers in order to improve trading quality on its platform. To do so, we use a principal-agent approach, where the agents (the market makers) optimise their quotes in a Nash equilibrium fashion, providing best response to the contract proposed by the principal (the exchange). This contract aims at attracting liquidity on the platform. This is because the wealth of the exchange depends on the arrival of market orders, which is driven by the spread of market makers. We compute the optimal contract in quasi explicit form and also derive the optimal spread policies for the market makers. Several new phenomena appears in this multi market maker setting. In particular we show that it is not necessarily optimal to have a large number of market makers in the presence of a contracting scheme.

Optimal incentives in a limit order book: a SPDE control approach

“…are increasing for all x ∈ (0, L); 4 As L can be taken arbitrarily large, this assumption is not restrictive for practical applications. 5 ut is the density of the order book at time t, i.e. the volume available at the first limit at the ask (for instance) at time t is given by δ 0 ut(x)dx, where δ is the tick size of the asset.…”

“…It is shown numerically that the contract effectively reduces the spreads and subsequently increases liquidity provision. This work has been extended in various ways, taking into account several market participants, the specificities of options market and enabling trading on dark liquidity pools, see [4,5,6]. However, the very design of make-take fees through a Principal-Agent has three main practical drawbacks.…”

Market making and incentives design in the presence of a dark pool: a deep reinforcement learning approach

“…Then we define the probability P 0 on (Ω, F ) under which W t and the N i,j,k t are independent, W t is a one-dimensional Brownian motion and the N i,j,k t , i ∈ {a, b}, j ∈ {l, d}, k ∈ V j are Poisson processes with intensity ǫ > 0 small enough. 3 Finally, we endow the space (Ω, F ) with the (P 0 −completed) canonical filtration F := (F t ) t∈[0,T ] generated by (X t ) t∈[0,T ] .…”

“…In most of these works, it is assumed that there is no make-take fees system on the market. The problem of relevant make-take fees is studied quantitatively in [3,10]. In these papers, the policies are designed in the context of traditional liquidity venues, or so-called "lit pools".…”

“…A key difference with [3,10] is the absence of a closed-form solution for the best response of the market maker to a given contract. Therefore, the HJB equation of the exchange cannot be solved explicitly.…”