[Paper Review] Dynamic slippage control and rejection feedback in spot FX market making

Alexander Barzykin|arXiv (Cornell University)|Mar 8, 2026

Game Theory and Applications0 citations

TL;DR

The paper extends Avellaneda-Stoikov style market making to include latency-driven rejection decisions and endogenized reputation feedback, deriving a dynamic programming solution and adiabatic quadratic approximations for practical policy design.

ABSTRACT

We study an OTC FX market-making problem, built on the Avellaneda-Stoikov tradition, in which a dealer streams size-dependent quotes on a discrete ladder and manages inventory risk over a finite horizon under Poisson arrivals of trade requests. Adverse selection is modelled through latency-driven price moves over a delay window, represented by Gaussian marks whose conditional means can depend on the quoted spread, capturing selective client reaction to stale quotes. The dealer can address latency risk through trade rejection when slippage breaches a tolerance threshold. We treat slippage tolerance as an explicit control jointly optimized with quotes: upon receiving a trade request, the dealer chooses an acceptance/rejection rule, which makes the trade economically akin to an embedded option written on the latency price move. We further introduce rejection feedback through an EMA-based rejection score used as a reputation proxy, so that client intensity is endogenously modulated by past rejections via a multiplicative factor. Using dynamic programming, we derive a Markov control problem with state variables (inventory, rejection-score) and show how rejection decision enters the HJB equation through Hamiltonians that include an expectation over the latency mark and a maximization over both quote and rejection rule parameters. For practical control evaluation, we develop an adiabatic-quadratic approximation: fixing reputation on the inventory-control time scale, expanding Hamiltonians to the second order, and adopting quadratic ansatz in inventory, yielding tractable Riccati-type ODE and closed-form expressions for approximate quotes and slippage thresholds. This approximation provides a fast surrogate for policy design and enables self-consistent calibration of rejection behaviour.

Motivation & Objective

• Motivate and model latency risk (stale quotes) in OTC spot FX market making with a finite horizon.
• Introduce an explicit rejection control (accept/reject) coupled with slippage tolerance as a state-dependent decision.
• Incorporate an EMA-based rejection score to capture reputation effects on future order flow.
• Derive a dynamic programming formulation and reduced HJB with an embedded option view of acceptance.
• Provide a fast adiabatic-quadratic approximation to design and calibrate rejection behavior.

Proposed method

• Model price dynamics as S_t with constant volatility on [0,T], and streams quotes on a size ladder with arrival intensities that depend on quote offsets and a reputation score.
• Represent latency as Gaussian marks with mean m_n(delta) and variance nu_n^2; trades are accepted or rejected with a rule ell; update rejection score R via an EMA.
• Formulate the value function U(t,x,q,R,S) with affine ansatz U = x + qS + V(t,q,R) to obtain a reduced HJB for V.
• Define the continuation value J and the marginal value p to express acceptance/rejection payoffs; derive bucket Hamiltonians H^n(p,J) and optimal quotes via first-order conditions.
• Develop an adiabatic-quadratic approximation by freezing R and expanding H^n in p up to second order; obtain a Riccati-type ODE for A(t) and closed-form-like expressions for delta_* and J.
• Specialize to constant slippage m_n(delta) = -theta_n and derive a shift rule delta*_n(p,J) = bar_delta_n(J) + p, enabling fast policy computation.
• Extend to symmetric tolerance protocols with capped slippage (epsilon) and derive closed-form expressions for expected increments G_n(delta, epsilon; p, J) and updated Hamiltonians.

Figure 1: Latency mark $\displaystyle Y\sim\mathcal{N}(m_{n}(\delta),\nu_{n}^{2})$ and embedded-option view of request-level payoff for unrestricted rejection policy. Red dashed line depicts optimal decision threshold: the request is accepted when $\displaystyle Y>=y_{*}^{n}(q,R)$ .

Experimental results

Research questions

• RQ1 How should a dealer optimally quote and decide to accept or reject trade requests under latency-induced adverse selection?
• RQ2 How does an endogenous reputation (rejection) score influence future order flow and optimal quoting?
• RQ3 Can we derive tractable approximations (adiabatic-quadratic) to design and calibrate rejection behavior in real time?
• RQ4 What are the effects of fair versus unrestricted rejection protocols on spreads, rejection rates, and dealer value under latency?
• RQ5 How does latency and adverse selection impact the embedded option value of accepting trades and the overall market-making performance?

Key findings

• Latency-driven rejection can tighten spreads when reputation feedback is present, even as rejection risk is embedded in an option-like payoff.
• An adiabatic-quadratic approximation yields a Riccati-type ODE for the inventory control, providing tractable closed-form-like quotes under constant slippage.
• Reputation feedback reduces average rejection rates and broadens the practical use of rejection under high latency scenarios.
• Fair protocols (e.g., symmetric tolerance) reduce rejection rates and utility gains compared to unrestricted rejection, highlighting trade-offs between efficiency and fairness.
• Numerical examples show how adverse selection and latency interact to widen spreads unless reputation dynamics discourage excessive rejections; the stationary reputation level R* is small under the tested parameters.

Figure 2: Top of book ( $\displaystyle z=z_{1}$ ) spread and rejection probability of optimal MM facing toxic flow with unrestricted rejection and no reputation feedback as a function of latency. The top dashed line corresponds to the spread with toxic flow, but no rejection, and the bottom dashed l