Paper: arXiv 2603.07752

Authors: Alexander Barzykin

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework extending the Avellaneda-Stoikov market-making model to incorporate optimal trade rejection (last look) and dynamic reputational feedback via HJB equations and an adiabatic-quadratic approximation. However, the provided excerpt focuses purely on theoretical formulation and optimal control derivations without empirical backtesting on real FX order flow data.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal FX Market Making<br/>with Latency, Slippage & Rejection Feedback] --> B[Model Formulation: Avellaneda-Stoikov +<br/>Gaussian Slippage Marks & EMA Reputation Score]
    B --> C[Dynamic Programming & HJB Equation:<br/>Joint Optimization of Quotes & Slippage Thresholds]
    C --> D[Adiabatic-Quadratic Approximation:<br/>Time-Scale Separation & 2nd-Order Expansion]
    D --> E[Key Outcome: Tractable Riccati ODEs &<br/>Closed-Form Policy for Dynamic Rejections]