[论文解读] Dynamic slippage control and rejection feedback in spot FX market making

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

Game Theory and Applications被引用 0

一句话总结

该论文将 Avellaneda-Stoikov 风格的做市扩展到包含时延驱动的拒绝决策和内生化声誉反馈，推导出动态规划解和用于实际策略设计的绝热二次近似。

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.

研究动机与目标

• 在有限 horizon 内对场外现货外汇市场的延迟风险（过时报价）进行动机说明与建模。
• 引入一个显式的拒绝控制（接受/拒绝）并联结滑价容忍作为状态相关决策。
• 纳入基于 EMA 的拒绝分数以捕捉声誉对未来订单流的影响。
• 推导动态规划表述及带嵌入式接受选项视角的简化 HJB。
• 提供快速的绝热-二次近似以设计和标定拒绝行为。

提出的方法

• 将价格动态建模为在 [0,T] 上具有常数波动率的 S_t，并在一个数量阶梯上流动报价，报价偏移与声誉分数相关的到达强度相关。
• 将时延表示为均值为 m_n(delta)、方差为 nu_n^2 的高斯标记；交易的接受或拒绝遵循 ell 规则；通过 EMA 更新拒绝分数 R。
• 将价值函数 U(t,x,q,R,S) 设定为仿射解 U = x + qS + V(t,q,R) 以获得 V 的简化 HJB。
• 定义继续价值 J 与边际价值 p 以表达接受/拒绝的收益；推导桶状哈密顿量 H^n(p,J) 与通过一阶条件得到的最优报价。
• 通过冻结 R 并将 H^n 对 p 展开至二阶来得到绝热-二次近似；得到一个 Riccati 型常微分方程 A(t) 及接近闭式的 δ_* 与 J 表达。
• 当常数滑移 m_n(delta) = -theta_n 时的特例，推导出平移规则 δ*_n(p,J) = bar_delta_n(J) + p，实现快速策略计算。
• 扩展至对称容忍协议与上限滑移 (epsilon) 的情形，并推导期望增量 G_n(delta, epsilon; p, J) 与更新后的哈密顿量的闭式表达。

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 $\displaystyle Y>=y_{*}^{n}(q,R)$ .

实验结果

研究问题

• RQ1 在延迟诱发的不利选举下，经销商应如何以最优方式报价并决定接受或拒绝交易请求？
• RQ2 内生化声誉（拒绝）分数如何影响未来订单流和最优报价？
• RQ3 是否可推导现实时间可用的可处理近似（绝热-二次）以设计和标定拒绝行为？
• RQ4 在延迟条件下，公平与无限制拒绝协议对点差、拒绝率和经销商价值有何影响？
• RQ5 延迟和不利选举如何影响接受交易的嵌入式期权价值与整体做市绩效？

主要发现

• 带有声誉反馈的时延驱动拒绝可以在避免风险的同时收紧点差，尽管拒绝风险被嵌入到类似期权的 payoff 中。
• 绝热-二次近似为库存控制提供了 Riccati 型常微分方程，在常数滑移下提供了可处理的接近闭式报价。
• 声誉反馈降低平均拒绝率，在高时延情形下扩大拒绝的实际使用范围。
• 公平协议（如对称容忍）会降低拒绝率与效用增益，相对于无限制拒绝，揭示效率与公平之间的权衡。
• 数值示例显示在声誉动态未被抑制的情况下，不利选举与时延交互会扩大点差；而稳态声誉水平 R* 在测试参数下较小。

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