AI 中文总结
针对Hawkes驱动的OTC市场做市问题，提出Volterra-Riccati近似层级策略，在基准和类幂律RFQ记忆模型中验证其可改善库存与P&L风险控制。
AI 中文摘要
我们构建了一个场外交易（OTC）市场做市问题，其中请求报价（RFQ）到达由一般Hawkes核建模，而成交则通过外生请求流的受控稀疏化实现。该建模选择源于即期外汇RFQ数据：在过滤并转换为经季节性调整的RFQ活动时间后，主要货币对的双向活动呈现出较大的拟合分支比和多尺度持续性。对于一般Hawkes核，该控制问题是路径依赖的：相关状态包含订单流历史，或等价地包含条件未来RFQ强度的远期曲线。指数核可实现精确的马尔可夫提升，但对于指数混合核会变为高维，且对于长记忆核不实用。因此，我们开发了一系列Volterra-Riccati近似：第一层用条件Volterra预测替代随机未来请求流；第二层添加强度不确定性的协方差修正；第三层用已实现的Hawkes记忆（或等价地用请求后的条件预测曲线）更新报价规则。该近似层级在指数Hawkes基准中得到验证，其中精确的提升HJB可数值求解。状态反馈Volterra-Riccati策略紧密跟踪精确基准，尤其在定向区间，而无记忆的Poisson策略则遭受显著遗憾。我们随后将相同的状态反馈规则应用于类幂律RFQ记忆模型：定向RFQ突发会改变未来流的条件预测，并通过延续价值影子价格转化为持续的报价偏斜；由此产生的内生OTC报价影响继承了RFQ预测响应的长记忆衰减，且相较于无 conditioning 的Poisson基准，改善了库存和盈亏（P&L）风险控制。
英文摘要
We formulate an over-the-counter (OTC) market-making problem in which request-for-quote (RFQ) arrivals are modelled by general Hawkes kernels and fills are controlled thinnings of the exogenous request flow. The modelling choice is motivated by spot-FX RFQ data: after filtering and transforming to seasonality-adjusted RFQ activity time, two-way activity in major currency pairs exhibits large fitted branching ratios and multi-scale persistence. For general Hawkes kernels the control problem is path-dependent: the relevant state contains the order-flow history, or equivalently the forward curve of conditional future RFQ intensities. Exact Markovian lifting is available for exponential kernels, but it becomes high-dimensional for mixtures of exponentials and impractical for long-memory kernels. We therefore develop a hierarchy of Volterra-Riccati approximations. The first level replaces random future request flow by its conditional Volterra forecast; the second adds a covariance correction for intensity uncertainty; the third updates the quote rule with the realized Hawkes memory, or equivalently with the post-request conditional forecast curve. The approximation hierarchy is validated in an exponential Hawkes benchmark, where the exact lifted HJB can be solved numerically. The state-feedback Volterra-Riccati policy closely tracks the exact benchmark, especially in directional regimes, while a memory-free Poisson policy suffers substantial regret. We then apply the same state-feedback rule to a power-law-like RFQ memory model. A directional RFQ burst changes the conditional forecast of future flow and is converted by the continuation-value shadow price into a persistent quote skew. The resulting endogenous OTC quote impact inherits the long-memory decay of the RFQ forecast response and improves inventory and P&L risk control relative to a no-conditioning Poisson benchmark.
Comments24 pages, 7 figures
