AI 中文总结
该研究针对场外交易场景，通过理论推导得出做市商订单失衡、报价偏斜与价差宽度间的简单调整关系，验证了相关启发式方法的合理性。
AI 中文摘要
我们考虑一个做市商，其只能通过响应一系列密封询价来获取和处置库存，且客户到达的意图存在失衡：卖方多于买方，或反之。假设最佳竞争响应围绕一个普遍可识别的公允价格呈指数分布，我们观察到稳态解中存在一种对称性，可将失衡问题压缩至完全平衡的问题。订单失衡会被做市商的偏斜平移、报价的加宽以及其有效持仓成本的增加所精确吸收。该调整方式简单，但其所调整的解并不简单，且除了可观测的市场宽度外，不涉及任何自由参数。指数假设仅在实际报价处局部需要，且所涉及的宽度为局部观测到的宽度。其推论包括：零库存的做市商仍应进行偏斜；偏斜对失衡的响应为一阶，而宽度仅在二阶响应；流行的“固定宽度、线性偏斜”启发式方法可作为平衡流和二次持仓成本特殊情况下的小偏斜解被推导出来。
英文摘要
We consider a market maker who can only obtain and dispose of inventory by responding to a sequence of sealed-bid enquiries, and whose customers arrive with imbalanced intent: sellers more often than buyers, or the reverse. Under the assumption that the best competing response is exponentially distributed around a commonly discerned fair price, we observe a symmetry in the steady state solution that compresses the imbalanced problem onto the perfectly balanced one. Order imbalance is absorbed, exactly, by a translation of the market maker's skew, a widening of her quotes, and a multiplication of her effective cost of carry. The adjustment is simple even though the solution it adjusts is not, and it involves no free parameter beyond the observable market width. The exponential assumption is needed only locally, at the quotes actually made, and the width that enters is the locally observed one. Among the consequences: a market maker with zero inventory should still skew; skew responds to imbalance at first order whereas width responds only at second order; and the popular "constant width, linear skew" heuristic is recovered as the small-skew solution in the special case of balanced flow and quadratic holding cost.
