SIAM Journal on Financial Mathematics, Volume 12, Issue 1, Page 254-294, January 2021.
Latency is the time delay between an exchange streaming market data to a trader, the trader processing information and deciding to trade, and the exchange receiving the order from the trader. Liquidity takers face a moving target problem as a consequence of their latency in the marketplace. They send market orders with a limit price that aim at a price and quantity they observed in the limit order book (LOB), and by the time their order is processed by the exchange, prices could have worsened, so the order may not be filled, or prices could have improved, so the order is filled at a better price. In this paper we provide a model to compute the price that liquidity takers would be willing to pay to reduce their latency in the marketplace. To this end, we derive a latency-optimal strategy that specifies the limit price of liquidity taking orders to increase the chances of filling orders if, due to latency, prices or quantities in the LOB have worsened. The latency-optimal strategy balances the trade-off between the costs of walking the LOB and targeting a desired percentage of filled orders over a period of time. We employ the cost of improving fills with the latency-optimal strategy to compute the shadow price of latency. Finally, we use a proprietary data set of foreign exchange (FX) to compute the maximum price that an FX trader would be willing to pay for colocation and hardware to reduce their latency in the marketplace.

中文翻译：

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延迟的影子价格：提高外汇市场的日内成交率

SIAM 金融数学杂志，第 12 卷，第 1 期，第 254-294 页，2021 年 1 月。
延迟是交易所将市场数据传输给交易者、交易者处理信息并决定交易以及交易所从交易者处接收订单之间的时间延迟。由于他们在市场上的延迟，流动性接受者面临着移动目标问题。他们发送限价的市价订单，其目标是他们在限价订单簿 (LOB) 中观察到的价格和数量，当他们的订单被交易所处理时，价格可能已经恶化，因此订单可能无法成交，或者价格可能会有所改善，因此订单以更好的价格成交。在本文中，我们提供了一个模型来计算流动性接受者愿意支付的价格以减少他们在市场上的延迟。为此，我们推导出一种延迟优化策略，该策略指定流动性接受订单的限制价格，以在 LOB 中的价格或数量因延迟而恶化时增加完成订单的机会。延迟优化策略平衡了遍历 LOB 的成本和在一段时间内针对已完成订单的所需百分比之间的权衡。我们使用延迟优化策略改进填充的成本来计算延迟的影子价格。最后，我们使用外汇 (FX) 的专有数据集来计算外汇交易者愿意为主机托管和硬件支付的最高价格，以减少他们在市场上的延迟。延迟优化策略平衡了遍历 LOB 的成本和在一段时间内针对已完成订单的所需百分比之间的权衡。我们使用延迟优化策略改进填充的成本来计算延迟的影子价格。最后，我们使用外汇 (FX) 的专有数据集来计算外汇交易者愿意为主机托管和硬件支付的最高价格，以减少他们在市场上的延迟。延迟优化策略平衡了遍历 LOB 的成本和在一段时间内针对已完成订单的所需百分比之间的权衡。我们使用延迟优化策略改进填充的成本来计算延迟的影子价格。最后，我们使用外汇 (FX) 的专有数据集来计算外汇交易者愿意为主机托管和硬件支付的最高价格，以减少他们在市场上的延迟。