The shadow price of latency: improving intraday fill ratios in foreign exchange markets - Cartea, Á; Sánchez-Betancourt, L (Society for Industrial and Applied Mathematics, 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.