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. We show how to choose the limit price of liquidity taking orders to walk the LOB 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 tradeoff between the costs of walking the LOB and targeting a desired percentage of filled orders over a period of time. We employ a proprietary data set of foreign exchange trades to analyze the performance of the strategy and build a function that maps latency of a trader to the percentage of orders filled by the trader's strategy. We employ this function to compute the shadow price of latency that a trader would be willing to pay for co-location and hardware to reduce their latency in the marketplace.

Álvaro Cartea is Associate Professor of Mathematics at the Mathematical Institute, University of Oxford. Álvaro is a member of the Mathematical and Computational Finance Group and an academic member of the Oxford-Man Institute. Before coming to Oxford Álvaro was a Reader in Mathematical Finance at University College London, Associate Professor of Finance at Universidad Carlos III, Madrid-Spain, and Lecturer (with tenure) in the School of Economics, Mathematics and Statistics at Birkbeck-University of London. He was previously JP Morgan Lecturer in Financial Mathematics, Exeter College, University of Oxford. Álvaro obtained his Doctorate from the University of Oxford in 2003.