Abstract: 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 marketable limit orders (MLOs) 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 provide three modelling approaches to account for latency in the optimal trading strategies that liquidity takers use.

In our first approach, a trader targets a fill ratio and minimises the cost of walking the LOB. We derive the optimal strategy in closed-form and employ a proprietary data set to compute the shadow price of latency in FX markets. In our second approach, we employ marked point processes to model the interaction of a trader with the LOB when there is latency. We employ a variational analysis approach to derive optimal strategies, characterise them as solutions to a new class of FBSDEs, prove existence and uniqueness of the FBSDEs, and for particular examples, solve them numerically. In our third approach, we show how traders use aggressive MLOs to liquidate a position when there are random delays in all the steps of a trade. We frame our model as a delayed impulse control problem in which the trader controls the times and the price limit of the MLOs she sends to the exchange. We introduce a new type of impulse control problem with stochastic (or deterministic) delay, not previously studied in the literature. We employ foreign exchange high-frequency trade data to implement the random-latency-optimal strategy and to compare it with various benchmarks.

Bio: I am a DPhil candidate in Mathematics at the University of Oxford under the supervision of Professor Álvaro Cartea. I am based in the Mathematical and Computational Finance group at the Mathematical Institute, Oxford. My research area is mathematical finance. In particular, I am interested in: (1) the mathematical theory of latency (delay effects) in order-driven markets, (2) rigorous mathematical models for market making in foreign exchange markets, and (3) multi-currency continuous-time portfolio theory.