Optimal Execution with Stochastic Delay

We show how traders use marketable limit orders (MLOs) to liquidate a position over a trading window when there is latency in the marketplace. MLOs are liquidity taking orders that specify a price limit and are for immediate execution only; however, if the price limit of the MLO precludes it from being filled, the exchange rejects the trade. We frame our model as an impulse control problem with stochastic latency where the trader controls the times and the price limits of the MLOs sent to the exchange. We show that impatient liquidity takers submit MLOs that may walk the book (capped by the limit price) to increase the probability of filling the trades. On the other hand, patient liquidity takers use speculative MLOs that are only filled if there has been an advantageous move in prices over the latency period. Patient traders who are fast do not use their speed to hit the quotes they observe, nor to finish the execution programme early; they use speed to complete the execution programme with as many speculative MLOs as possible. We use foreign exchange data to implement the random-latency-optimal strategy and to compare it with four benchmarks: execution with deterministic latency, execution with zero latency, time-weighted average price, and execution of the entire order at the best quote in the LOB at the beginning of the trading window. We find that the performances of the random-latency and the deterministic-latency strategies are similar. For patient traders, these two strategies outperform the other three benchmarks by an amount that is greater than the transaction costs paid by liquidity takers in foreign exchange markets. Around news announcements, the value of the outperformance is between two and ten times the value of the transaction costs. The superiority of the latency-optimal strategies is due to both the speculative MLOs that are filled and the price protection of the MLOs