Latency and Liquidity Risk

Abstract

Latency (i.e., time delay) in electronic markets affects the efficacy of liquidity taking strategies. During the time liquidity takers process information and send marketable limit orders (MLOs) to the exchange, the limit order book (LOB) might undergo updates, so there is no guarantee that MLOs are filled. We develop a latency-optimal trading strategy that improves the marksmanship of liquidity takers. The interaction between the LOB and MLOs is modelled as a marked point process. Each MLO specifies a price limit so the order can receive worse prices and quantities than those the liquidity taker targets if the updates in the LOB are against the interest of the trader. In our model, the liquidity taker balances the tradeoff between the costs of missing trades and the costs of walking the book. In particular, we show how to build cost-neutral strategies, that on average, trade price improvements for fewer misses. We employ techniques of variational analysis to obtain the price limit of each MLO the agent sends. The price limit of a MLO is characterized as the solution to a class of forward-backward stochastic differential equations (FBSDEs) driven by random measures. We prove the existence and uniqueness of the solution to the FBSDE and numerically solve it to illustrate the performance of the latency-optimal strategies.

Keywords: Marked point processes, high-frequency trading, algorithmic trading, latency, forward-backward stochastic differential equations