# Latency and Liquidity Risk

## TL;DR

This paper develops a latency-optimal trading strategy for electronic markets, modeling the interaction between limit order books and marketable limit orders using advanced stochastic processes to improve liquidity takers' effectiveness.

## Contribution

It introduces a novel model using marked point processes and FBSDEs to optimize order placement considering latency and market dynamics, a significant advancement over existing methods.

## Key findings

- The model effectively balances missing trades and order execution costs.
- Numerical solutions demonstrate improved trading performance.
- Theoretical proofs ensure the model's mathematical soundness.

## 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 missing trades and the costs of walking the book. We employ techniques of variational analysis to obtain the optimal price limit of each MLO the agent sends. The price limit of a MLO is characterized as the solution to a new 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.