Optimal execution and speculation with trade signals

TL;DR

This paper develops a sophisticated model of market impact incorporating trade signals and order flow dynamics, demonstrating how traders can optimize execution and speculation by leveraging short-term signals within a stochastic framework.

Contribution

It introduces a novel price impact model driven by order flow and liquidity dynamics, integrating short-term signals and Marcus-type SDEs for optimal trading strategies.

Findings

Signals improve execution performance

Optimal strategies adapt to market liquidity fluctuations

Numerical solutions demonstrate strategy effectiveness

Abstract

We propose a price impact model where changes in prices are purely driven by the order flow in the market. The stochastic price impact of market orders and the arrival rates of limit and market orders are functions of the market liquidity process which reflects the balance of the demand and supply of liquidity. Limit and market orders mutually excite each other so that liquidity is mean reverting. We use the theory of Meyer-$\sigma$-fields to introduce a short-term signal process from which a trader learns about imminent changes in order flow. Her trades impact the market through the same mechanism as other orders. With a novel version of Marcus-type SDEs we efficiently describe the intricate timing of market dynamics at moments when her orders concur with that of others. In this setting, we examine an optimal execution problem and derive the Hamilton--Jacobi--Bellman (HJB) equation for the value function of the trader. The HJB equation is solved numerically and we illustrate how the trader uses the signals to enhance the performance of execution problems and to execute speculative strategies.