Optimal Execution and Speculation Using Short-Term Order-Flow Signals

Summary

The paper models prices as moving in response to order flow. Market-order price impact and the arrival rates of market and limit orders depend on a liquidity process, with the two order types mutually exciting one another so that liquidity tends to revert. A trader receives a short-term signal about imminent order-flow changes and affects the market through the same order mechanism as other participants.

The authors use Meyer sigma-fields to represent the signal and a Marcus-type stochastic differential equation to handle the timing of simultaneous orders. They formulate the trader’s problem through a Hamilton–Jacobi–Bellman equation and solve it numerically. The reported illustrations show how signals can improve execution and support speculative trades, but the document provides no numerical performance measures or empirical market validation. The framework’s usefulness therefore depends on its model assumptions and calibration.

Key ideas

• Prices are driven by order flow, while order impact and order arrival rates vary with liquidity.
• Mutual excitation between limit and market orders produces mean-reverting liquidity.
• A short-term signal informs the trader about likely near-term order-flow changes.
• The optimal trading problem is formulated as an HJB equation and solved numerically.
• The model illustrates signal use in execution and speculative strategies.

Tags

# Optimal execution and speculation with trade signals


# Optimal execution and speculation with trade signals









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-$σ$-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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.