General Intensity Shapes in Optimal Liquidation

TL;DR

This paper introduces a generalized model for optimal liquidation using limit orders, incorporating both price and non-execution risks, and extends existing models to include risk-averse agents and more flexible execution intensity functions.

Contribution

It develops a comprehensive framework for optimal liquidation with limit orders, generalizes prior models, and connects to Almgren-Chriss models as a limit case.

Findings

Generalized the modeling of limit order liquidation.

Extended to risk-averse agents.

Linked to Almgren-Chriss models as a limit.

Abstract

The classical literature on optimal liquidation, rooted in Almgren-Chriss models, tackles the optimal liquidation problem using a trade-off between market impact and price risk. Therefore, it only answers the general question of the optimal liquidation rhythm. The very question of the actual way to proceed with liquidation is then rarely dealt with. Our model, that incorporates both price risk and non-execution risk, is an attempt to tackle this question using limit orders. The very general framework we propose to model liquidation generalizes the existing literature on optimal posting of limit orders. We consider a risk-adverse agent whereas the model of Bayraktar and Ludkovski only tackles the case of a risk-neutral one. We consider very general functional forms for the execution process intensity, whereas Gu\'eant et al. is restricted to exponential intensity. Eventually, we link the execution cost function of Almgren-Chriss models to the intensity function in our model, providing then a way to see Almgren-Chriss models as a limit of ours.