Optimal execution and block trade pricing: a general framework

TL;DR

This paper introduces a comprehensive framework for optimal trade execution and block trade pricing, including existence proofs, strategy regularity, Hamiltonian characterization, and a closed-form pricing formula for unconstrained liquidation.

Contribution

It presents a novel, general approach to optimal execution and block trade valuation, with new theoretical results and practical numerical methods.

Findings

Existence of optimal liquidation strategies established.

Hamiltonian approach enables numerical approximation.

Closed-form formula for block trade price without time constraints.

Abstract

In this article, we develop a general framework to study optimal execution and to price block trades. We prove existence of optimal liquidation strategies and we provide regularity results for optimal strategies under very general hypotheses. We exhibit a Hamiltonian characterization for the optimal strategy that can be used for numerical approximation. We also focus on the important topic of block trade pricing and we propose a methodology to give a price to financial (il)liquidity. In particular, we provide a closed-form formula for the price of a block trade when there is no time constraint to liquidate.