Optimal order execution under price impact: a hybrid model

• Published in: Annals of operations research Vol. 336; no. 1-2; pp. 605 - 636
• Main Authors: Di Giacinto, Marina, Tebaldi, Claudio, Wang, Tai-Ho
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2024; Springer; Springer Nature B.V
• Subjects: Analysis; Business and Management; Combinatorics; Costs; Differential equations; Expected utility; Inventory; Liquidation; Liquidity; Markets (Economics); Operations research; Operations Research/Decision Theory; Optimal control; Original Research; Prices; Profits; Riccati equation; Securities trading; Stochastic processes; Theory of Computation; Italy; Order fill uncertainty; Stochastic optimal control; Optimal execution; G11; G10; Inventory cost; Price impact; C61
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-022-05082-8

In this paper we explore optimal liquidation in a market populated by a number of heterogeneous market makers that have limited inventory-carrying and risk-bearing capacity. We derive a reduced form model for the dynamics of their aggregated inventory considering a proper scaling limit. The resulting price impact profile is shown to depend on the characteristics and relative importance of their inventories. The model is flexible enough to reproduce the empirically documented power law behavior of the price impact function. For any choice of the market makers characteristics, optimal execution within this modeling approach can be recast as a linear-quadratic stochastic control problem. The value function and the associated optimal trading rate can be obtained semi-explicitly subject to solving a differential matrix Riccati equation. Numerical simulations are conducted to illustrate the performance of the resulting optimal liquidation strategy in relation to standard benchmarks. Remarkably, they show that the increase in performance is determined by a substantial reduction of higher order moment risk.