Stochastic Liquidity as a Proxy for Nonlinear Price Impact

33 Pages Posted: 11 Dec 2022 Last revised: 13 Nov 2023

See all articles by Johannes Muhle-Karbe

Johannes Muhle-Karbe

Imperial College London - Department of Mathematics

Zexin Wang

Imperial College London - Department of Mathematics

Kevin Webster

Columbia University

Date Written: November 2, 2023

Abstract

Optimal execution and trading algorithms rely on price impact models, like the propagator model, to quantify trading costs. Empirically, price impact is concave in trade sizes, leading to nonlinear models for which optimization problems are intractable and even qualitative properties such as price manipulation are poorly understood. However, we show that in the diffusion limit of small and frequent orders, the nonlinear model converges to a tractable linear model. In this high-frequency limit, a stochastic liquidity parameter approximates the original impact function's nonlinearity. We illustrate the approximation's practical performance using limit-order data.

Keywords: nonlinear price impact; propagator model; scaling limit; optimal trading

JEL Classification: C51, C61, G11,

Suggested Citation

Muhle-Karbe, Johannes and Wang, Zexin and Webster, Kevin, Stochastic Liquidity as a Proxy for Nonlinear Price Impact (November 2, 2023). Available at SSRN: https://ssrn.com/abstract=4286108 or http://dx.doi.org/10.2139/ssrn.4286108

Johannes Muhle-Karbe (Contact Author)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 1NE
United Kingdom

HOME PAGE: http://www.ma.imperial.ac.uk/~jmuhleka/

Zexin Wang

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

Kevin Webster

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

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