Stochastic Liquidity as a Proxy for Nonlinear Price Impact

Johannes Muhle-Karbe (), Zexin Wang () and Kevin Webster ()
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Johannes Muhle-Karbe: Department of Mathematics, Imperial College London, London SW7 1NE, United Kingdom
Zexin Wang: Department of Mathematics, Imperial College London, London SW7 1NE, United Kingdom
Kevin Webster: Department of Mathematics, Imperial College London, London SW7 1NE, United Kingdom

Operations Research, 2024, vol. 72, issue 2, 444-458

Abstract: Optimal execution and trading algorithms rely on price impact models, such as 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: Financial Engineering; finance; portfolio; probability; stochastic model applications; dynamic programming; optimal control (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:72:y:2024:i:2:p:444-458

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