Tackling nonlinear price impact with linear strategies

Xavier Brokmann, David Itkin, Johannes Muhle-Karbe and Peter Schmidt

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: Empirical studies in various contexts find that the price impact of large trades approximately follows a power law with exponent between 0.4 and 0.7. Yet, tractable formulas for the portfolios that trade off predictive trading signals, risk, and trading costs in an optimal manner are only available for quadratic costs corresponding to linear price impact. In this paper, we show that the resulting linear strategies allow to achieve virtually optimal performance also for realistic nonlinear price impact, if the “effective” quadratic cost parameter is chosen appropriately. To wit, for a wide range of risk levels, this leads to performance losses below 2% compared to a numerical algorithm proposed by Kolm and Ritter, run at very high accuracy. The effective quadratic cost depends on the portfolio risk and concavity of the impact function, but can be computed without any sophisticated numerics by simply maximizing an explicit scalar function.

JEL-codes: C51 C61 G11 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2024-10-15
New Economics Papers: this item is included in nep-mst
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Published in Mathematical Finance, 15, October, 2024. ISSN: 0960-1627

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