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 LOBSTER limit-order data.
Underlying paper: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4286108
Personal website of Johannes Muhle-Karbe
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