Optimal Execution with Nonlinear Transient Market Impact

Curato, Gianbiagio; Gatheral, Jim; Lillo, Fabrizio

doi:10.2139/ssrn.2539240

Cited by 6 publications

(7 citation statements)

References 66 publications

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“…This linear approximation is therefore valid for very small trading rates m s , but breaks down for more aggressive executions, for which a more precise analysis is needed. An ad-hoc non-linear generalisation of the propagator model was suggested by Gatheral [24], but is difficult to justify theoretically (and leads to highly singular optimal trading schedules in the continuous time limit [25]). We believe that Eq.…”

Section: Price Dynamics Within a Locally Linear Order Book (Llob)mentioning

confidence: 99%

A fully consistent, minimal model for non-linear market impact

Donier

Bonart

Mastromatteo

et al. 2015

Quantitative Finance

103

164

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We propose a minimal theory of non-linear price impact based on the fact that the (latent) order book is locally linear, as suggested by diffusion-reaction models and general arguments. Our framework allows one to compute the average price trajectory in the presence of a meta-order, that consistently generalizes previously proposed propagator models. We account for the universally observed square-root impact law, and predict non-trivial trajectories when trading is interrupted or reversed. We prove that our framework is free of price manipulation, and that prices can be made diffusive (albeit with a generic short-term mean-reverting contribution). Our model suggests that prices can be decomposed into a transient "mechanical" impact component and a permanent "informational" component.

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Section: Price Dynamics Within a Locally Linear Order Book (Llob)mentioning

confidence: 99%

A fully consistent, minimal model for non-linear market impact

Donier

Bonart

Mastromatteo

et al. 2015

Quantitative Finance

103

164

View full text Add to dashboard Cite

show abstract

“…In the case of linear market impact, f (q) = q, Gatheral et al [29] obtained the optimal condition and derived the explicit form of the optimal strategy in a expected cost minimisation problem. In the general case of non linear impact the problem is more involved [30,31]. In this paper we are not interested in solving the optimisation problem but rather in calculating the market impact for different classes of trading strategies.…”

Section: The Propagator Modelmentioning

confidence: 99%

Beyond the Square Root: Evidence for Logarithmic Dependence of Market Impact on Size and Participation Rate

Zarinelli¹,

Treccani²,

Farmer

et al. 2015

Mark. Microstructure Liq.

Self Cite

112

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We make an extensive empirical study of the market impact of large orders (metaorders) executed in the U.S. equity market between 2007 and 2009. We show that the square root market impact formula, which is widely used in the industry and supported by previous published research, provides a good fit only across about two orders of magnitude in order size. A logarithmic functional form fits the data better, providing a good fit across almost five orders of magnitude. We introduce the concept of an "impact surface" to model the impact as a function of both the duration and the participation rate of the metaorder, finding again a logarithmic dependence. We show that during the execution the price trajectory deviates from the market impact, a clear indication of non-VWAP executions. Surprisingly, we find that sometimes the price starts reverting well before the end of the execution. Finally we show that, although on average the impact relaxes to approximately 2/3 of the peak impact, the precise asymptotic value of the price depends on the participation rate and on the duration of the metaorder. We present evidence that this might be due to a herding phenomenon among metaorders.

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“…a constant G) plus a temporary impact affecting only costs. A significant part of the literature has considered the problem of price manipulation and dynamic arbitrage under different market impact models [15,4,14,10,8,26]. An impact model admits price manipulation when there exists a round trip strategy leaving some profit on expectation [14].…”

Section: The Transient Impact Modelmentioning

confidence: 99%

Optimal VWAP Execution Under Transient Price Impact

Barzykin

Lillo

2019

SSRN Journal

Self Cite

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We solve the problem of optimal liquidation with Volume-Weighted Average Price (VWAP) benchmark when the market impact is linear and transient. Our setting is indeed more general as it considers the case when the trading interval is not necessarily coincident with the benchmark interval: Implementation Shortfall and Target Close execution are shown to be particular cases of our setting. We find explicit solutions in continuous and discrete time considering risk averse investors having a CARA utility function. Finally, we show that, contrary to what is observed for Implementation Shortfall, the optimal VWAP solution contains both buy and sell trades also when the decay kernel is convex.

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Optimal Execution with Nonlinear Transient Market Impact

Cited by 6 publications

References 66 publications

A fully consistent, minimal model for non-linear market impact

A fully consistent, minimal model for non-linear market impact

Beyond the Square Root: Evidence for Logarithmic Dependence of Market Impact on Size and Participation Rate

Optimal VWAP Execution Under Transient Price Impact

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