Optimal execution with non-linear transient market impact

Curato, Gianbiagio; Gatheral, Jim; Lillo, Fabrizio

doi:10.1080/14697688.2016.1181274

Cited by 39 publications

(32 citation statements)

References 48 publications

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“…Gatheral et al [2011] show that any decay kernel that is non-singular at time zero is inconsistent with non-linear f (·). Moreover Gatheral [2010] sets some necessary constraints for no arbitrage for power law dependence of f and G and Curato et al [2017] show that inconsistencies can also arise for power-law f (·) and G(·) even when necessary conditions derived in Gatheral [2010] are not violated.…”

Section: Price Process and Cost Of Tradingmentioning

confidence: 99%

Cross-impact and no-dynamic-arbitrage

Schneider

Lillo

2018

Quantitative Finance

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We extend the "No-dynamic-arbitrage and market impact"-framework of Jim Gatheral [Quantitative Finance, 10 (7): 749-759 (2010)] to the multidimensional case where trading in one asset has a cross-impact on the price of other assets. From the condition of absence of dynamical arbitrage we derive theoretical limits for the size and form of cross-impact that can be directly verified on data. For bounded decay kernels we find that cross-impact must be an odd and linear function of trading intensity and cross-impact from asset i to asset j must be equal to the one from j to i. To test these constraints we estimate cross-impact among sovereign bonds traded on the electronic platform MOT. While we find significant violations of the above symmetry condition of cross-impact, we show that these are not arbitrageable with simple strategies because of the presence of the bid-ask spread.

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Section: Price Process and Cost Of Tradingmentioning

confidence: 99%

Cross-impact and no-dynamic-arbitrage

Schneider

Lillo

2018

Quantitative Finance

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“…Jin [14] studied the optimal execution problem with an optimization objective of loss probability and talked about the liquidity adjusted VaR. Curato et al [15] studied the transient impact model with nonlinear impact function and solved the optimal executing problem numerically.…”

Section: Introductionmentioning

confidence: 99%

Optimal Execution considering Trading Signal and Execution Risk Simultaneously

Cheng

2021

Mathematical Problems in Engineering

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In this paper, we study the optimal execution problem by considering the trading signal and the transaction risk simultaneously. We propose an optimal execution problem by taking into account the trading signal and the execution risk with the associated decay kernel function and the transient price impact function being of generalized forms. In particular, we solve the stochastic optimal control problems under the assumptions that the decay kernel function is the Dirac function and the transient price function is a linear function. We give the optimal executing strategies in state-feedback form and the Hamilton‐Jacobi‐Bellman equations that the corresponding value functions satisfy in the cases of a constant execution risk and a linear execution risk. We also demonstrate that our results can recover previous results when the process of the trading signal degenerates.

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“…He gave the specific form of the optimal investment behaviour from the case of fixed and temporary market impact with different decay factors. Curato et al [9] investigated the optimal execution of a large trade when the model has nonlinear transient impact and decay factors. ey got the specific forms of the optimal strategy in some special cases.…”

Section: Introductionmentioning

confidence: 99%

“…In the last part, we discuss the optimal liquidation behaviour of investors when the temporary market impact is a linear function. Meanwhile, Almgren [3], Gatheral [8], Curato et al [9], and Horst and Naujokat [17] studied the optimal liquidation behaviour of investors when the temporary impact is nonlinear in different cases. When the market is accompanied by a decay factor and the temporary market impact is nonlinear, the optimal liquidation behaviour of investors is not studied by Caye and Muhle-Karbe [15].…”

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confidence: 99%

Optimal Liquidation Behaviour Analysis for Stochastic Linear and Nonlinear Systems of Self-Exciting Model with Decay

Luo

2021

Complexity

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When the market environment changes, we extend the self-exciting price impact model and further analysis of investors’ liquidation behaviour. It is assumed that the model is accompanied by an exponential decay factor when the temporary impact and its coefficient are linear and nonlinear. Using the optimal control method, we obtain that the optimal liquidation behaviours satisfy the second-order nonlinear ODEs with variable coefficients in the case of linear and nonlinear temporary impact. Next, we solve the ODEs and get the form of the investors’ optimal liquidation behaviour in four cases. Furthermore, we prove the decreasing properties of the optimal liquidation behaviour under the linear temporary impact. Through numerical simulation, we further explain the influence of the changed parameters ρ , a , b , x , and α on the investors’ liquidation strategy X t in twelve scenarios. Some interesting properties have been found.

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Optimal execution with non-linear transient market impact

Cited by 39 publications

References 48 publications

Cross-impact and no-dynamic-arbitrage

Cross-impact and no-dynamic-arbitrage

Optimal Execution considering Trading Signal and Execution Risk Simultaneously

Optimal Liquidation Behaviour Analysis for Stochastic Linear and Nonlinear Systems of Self-Exciting Model with Decay

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