Optimal execution with uncertain order fills in Almgren–Chriss framework

Cheng, Xue; Giacinto, Marina Di; Wang, Tai‐Ho

doi:10.1080/14697688.2016.1185531

Cited by 22 publications

(37 citation statements)

References 14 publications

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“…Investor's trading strategy. Following [6,7] the evolution of the investor's position X satisfies the following stochastic differential equation…”

Section: Model Setupmentioning

confidence: 99%

“…Penalty of final block trade. Following [6,7], we take into consideration as a penalty for a final block trade of size x ∈ R a quadratic function…”

Section: Model Setupmentioning

confidence: 99%

“…Parameters for price impact are selected so as to be in line with those in [1] and [6,7]: the investor is assumed to liquidate within one day the amount of 200, 000 shares of a certain stock. The current stock price is assumed S 0 = 50, though the price itself is irrelevant in the implementations of the strategies under consideration.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Optimal order execution under price impact: A hybrid model

Giacinto¹,

Tebaldi²,

Wang³

2021

Preprint

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In this paper we explore optimal execution in a market populated by a number of heterogeneous market makers that have limited inventory-carrying and risk-bearing capacity and operate in the market maximizing their profits. We show that in a proper scaling limit, optimal execution within this model can be recast as a linear-quadratic stochastic control problem. Value function and the associated optimal trading rate can be obtained semi-explicitly subject to solving a differential matrix Riccati equation. Numerical simulations are conducted to illustrate the dependence of the optimal execution strategies from the structural characteristics and the distribution of market makers.

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“…Investor's trading strategy. Following [6,7] the evolution of the investor's position X satisfies the following stochastic differential equation…”

Section: Model Setupmentioning

confidence: 99%

“…Penalty of final block trade. Following [6,7], we take into consideration as a penalty for a final block trade of size x ∈ R a quadratic function…”

Section: Model Setupmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

See 1 more Smart Citation

Optimal order execution under price impact: A hybrid model

Giacinto¹,

Tebaldi²,

Wang³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In a market events perspective closer to the limit order book, Hewlett (2006) uses bivariate Hawkes processes for buy and sell trades occurring on the FX markets modelling. He then applies them for optimal trading strategies purposes as developed by Almgren (2003), Almgren (2000), Bertsimas and Lo (1998), Obizhaeva and Wang (2012) and more recently Cheng, Di Giacinto et al (2017), assuming the market maker considers buy and sell orders arrival to follow Hawkes processes. Shek (2011) also uses a bivariate mutually-exciting model for buy and sell trades occurrence.…”

Section: Introductionmentioning

confidence: 99%

Deep limit order book events dynamics

Bilodeau

2020

SSRN Journal

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This paper analyzes the limit order book events arrival dependency structure using highdimensional Hawkes processes. We seek for recurrent relationships among events from a set of 86 event types which in addition to transactions, includes limit order submissions and cancellations taking place up to the 20th depth level of the order book. We focus on BMW, SAP, and ADS, three liquid DAX 30 index stocks for which we have a microsecond stamped high-frequency dataset covering the 61 trading day period going from February 1 to March 31, 2013. For each stock, we build a tailored descriptive model by selecting recurrent events relationships. Estimated on a daily basis, we find that the selected models offer interesting data fitting performance, particularly for limit order submissions and cancellations occurring on the first five price levels of the order book. Finally, we use the comprehensive sets of estimated parameters to describe a global events arrival dynamics that we relate to the potential behaviors of market participants having different objectives and directional views.

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“…Forsyth et al [11] suggested that using quadratic variation as risk measure was time-consistent in the dynamic programming. Cheng et al [12] summarized the risk criterions and obtained closed-form strategies with uncertain order fills in Almgren-Chriss framework.…”

Section: Introductionmentioning

confidence: 99%

Optimal Trade Execution under Jump Diffusion Process: A Mean-VaR Approach

Zhou

Jia

2018

Discrete Dynamics in Nature and Society

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In the classical optimal execution problem, the basic assumption of underlying asset price is Arithmetic Brownian Motion (ABM) or Geometric Brownian Motion (GBM). However, many empirical researches show that the return distribution of assets may have heavy tails than those of normal distribution. The uncertain information impact on financial market may be considered as one of the main reasons for heavy tails of return distribution. To introduce this information impact, our paper proposes a Jump Diffusion model for optimal execution problem. The jumps in our model are described by the compound Poisson process where random jump amplitude depicts the information impact on price process. In particular, the model is simple enough to derive closed-form strategies under risk neutral and Mean-VaR criterion. Simulation analysis of the model is also presented.

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Optimal execution with uncertain order fills in Almgren–Chriss framework

Cited by 22 publications

References 14 publications

Optimal order execution under price impact: A hybrid model

Optimal order execution under price impact: A hybrid model

Deep limit order book events dynamics

Optimal Trade Execution under Jump Diffusion Process: A Mean-VaR Approach

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