A Law of Large Numbers for Limit Order Books

Horst, Ulrich; Paulsen, Michael

doi:10.1287/moor.2017.0848

Cited by 30 publications

(73 citation statements)

References 33 publications

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“…In this subsection, we introduce a class of LOB models driven by Hawkes random measures and state the main assumptions on the modelling parameters and the main convergence results. The event-by-event dynamics of the order book follows [22], to which we refer for any unspecified modelling details. Throughout, all random processes are defined on a filtered probability space (Ω, F , {F t } t∈[0,T ] , P).…”

Section: The Lob Modelmentioning

confidence: 99%

A Scaling Limit for Limit Order Books Driven by Hawkes Processes

Horst¹,

Xu²

2019

SIAM J. Finan. Math.

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In this paper we derive a scaling limit for an infinite dimensional limit order book model driven by Hawkes random measures. The dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator. With our choice of scaling the dynamics converges to a coupled SDE-ODE system where limiting best bid and ask price processes follows a diffusion dynamics, the limiting volume density functions follows an ODE in a Hilbert space and the limiting order arrival and cancellation intensities follow a Volterra-Fredholm integral equation.

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Section: The Lob Modelmentioning

confidence: 99%

A Scaling Limit for Limit Order Books Driven by Hawkes Processes

Horst¹,

Xu²

2019

SIAM J. Finan. Math.

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“…To this end, we consider a queuing-theoretic order book model similar to Cont and de Larrard (2013) and Horst and Paulsen (2017) with constant spread p 0 from the mid price; most liquid stocks are traded at a fixed spread, usually with one tick. The tick size is denoted ∆ and p i := p 0 + i∆ (i = 1, 2, ...) denotes the price level i ticks into the bid side of the book.…”

Section: Market Microstructure and Market Impactmentioning

confidence: 99%

“…There is a significant economic and econometric literature on order books including Biais et al (1995), Easley and O'Hara (1987), and Glosten and Milgrom (1985) that emphazises on the realistic modelling of the working of the order book, and on its interaction with traders' order submission strategies. More recently, a series of high-frequency limits for structural order book models has been established in financial mathematics literature; see Abergel and Jedidi (2013), Cont and de Larrard (2013) and Horst and Paulsen (2017) and references therein. At high frequency, the order book provides comprehensive statistical characteristics of the underlying variables such as price resilience and order arrivals.…”

Section: Introductionmentioning

confidence: 99%

Portfolio Liquidation Under Transient Price Impact – Theoretical Solution and Implementation With 100 NASDAQ Stocks

Chen

Horst²,

Tran

2019

SSRN Journal

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We derive an explicit solution for deterministic market impact parameters in the Graewe and Horst (2017) portfolio liquidation model. The model allows to combine various forms of market impact, namely instantaneous, permanent and temporary. We show that the solutions to the two benchmark models of Almgren and Chriss (2001) and of Obizhaeva and Wang (2013) are obtained as special cases. We relate the different forms of market impact to the microstructure of limit order book markets and show how the impact parameters can be estimated from public market data. We investigate the numerical performance of the derived optimal trading strategy based on high frequency limit order books of 100 NASDAQ stocks that represent a range of market impact profiles. It shows the strategy achieves significant cost savings compared to the benchmark models of Almgren and Chriss (2001) and Obizhaeva and Wang (2013) .

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“…The assumption that incoming market orders match precisely against the liquidity at the top of the book follows [5,12,13]. Although the assumption is made primarily for mathematical convenience there is some empirical evidence supporting it.…”

Section: Setup and First Order Approximationmentioning

confidence: 99%

Second order approximations for limit order books

Horst

Kreher

2018

Finance Stoch

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In this paper we derive a second order approximation for an infinite dimensional limit order book model, in which the dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator (e.g. the volume standing at the top of the book). We study the fluctuations of the price and volume process relative to their first order approximation given in ODE-PDE form under two different scaling regimes. In the first case we suppose that price changes are really rare, yielding a constant first order approximation for the price. This leads to a measure-valued SDE driven by an infinite dimensional Brownian motion in the second order approximation of the volume process. In the second case we use a slower rescaling rate, which leads to a non-degenerate first order approximation and gives a PDE with random coefficients in the second order approximation for the volume process. Our results can be used to derive confidence intervals for models of optimal portfolio liquidation under market impact.2010 Mathematics Subject Classification. 60F17, 91G80. Key words and phrases. Functional central limit theorem, second order approximation, high frequency limit, limit order book.Financial support through the CRC TRR 190 is gratefully acknowledged.

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A Law of Large Numbers for Limit Order Books

Cited by 30 publications

References 33 publications

A Scaling Limit for Limit Order Books Driven by Hawkes Processes

A Scaling Limit for Limit Order Books Driven by Hawkes Processes

Portfolio Liquidation Under Transient Price Impact – Theoretical Solution and Implementation With 100 NASDAQ Stocks

Second order approximations for limit order books

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