A Stochastic Partial Differential Equation Model for Limit Order Book Dynamics

Cont, Rama; Mueller, Marvin S.

doi:10.2139/ssrn.3366536

Cited by 6 publications

(4 citation statements)

References 42 publications

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“…The price of the stock in time t is mean of bid and ask price on that time. 31 Questions Q3 and Q4 investigate the different aspects of the liquidity feature which is calculated from message type, price, and volume. Based on US Securities and Exchange Commission, d stock’s liquidity generally refers to how rapidly shares of a stock can be bought or sold without substantially impacting the stock price.…”

Section: Data and User Questionsmentioning

confidence: 99%

HFTViz: Visualization for the exploration of high frequency trading data

Yaali

Grégoire

Hurtut

2021

Information Visualization

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High Frequency Trading (HFT), mainly based on high speed infrastructure, is a significant element of the trading industry. However, trading machines generate enormous quantities of trading messages that are difficult to explore for financial researchers and traders. Visualization tools of financial data usually focus on portfolio management and the analysis of the relationships between risk and return. Beside risk-return relationship, there are other aspects that attract financial researchers like liquidity and moments of flash crashes in the market. HFT researchers can extract these aspects from HFT data since it shows every detail of the market movement. In this paper, we present HFTViz, a visualization tool designed to help financial researchers explore the HFT dataset provided by NASDAQ exchange. HFTViz provides a comprehensive dashboard aimed at facilitate HFT data exploration. HFTViz contains two sections. It first proposes an overview of the market on a specific date. After selecting desired stocks from overview visualization to investigate in detail, HFTViz also provides a detailed view of the trading messages, the trading volumes and the liquidity measures. In a case study gathering five domain experts, we illustrate the usefulness of HFTViz.

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Section: Data and User Questionsmentioning

confidence: 99%

HFTViz: Visualization for the exploration of high frequency trading data

Yaali

Grégoire

Hurtut

2021

Information Visualization

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“…The evolution of the OB results from the interaction of buy and sell orders through a rather complex dynamic process. Order book dynamics has been extensively studied in the market microstructure and econophysics literature (Biais et al (1995), Smith et al (2003), Bouchaud et al (2009)), more recently, based on empirical characteristics presented in these studies, several models for the evolution of the OB have been proposed, see for instance Cont et al (2010), Avellaneda et al (2011), Cont and De Larrard (2013), Cont and Mueller (2019). These models, which are Markovian queueing systems, they generally implicitly assume uninterrupted high liquidity, i.e., they assume a abundant availability of limited orders in the OB.…”

Section: Introductionmentioning

confidence: 99%

Order Book Dynamics with Liquidity Fluctuations: Limit Theorems and Large Deviations

Rojas¹,

Yambartsev²,

Logachov³

2021

Preprint

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We propose a class of stochastic models for a dynamics of limit order book with different type of liquidities. Within this class of models we study the one where a spread decreases uniformly, belonging to the class of processes known as a population processes with uniform catastrophes. The law of large numbers (LLN), central limit theorem (CLT) and large deviations (LD) are proved for our model with uniform catastrophes. Our results allow us to satisfactorily explain the volatility and local trends in the prices, relevant empirical characteristics that are observed in this type of markets. Furthermore, it shows us how these local trends and volatility are determined by the typical values of the bid-ask spread. In addition, we use our model to show how large deviations occur in the spread and prices, such as those observed in flash crashes.

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“…However this extension did not give realistic price dynamics either. Very recently Cont and Müller [10] proposed a stochastic partial differential equation with multiplicative noise, which reproduces statistical properties of real price dynamics.…”

Section: Introductionmentioning

confidence: 99%

Data assimilation in price formation

Burger¹,

Pietschmann²,

Wolfram³

2020

Inverse Problems

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We consider the problem of estimating the density of buyers and vendors in a nonlinear parabolic price formation model using measurements of the price and the transaction rate. Our approach is based on a work by Puel et al., see [20], and results in a optimal control problem. We analyse this problems and provide stability estimates for the controls as well as the unknown density in the presence of measurement errors. Our analytic findings are supported with numerical experiments.The positive part f + = max(f, 0) of the function f = f (x, t) corresponds to the distribution of buyers over the price x ∈ Ω, the negative part f . = min(f, 0) to the is the vendor distribution over the price. The free boundary p = p(t) corresponds to the price where f (·, t) = 0, the function Λ to the total number of transactions executed at that price. The immediate placement and execution of new bids and orders after the trading event are modeled by the Delta Diracs at the shifted prices p(t) + a and p(t) − a, where a ∈ R + denotes the transaction

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A Stochastic Partial Differential Equation Model for Limit Order Book Dynamics

Cited by 6 publications

References 42 publications

HFTViz: Visualization for the exploration of high frequency trading data

HFTViz: Visualization for the exploration of high frequency trading data

Order Book Dynamics with Liquidity Fluctuations: Limit Theorems and Large Deviations

Data assimilation in price formation

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