Price Dynamics in a Markovian Limit Order Market

By Rama Cont, Adrien de Larrard. 2011

306 citations recorded by the source corpus.

We propose and study a simple stochastic model for the dynamics of a limit order book, in which arrivals of market order, limit orders and order cancellations are described in terms of a Markovian queueing system. Through its analytical tractability, the model allows to obtain analytical expressions for various quantities of interest such as the distribution of the duration between price changes, the distribution and autocorrelation of price changes, and the probability of an upward move in the price, conditional on the state of the order book. We study the diffusion limit of the price process and express the volatility of price changes in terms of parameters describing the arrival rates of buy and sell orders and cancelations. These analytical results provide some insight into the relation between order flow and price dynamics in order-driven markets.

Subfields: Economics and Econometrics, Management Information Systems

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Citations in the corpus

Universal features of price formation in financial markets: perspectives from deep learning (2018, background): “Such relations have been studied in queueing models of limit order book dynamics (Cont et al. 2010, Cont and de Larrard 2013).”
A High Frequency Trade Execution Model for Supervised Learning (2017, unknown): “Guided by the reduced order book models of Cont and de Larrard (2013), our approach selects similar exogenous variables.”
Sequence classification of the limit order book using recurrent neural networks (2017, background): “Guidedby the reduced order book models of Cont and de Larrard (2013), our approach selects similar exogenous variables.”
Price jump prediction in a limit order book (2012, background): “[3-6] for the latest developments in the econophysics of order-driven markets.”
Deep learning for limit order books (2016, unknown): “Cont et al. (2010), Cont and De Larrard (2013), Cont and De Larrard (2012), Abergel and Jedidi (2013), Donier et al. (2015), Moallemi and Saglam (2013), Maglaras et al. (2014), Carmona and Webster (2013), Carmona and Webster (2012a), Carmona and Webster (2012b), Avellaneda and Stoikov (2008),…”
Order Book Dynamics in Liquid Markets: Limit Theorems and Diffusion Approximations (2012, methodology): “More recently, Cont, Stoikov and Talreja Cont et al. (2010b) have studied a Markovian queueing model of a limit order book, in which arrivals of market orders and limit orders at each price level are modeled as independent Poisson processes.”
Anomalous price impact and the critical nature of liquidity in financial markets (2011, methodology): “…paper we allowed two trading strategies for the execution of the metaorder: a) “ζexecution”, where the extra agent trades exactly as the rest of the market, by sending a market order of volume f × qbest, where f is chosen according to Pζ(f) above and b) “unit-execution”, where the market orders…”
Optimal placement in a limit order book: an analytical approach (2016, unknown): “For instance, in Cont and deLarrard [21], it was shown that p < 1 2 is equivalent to the negative autocorrelation of limit order book price at the first lag, and they confirmed this mean-reversion with most”
Statistical Modeling of High-Frequency Financial Data (2011, methodology): “For example, in a Markovian model for a symmetric Level 1 order book, Cont & Larrard [19] derive the following relation between the standard deviation 𝜎 of price increments 𝑆 ( 𝑡 + 𝑇 ) − 𝑆 ( 𝑡 ) and the statistics of order ﬂow: where 𝜆 = 1 /𝜏 0 is the order ﬂow in shares per unit time, is…”
A one-level limit order book model with memory and variable spread (2017, methodology): “Ourmain inspiration for the present work is drawn from [6]’s seminal work, where a Markovian model is proposed for the dynamics of the LOB’s level I (i.e., the limit orders with the best prices to sell or buy the asset).”
No‐arbitrage implies power‐law market impact and rough volatility (2018, background): “is a generalization of the Poisson process which is usually considered when modeling order flows, see among others [7, 8, 28].”