Statistical theory of the continuous double auction

By Eric Smith, J. Farmer, L. Gillemot, S. Krishnamurthy. 2002

373 citations recorded by the source corpus.

Abstract Most modern financial markets use a continuous double auction mechanism to store and match orders and facilitate trading. In this paper we develop a microscopic dynamical statistical model for the continuous double auction under the assumption of IID random order flow, and analyse it using simulation, dimensional analysis, and theoretical tools based on mean field approximations. The model makes testable predictions for basic properties of markets, such as price volatility, the depth of stored supply and demand versus price, the bid–ask spread, the price impact function, and the time and probability of filling orders. These predictions are based on properties of order flow and the limit order book, such as share volume of market and limit orders, cancellations, typical order size, and tick size. Because these quantities can all be measured directly there are no free parameters. We show that the order size, which can be cast as a non-dimensional granularity parameter, is in most cases a more significant determinant of market behaviour than tick size. We also provide an explanation for the observed highly concave nature of the price impact function. On a broader level, this work suggests how stochastic models based on zero intelligence agents may be useful to probe the structure of market institutions. Like the model of perfect rationality, a stochastic zero intelligence model can be used to make strong predictions based on a compact set of assumptions, even if these assumptions are not fully believable.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/442b6bd3ac58c70bf591cd401a2b50cb0d4d256f

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Citations in the corpus

Order Book Dynamics in Liquid Markets: Limit Theorems and Diffusion Approximations (2012, background): “The state of the order book is modiﬁed by order book events : limit orders (at the bid or ask), market orders and cancelations (see Cont et al. (2010b,a), Smith et al. (2003)).”
Micro-price trading in an order-driven market (2014, methodology): “The basic statistical properties of limit order books have been established using a random order book simulation [11].”
Statistical Modeling of High-Frequency Financial Data (2011, methodology): “Order books presents a rich palette of statistical features [14, 29, 34, 41, 55] which are challenging to incorporate in a statistical model, partly because of the high dimensionality of the order book and the complexity of its evolution.”
High-frequency trading in a limit order book (2008, methodology): “One of the important achievements of this literature has been to explain the statistical properties of the limit order book (see Bouchaud et al. 2002, Luckock 2003, Potters and Bouchaud 2003, Smith et al. 2003).”
Limit order books (2010, methodology): “Cont et al. (2010) recently introduced a variant of the Daniels et al. (2003) and Smith et al. (2003) model to understand how the occurrence frequency of certain events is conditional on L(t).”
Price Dynamics in a Markovian Limit Order Market (2011, background): “The state of the order book is modiﬁed by order book events : limit orders (at the bid or ask), market orders and cancelations (see Cont et al. (2010b,a), Smith et al. (2003)).”
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].”
Relation between bid–ask spread, impact and volatility in order-driven markets (2006, background): “…market order flows have been analysed to understand the distribution of the bid–ask spread, and relate its average value to flow and cancellation rates (Biais et al. 1997, Foucault 1999, Bouchaud et al. 2002, Daniels et al. 2003, Foucault et al. 2003, Luckock 2003, Smith et al. 2003, Rosu 2005).”
A Stochastic Model for Order Book Dynamics (2010, neutral): “Bouchaud et al. (2008), Smith et al. (2003) , Bovier et al. (2006), Luckock (2003), and Maslov and Mills (2001) propose stochastic models of order book dynamics in the spirit of the one proposed here but focus on unconditional / steady–state distributions of various quantities rather than the condi”
Random walks, liquidity molasses and critical response in financial markets (2004, positive): “The last assumption is motivated by theoretical and empirical results (Daniels et al. 2003, Potters and Bouchaud 2003, Smith et al. 2003, Bouchaud et al. 2004), where f(V) is found to be a power-law with a small exponent fðVÞ V (Plerou et al. 2002, Lillo et al. 2003, Farmer and Lillo 2004) or a…”
Ergodicity and scaling limit of a constrained multivariate Hawkes process (2013, neutral): “On the one hand, an extensive statistical study on the limit order book dynamics and limit order book information content can be found in [9, 26, 39, 19, 30, 10, 25, 14, 41]; on the other hand, many researchers have endeavored to propose different models, including equilibrium model, agent-based mod”
Hawkes Processes in Finance (2015, methodology): “In [55], Muni Toke generalized the zero-intelligence model introduced in [64] to the Hawkes framework.”
Statistical inference for ergodic point processes and application to Limit Order Book (2015, background): “The seminal work about this basic representation [34] has been followed by many extensions, see e.”
Econophysics review: II. Agent-based models (2011, neutral): “( 2003 ) also propose some sort of mean-field approximation for zero-intelligence models.”
What really causes large price changes? (2003, background): “[13, 58] to include nonuniform order placement, more closely reflecting the empirical order placement distribution [6, 64], which has an approximate power law tail.”
Hawkes model for price and trades high-frequency dynamics (2013, background): “Let us note that point processes have been involved in many studies in high-frequency finance from the famous ‘zero-intelligence’ order-book models Smith et al. (2003), Farmer et al. (2005) to models for trade Hewlett (2006), Large (2007), Bauwens and Hautsch (2009) or book events Muni Toke (2011),…”