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2009), “How markets slowly digest changes in supply and demand,” (North-Holland (0)

by J P Bouchaud, J D Farmer, F Lillo
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Talreja: A stochastic model for order book dynamics

by Rama Cont, Sasha Stoikov, Rishi Talreja , 2003
"... We propose a stochastic model for the continuous-time dynamics of a limit order book. The model strikes a balance between two desirable features: it captures key empirical properties of order book dynamics and its analytical tractability allows for fast computation of various quantities of interest ..."
Abstract - Cited by 67 (2 self) - Add to MetaCart
We propose a stochastic model for the continuous-time dynamics of a limit order book. The model strikes a balance between two desirable features: it captures key empirical properties of order book dynamics and its analytical tractability allows for fast computation of various quantities of interest without resorting to simulation. We describe a simple parameter estimation procedure based on high-frequency observations of the order book and illustrate the results on data from the Tokyo stock exchange. Using Laplace transform methods, we are able to efficiently compute probabilities of various events, conditional on the state of the order book: an increase in the mid-price, execution of an order at the bid before the ask quote moves, and execution of both a buy and a sell order at the best quotes before the price moves. Comparison with high-frequency data shows that our model can capture accurately the short term dynamics of the limit order book.

Price dynamics in a Markovian limit order market.

by Rama Cont , Adrien De Larrard - SIAM J. Financial Math. , 2013
"... 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 expression ..."
Abstract - Cited by 17 (0 self) - Add to MetaCart
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.
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...amics of prices in such markets are not only interesting from the viewpoint of market participants –for trading and order execution (Alfonsi et al. (2010), Predoiu et al. (2011))– but also from a fundamental perspective, since they provide a rare glimpse into the dynamics of supply and demand and their role in price formation. Equilibrium models of price formation in limit order markets (Parlour (1998), Rosu (2009)) have shown that the evolution of the price in such markets is rather complex and depends on the state of the order book. On the other hand, empirical studies on limit order books (Bouchaud et al. (2008), Farmer et al. (2004), Gourieroux et al. (1999), Hollifield et al. (2004), Smith et al. (2003)) provide an extensive list of statistical features of order book dynamics that are challenging to incorporate in a single model. While most of these studies have focused on unconditional/steady– state distributions of various features of the order book, empirical studies (see e.g. Harris and Panchapagesan (2005)) show that the state of the order book contains information on short-term price movements so it is of interest to provide forecasts of various quantities conditional on the state of the orde...

A mathematical approach to order book modeling

by Frédéric Abergel, Aymen Jedidi - International Journal of Theoretical and Applied Finance , 2013
"... Abstract. Motivated by the desire to bridge the gap between the microscopic description of price formation (agent-based modeling) and the stochastic differential equations approach used classically to describe price evolution at macroscopic time scales, we present a mathematical study of the order b ..."
Abstract - Cited by 17 (2 self) - Add to MetaCart
Abstract. Motivated by the desire to bridge the gap between the microscopic description of price formation (agent-based modeling) and the stochastic differential equations approach used classically to describe price evolution at macroscopic time scales, we present a mathematical study of the order book as a multidimensional continuous-time Markov chain and derive several mathematical results in the case of independent Poissonian arrival times. In particular, we show that the cancellation structure is an important factor ensuring the existence of a stationary distribution and the exponential convergence towards it. We also prove, by means of the functional central limit theorem (FCLT), that the rescaled-centered price process converges to a Brownian motion. We illustrate the analysis with numerical simulation and comparison against market data.
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...actual trade prices looks much flatter compared to the simulation (See figure 9.) This was discovered and discussed in detail by Bouchaud et al. in [3], and Lillo and Farmer in [13] (See also [9] and =-=[2]-=-.) They note that actual order signs exhibit positive long-ranged correlations. They also note that actual prices are diffusive—the signature plot is flat—even at small time scales. They solve this ap...

Stability Analysis of Financial Contagion Due to Overlapping Portfolios. Working Paper 2012-10-018, Santa Fe Institute

by Fabio Caccioli, Munik Shrestha, Cristopher Moore, J. Doyne Farmer, Fabio Caccioli, Munik Shrestha, Cristopher Moore, J. Doyne Farmer , 2012
"... SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peer-reviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for pap ..."
Abstract - Cited by 15 (3 self) - Add to MetaCart
SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peer-reviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty, papers must be based on work done at SFI, inspired by an invited visit to or collaboration at SFI, or funded by an SFI grant. ©NOTICE: This working paper is included by permission of the contributing author(s) as a means to ensure timely distribution of the scholarly and technical work on a non-commercial basis. Copyright and all rights therein are maintained by the author(s). It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may be reposted only with the explicit permission of the copyright holder. www.santafe.edu SANTA FE INSTITUTEStability analysis of financial contagion due to overlapping portfolios
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...etical evidence indicates that market impact for large trades is a concave function of the number of traded shares, which under normal conditions impact is well approximated by a square-root function =-=[21]-=-. By normal conditions we mean that execution is slow enough for the order book to replenish between successive trades. Under extreme conditions, like those of a fire sale, market impact is expected t...

Crises and Collective Socio-Economic Phenomena: Simple Models and Challenges,

by J P Bouchaud - Journal of Statistical Physics , 2013
"... ..."
Abstract - Cited by 14 (1 self) - Add to MetaCart
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Modelling trades-through in a limit order book using Hawkes processes

by Ioane Muni Toke , Fabrizio Pomponio , Ecole Centrale Paris , Bnp Paribas , Paris - Economics: The Open-Access, Open-Assessment E-Journal , 2012
"... Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, ..."
Abstract - Cited by 11 (0 self) - Add to MetaCart
Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract The authors model trades-through, i.e. transactions that reach at least the second level of limit orders in an order book. Using tick-by-tick data on Euronext-traded stocks, they show that a simple bivariate Hawkes process fits nicely their empirical observations of tradesthrough. The authors show that the cross-influence of bid and ask trades-through is weak. Terms of use: Documents in EconStor may
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...me-dependent base intensity. 2 Trades-through 2.1 Orders splitting and trades-through It has been shown several times that the time series built from trading flows are long-memory processes (see e.g. =-=Bouchaud et al., 2009-=-). Lillo and Farmer (2004) argue that this is mainly explained by the splitting of large orders. Indeed, let us assume that a trader wants to trade a large order. He does not want to reveal its intent...

THE ENDOGENOUS DYNAMICS OF MARKETS: PRICE IMPACT AND FEEDBACK LOOPS

by Jean-Philippe Bouchaud
"... ..."
Abstract - Cited by 10 (4 self) - Add to MetaCart
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Correlation of financial markets in times of crisis

by Leonidas Sandoval Junior, Italo De, Paula Franca - Physica A Statistical Mechanics and its Applications
"... ar ..."
Abstract - Cited by 7 (0 self) - Add to MetaCart
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...etween the two variables along this period is 0.62. One can also note that markets are much more correlated after the period of crisis, and this behavior tends to endure for some time after the crash =-=[154]-=-, although one must take into account that the averaging procedure for the average correlation makes the curve smoother and thus decreasing less steeply. Figure 12 shows the evolution of the covarianc...

A proposal for impact-adjusted valuation: Critical leverage and execution risk,” ArXiv e-prints

by Fabio Caccioli, J. Doyne Farmer, F. Caccioli, J. -p. Bouchaud, J. -d. Farmer , 2012
"... SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peer-reviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for pap ..."
Abstract - Cited by 5 (4 self) - Add to MetaCart
SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peer-reviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty, papers must be based on work done at SFI, inspired by an invited visit to or collaboration at SFI, or funded by an SFI grant. ©NOTICE: This working paper is included by permission of the contributing author(s) as a means to ensure timely distribution of the scholarly and technical work on a non-commercial basis. Copyright and all rights therein are maintained by the author(s). It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may be reposted only with the explicit permission of the copyright holder. www.santafe.edu SANTA FE INSTITUTE Impact-adjusted valuation and the criticality of leverage
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...titative model of market impact Understanding the nature of market impact has now been the focus of a large number of empirical studies, both from academics and practitioners (for recent reviews, see =-=[11, 12, 3, 4, 13, 14, 5]-=-), and a consensus is beginning to emerge. Here we are particularly concerned with the liquidation of large positions, which must either be sold in a block market or broken into pieces and executed in...

Market microstructure and modelling of the trading flow

by Khalil Antoine Al Dayri , 2011
"... ..."
Abstract - Cited by 5 (2 self) - Add to MetaCart
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