Market impact as anticipation of the order flow imbalance

In this paper, we assume that the permanent market impact of metaorders is linear and that the price is a martingale. Those two hypotheses enable us to derive the evolution of the price from the dynamics of the flow of market orders. For example, if the market order flow is assumed to follow a nearly unstable Hawkes process, we retrieve the apparent long memory of the flow together with a power law impact function, which is consistent with the celebrated square root law. We also link the long memory exponent of the sign of market orders with the impact function exponent. One of the originalities of our approach is that our results are derived without assuming that market participants are able to detect the beginning of metaorders.

[1]  Emmanuel Bacry,et al.  Modelling microstructure noise with mutually exciting point processes , 2011, 1101.3422.

[2]  E. Bacry,et al.  Some limit theorems for Hawkes processes and application to financial statistics , 2013 .

[3]  Laurent Massoulié,et al.  Hawkes branching point processes without ancestors , 2001, Journal of Applied Probability.

[4]  E. Bacry,et al.  Non-parametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data , 2011, 1112.1838.

[5]  J. Bouchaud,et al.  How Markets Slowly Digest Changes in Supply and Demand , 2008, 0809.0822.

[6]  The non-linear market impact of large trades: evidence from buy-side order flow , 2013 .

[7]  Anna A. Obizhaeva.  Information vs. Liquidity: Evidence from Portfolio Transition Trades , 2007 .

[8]  Anna A. Obizhaeva,et al.  Market Microstructure Invariants , 2009 .

[9]  V. Plerou,et al.  Institutional Investors and Stock Market Volatility , 2005 .

[10]  A. Hawkes,et al.  A cluster process representation of a self-exciting process , 1974, Journal of Applied Probability.

[11]  Joshua D. Coval,et al.  Asset Fire Sales (and Purchases) in Equity Markets , 2005 .

[12]  J. Bouchaud,et al.  Slow Decay of Impact in Equity Markets , 2014, 1407.3390.

[13]  Emmanuel Bacry,et al.  Hawkes model for price and trades high-frequency dynamics , 2013, 1301.1135.

[14]  Anna A. Obizhaeva,et al.  Market Microstructure Invariants: Theory and Implications of Calibration , 2011 .

[15]  F. Lillo,et al.  The Long Memory of the Efficient Market , 2003, cond-mat/0311053.

[16]  Market Impact with Autocorrelated Order Flow under Perfect Competition , 2012, 1212.4770.

[17]  Yacine Ait-Sahalia,et al.  Modeling Financial Contagion Using Mutually Exciting Jump Processes , 2010 .

[18]  Emmanuel Bacry,et al.  Second order statistics characterization of Hawkes processes and non-parametric estimation , 2014, 1401.0903.

[19]  Jean-Philippe Bouchaud,et al.  Anomalous Price Impact and the Critical Nature of Liquidity in Financial Markets , 2011, 1105.1694.

[20]  Kay Giesecke,et al.  Affine Point Processes and Portfolio Credit Risk , 2010, SIAM J. Financial Math..

[21]  Mathieu Rosenbaum,et al.  Limit theorems for nearly unstable Hawkes processes , 2013, 1310.2033.

[22]  Clive G. Bowsher.  Modelling Security Market Events in Continuous Time: Intensity Based, Multivariate Point Process Models , 2003 .

[23]  W. Sharpe.  CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK* , 1964 .

[24]  Fabrizio Lillo,et al.  Why Is Equity Order Flow so Persistent , 2011, 1108.1632.

[25]  Erik Stafford,et al.  Price Pressure Around Mergers , 2002 .

[26]  Henri Waelbroeck,et al.  Is Market Impact a Measure of the Information Value of Trades? Market Response to Liquidity vs. Informed Trades , 2013 .

[27]  Jim Gatheral.  No-dynamic-arbitrage and market impact , 2009 .

[28]  R. Rebonato,et al.  Closed-form solutions for option pricing in the presence of volatility smiles: a density-function approach , 2001 .

[29]  Alexander Schied,et al.  TRANSIENT LINEAR PRICE IMPACT AND FREDHOLM INTEGRAL EQUATIONS , 2010 .

[30]  J. Bouchaud,et al.  Fluctuations and Response in Financial Markets: The Subtle Nature of 'Random' Price Changes , 2003, cond-mat/0307332.

[31]  F. Lillo,et al.  How efficiency shapes market impact , 2011, 1102.5457.

[32]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[33]  Alexander Fadeev,et al.  Optimal execution for portfolio transactions , 2006 .

[34]  Dmitry Rakhlin,et al.  The non-linear market impact of large trades: evidence from buy-side order flow , 2013 .

[35]  A. Kyle.  Continuous Auctions and Insider Trading , 1985 .

[36]  Ananth N. Madhavan,et al.  Why Do Security Prices Change? A Transaction-Level Analysis of Nyse Stocks , 1996 .

[37]  Didier Sornette,et al.  Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data , 2013, 1308.6756.

[38]  Paul R. Milgrom,et al.  Bid, ask and transaction prices in a specialist market with heterogeneously informed traders , 1985 .

[39]  F. Lillo,et al.  A Theory for Long-Memory in Supply and Demand , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  Stephen J. Hardiman,et al.  Critical reflexivity in financial markets: a Hawkes process analysis , 2013, 1302.1405.

[41]  Gur Huberman,et al.  Price Manipulation and Quasi-Arbitrage , 2004 .

[42]  F. Lillo,et al.  Why is order flow so persistent? , 2011 .

[43]  A. Hawkes.  Point Spectra of Some Mutually Exciting Point Processes , 1971 .

[44]  E. Bacry,et al.  Estimation of slowly decreasing Hawkes kernels: Application to high frequency order book modelling , 2014, 1412.7096.

[45]  Gordon J. Alexander,et al.  Does Motivation Matter When Assessing Trade Performance? An Analysis of Mutual Funds , 2006 .

[46]  Jeremy H. Large.  Measuring the resiliency of an electronic limit order book , 2007 .

[47]  Esteban Moro,et al.  Market impact and trading profile of hidden orders in stock markets. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  J. Bouchaud,et al.  Price Impact , 2009, 0903.2428.

[49]  Emmanuel Bacry,et al.  Scaling limits for Hawkes processes and application to financial statistics , 2012, 1202.0842.

[50]  J. Bouchaud,et al.  A fully consistent, minimal model for non-linear market impact , 2014, 1412.0141.

[51]  Mathieu Rosenbaum,et al.  Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes , 2015, 1504.03100.