F. Abergel and A. Jedidi, A mathematical approach to order book modeling, International Journal of Theoretical and Applied Finance, vol.16, issue.05, p.1350025, 2013.

F. Abergel and A. Jedidi, Long-time behavior of a Hawkes process-based limit order book, SIAM Journal on Financial Mathematics, vol.6, issue.1, pp.1026-1043, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01121711

F. Abergel, C. Lehalle, and M. Rosenbaum, Understanding the stakes of high-frequency trading, The Journal of Trading, vol.9, issue.4, pp.49-73, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01108122

T. Adrian, A. Capponi, E. Vogt, and H. Zhang, Intraday market making with overnight inventory costs. Available at SSRN 2844881, 2016.

Y. Ait, -. Sahalia, and M. Saglam, High frequency market making: Optimal quoting. Available at SSRN 2331613, 2017.

R. Almgren, C. Thum, E. Hauptmann, and H. Li, Direct estimation of equity market impact, Risk, vol.18, issue.7, pp.58-62, 2005.

Y. Amihud and H. Mendelson, Dealership market: Market-making with inventory, Journal of Financial Economics, vol.8, issue.1, pp.31-53, 1980.

, Autorité des Marchés Financiers. Study of the behaviour of high-frequency traders on Euronext Paris. Risk and Trend Mapping, 2017.

, Autorité des Marchés Financiers. MIFID II: Impact of the new tick size regime, 2018.

E. Bacry, A. Iuga, M. Lasnier, and C. Lehalle, Market impacts and the life cycle of investors orders, Market Microstructure and Liquidity, vol.1, issue.02, p.1550009, 2015.

M. Baron, J. Brogaard, B. Hagströmer, and A. Kirilenko, Risk and return in high-frequency trading, Journal of Financial and Quantitative Analysis, vol.54, pp.993-1024, 2019.

S. Baruch and . Lawrence-r-glosten, Tail expectation, imperfect competition, and the phenomenon of Øickering quotes in limit order book markets. Unpublished Manuscript, 2017.

C. Bayer, U. Horst, and J. Qiu, A functional limit theorem for limit order books with state dependent price dynamics, The Annals of Applied Probability, vol.27, issue.5, pp.2753-2806, 2017.

R. Paul and . Beesack, On some Gronwall-type integral inequalities in n independent variables, Journal of Mathematical Analysis and Applications, vol.100, issue.2, pp.393-408, 1984.

M. Bellia, L. Pelizzon, M. G. Subrahmanyam, J. Uno, and D. Yuferova, Low-latency trading and price discovery: Evidence from the Tokyo stock exchange in the pre-opening and opening periods, 2017.

D. Bernhardt and E. Hughson, Splitting orders. The Review of Financial Studies, vol.10, pp.69-101, 1997.

B. Biais, F. Declerck, and S. Moinas, Who supplies liquidity, how and when? Available at SSRN 2789736, 2016.

B. Biais and T. Foucault, HFT and market quality. Bankers, Markets & Investors, vol.128, pp.5-19, 2014.

B. Biais, T. Foucault, and S. Moinas, Equilibrium fast trading, Journal of Financial Economics, vol.116, issue.2, pp.292-313, 2015.
URL : https://hal.archives-ouvertes.fr/halshs-01400252

B. Biais, D. Martimort, and J. Rochet, Competing mechanisms in a common value environment, Econometrica, vol.68, issue.4, pp.799-837, 2000.

P. Billingsley, Convergence of probability measures. Wiley Series in Probability and Statistics: Probability and Statistics, 1999.

P. Blanc, J. Donier, and J. Bouchaud, Quadratic Hawkes processes for AEnancial prices, Quantitative Finance, vol.17, issue.2, pp.171-188, 2017.

J. Bouchaud, J. Doyne, F. Farmer, and . Lillo, How markets slowly digest changes in supply and demand, Handbook of AEnancial markets: dynamics and evolution, pp.57-160, 2009.

S. Boussetta, L. Lescourret, and S. Moinas, The role of pre-opening mechanisms in fragmented markets. Available at SSRN 2939502, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02156137

A. Bouveret, C. Guillaumie, C. A. Roqueiro, C. Winkler, and . Ste-en-nauhaus, High-frequency trading activity in EU equity markets, ESMA Report on Trends, Risks and Vulnerabilities, vol.1, pp.41-47, 2014.

P. Brémaud and L. Massoulié, Stability of nonlinear Hawkes processes. The Annals of Probability, pp.1563-1588, 1996.

J. Brogaard, High frequency trading and its impact on market quality, 2010.

J. Brogaard, A. Carrion, T. Moyaert, R. Riordan, A. Shkilko et al., High frequency trading and extreme price movements, Journal of Financial Economics, vol.128, issue.2, pp.253-265, 2018.

J. Brogaard, T. Hendershott, and R. Riordan, High-frequency trading and price discovery, The Review of Financial Studies, vol.27, issue.8, pp.2267-2306, 2014.

E. Budish, P. Cramton, and J. Shim, The high-frequency trading arms race: frequent batch auctions as a market design response, The Quarterly Journal of Economics, vol.130, issue.4, pp.1547-1621, 2015.

A. Capponi, J. Albert, H. Menkveld, and . Zhang, Large orders in small markets: On optimal execution with endogenous liquidity supply. Available at SSRN 3326313, 2019.

P. Cardaliaguet and C. Lehalle, Mean AEeld game of controls and an application to trade crowding, Mathematics and Financial Economics, vol.12, pp.1-29, 2017.

A. Chaboud, S. Chernenko, and J. Wright, Trading activity and macroeconomic announcements in high-frequency exchange rate data, Journal of the European Economic Association, vol.6, issue.2-3, pp.589-596, 2008.

A. Chaboud, B. Chiquoine, E. Hjalmarsson, and C. Vega, Rise of the machines: Algorithmic trading in the foreign exchange market, The Journal of Finance, vol.69, issue.5, pp.2045-2084, 2014.

T. Chordia, R. Roll, and A. Subrahmanyam, Market liquidity and trading activity, The Journal of Finance, vol.56, issue.2, pp.501-530, 2001.

, Commission Européenne, 2016.

, High-frequency trading in the foreign exchange market. Bank for International Settlements, Markets Committee, 2011.

R. Cont and A. De-larrard, Price dynamics in a Markovian limit order market, SIAM Journal on Financial Mathematics, vol.4, issue.1, pp.1-25, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00832155

R. Cont, S. Stoikov, and R. Talreja, A stochastic model for order book dynamics, Operations Research, vol.58, issue.3, pp.549-563, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00497666

J. Daryl and D. Daley, An introduction to the theory of point processes: volume II: general theory and structure, 2007.

K. Dayri and M. Rosenbaum, Large tick assets: implicit spread and optimal tick size, Market Microstructure and Liquidity, vol.1, issue.01, p.1550003, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01263181

L. Joseph and . Doob, Stochastic processes, p.215, 1990.

. Bibliography,

. Euronext, Launch of a new service: Retail matching facility, 2012.

. Euronext, Volatility indices rule book version 16-01, 2016.

, Supplementing directive 2014/65/eu of the European parliament and of the council on markets in AEnancial instruments with regard to regulatory technical standards specifying the requirements on market making agreements and schemes, 2016.

J. Doyne, L. Farmer, F. Gillemot, S. Lillo, A. Mike et al., What really causes large price changes?, Quantitative Finance, vol.4, issue.4, pp.383-397, 2004.

. Fidessa, Fidessa online fragmentation index, 2017.

T. Foucault, Order Øow composition and trading costs in a dynamic limit order market, Journal of Financial Markets, vol.2, issue.2, pp.99-134, 1999.

T. Foucault, J. Hombert, and I. Ro?u, News trading and speed, The Journal of Finance, vol.71, issue.1, pp.335-382, 2016.
URL : https://hal.archives-ouvertes.fr/hal-00713372

T. Foucault, R. Kozhan, and W. Tham, Toxic arbitrage. The Review of Financial Studies, vol.30, pp.1053-1094, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02058262

. Lawrence-r-glosten, Is the electronic open limit order book inevitable?, The Journal of Finance, vol.49, issue.4, pp.1127-1161, 1994.

R. Lawrence, . Glosten, and . Paul-r-milgrom, Bid, ask and transaction prices in a specialist market with heterogeneously informed traders, Journal of Financial Economics, vol.14, issue.1, pp.71-100, 1985.

D. Martin, . Gould, A. Mason, S. Porter, M. Williams et al., Limit order books, Quantitative Finance, vol.13, issue.11, pp.1709-1742, 2013.

M. Hairer, Ergodic properties of a class of non-markovian processes trends in stochastic analysis, 2009.

L. Harris, What to do about high-frequency trading, 2013.

T. Hayashi and Y. Koike, Wavelet-based methods for high-frequency lead-lag analysis, SIAM Journal on Financial Mathematics, vol.9, issue.4, pp.1208-1248, 2018.

T. Hendershott, M. Charles, A. J. Jones, and . Menkveld, Does algorithmic trading improve liquidity?, The Journal of Finance, vol.66, issue.1, pp.1-33, 2011.

S. Thomas, H. Ho, and . Stoll, Optimal dealer pricing under transactions and return uncertainty, Journal of Financial Economics, vol.9, issue.1, pp.47-73, 1981.

S. Thomas, H. Ho, and . Stoll, The dynamics of dealer markets under competition, The Journal of Finance, vol.38, issue.4, pp.1053-1074, 1983.

M. Ho-mann, M. Rosenbaum, and N. Yoshida, Estimation of the lead-lag parameter from non-synchronous data, Bernoulli, vol.19, issue.2, pp.426-461, 2013.

D. Roger, H. Huang, and . Stoll, The components of the bid-ask spread: A general approach, The Review of Financial Studies, vol.10, issue.4, pp.995-1034, 1997.

W. Huang, C. Lehalle, and M. Rosenbaum, Simulating and analyzing order book data: The queue-reactive model, Journal of the American Statistical Association, vol.110, issue.509, pp.107-122, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01172326

W. Huang, C. Lehalle, and M. Rosenbaum, How to predict the consequences of a tick value change? Evidence from the Tokyo Stock Exchange pilot program, Market Microstructure and Liquidity, vol.2, issue.03n04, p.1750001, 2016.

W. Huang and M. Rosenbaum, Ergodicity and di usivity of Markovian order book models: a general framework, SIAM Journal on Financial Mathematics, vol.8, issue.1, pp.874-900, 2017.

W. Huang, M. Rosenbaum, and P. Saliba, From Glosten-Milgrom to the whole limit order book and applications to AEnancial regulation, Available at SSRN, vol.3343779, 2019.

N. Huth and F. Abergel, High frequency lead/lag relationships: Empirical facts, Journal of Empirical Finance, vol.26, pp.41-58, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00645685

J. Jacod, Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingales. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, vol.31, pp.235-253, 1975.

. Thibault-jaisson, Market impact as anticipation of the order Øow imbalance. Quantitative Finance, vol.15, pp.1123-1135, 2015.

J. George, I. Jiang, G. Lo, and . Valente, High-frequency trading around macroeconomic news announcements: Evidence from the us treasury market, Bank of Canada Working Paper, 2014.

M. Charles and . Jones, What do we know about high-frequency trading? Available at SSRN 2236201, 2013.

B. Jovanovic and A. J. Menkveld, Middlemen in limit order markets. Available at SSRN 1624329, 2016.

P. Jusselin and M. Rosenbaum, No-arbitrage implies power-law market impact and rough volatility, 2018.

A. Kirilenko, S. Albert, M. Kyle, T. Samadi, and . Tuzun, The Øash crash: high frequency trading in an electronic market, The Journal of Finance, vol.72, issue.3, pp.967-998, 2017.

P. Kosulaje, Sur la répartition de la partie fractionnaire d'une variable, Matematiceskij Sbornik, vol.2, issue.5, pp.1017-1019, 1937.

S. Albert and . Kyle, Continuous auctions and insider trading, Econometrica: Journal of the Econometric Society, vol.53, pp.1315-1335, 1985.

A. Lachapelle, J. Lasry, C. Lehalle, and P. Lions, E ciency of the price formation process in presence of high frequency participants: a mean AEeld game analysis, Mathematics and Financial Economics, vol.10, issue.3, pp.223-262, 2016.

S. Laruelle, M. Rosenbaum, and E. Savku, Assessing MiFID II regulation on tick sizes: A transaction costs analysis viewpoint. Available at SSRN 3256453, 2018.

G. Last, On dependent marking and thinning of point processes. Stochastic processes and their applications, vol.45, pp.73-94, 1993.

C. , A. Lehalle, and S. Laruelle, Market Microstructure in Practice. World ScientiAEc publishing, 2013.

C. , A. Lehalle, and O. Mounjid, Limit order strategic placement with adverse selection risk and the role of latency, Market Microstructure and Liquidity, vol.3, issue.01, p.1750009, 2017.

C. Lehalle, O. Mounjid, and M. Rosenbaum, Optimal liquiditybased trading tactics, 2018.

A. Peter, G. S. Lewis, and . Shedler, Simulation of nonhomogeneous Poisson processes by thinning, Naval research logistics quarterly, vol.26, issue.3, pp.403-413, 1979.

A. Madhavan, Market microstructure: A survey, Journal of Financial Markets, vol.3, issue.3, pp.205-258, 2000.

A. Madhavan, Exchange-traded funds, market structure, and the Øash crash, Financial Analysts Journal, vol.68, issue.4, pp.20-35, 2012.

A. Madhavan, M. Richardson, and M. Roomans, Why do security prices change? a transaction-level analysis of nyse stocks, Review of Financial Studies, vol.10, issue.4, pp.1035-1064, 1997.

N. Megarbane, P. Saliba, C. Lehalle, and M. Rosenbaum, The behavior of high frequency traders under di erent market stress scenarios, Market Microstructure and Liquidity, vol.3, issue.03n04, p.1850005, 2017.

J. Albert and . Menkveld, High frequency trading and the new market makers, Journal of Financial Markets, vol.16, issue.4, pp.712-740, 2013.

P. Sean, . Meyn, and . Richard-l-tweedie, Stability of Markovian processes i: Criteria for discrete-time chains, Advances in Applied Probability, vol.24, issue.3, pp.542-574, 1992.

P. Sean, . Meyn, and . Richard-l-tweedie, Markov chains and stochastic stability, 2012.

C. Ciamac, K. Moallemi, and . Yuan, A model for queue position valuation in a limit order book. Working paper, 2016.

M. Morariu and -. Mikko-s-pakkanen, State-dependent hawkes processes and their application to limit order book modelling, 2018.

E. Moro, J. Vicente, G. Luis, A. Moyano, . Gerig et al., Market impact and trading proAEle of hidden orders in stock markets, Physical Review E, vol.80, issue.6, p.66102, 2009.

J. R. Norris, Markov Chains (Cambridge Series in Statistical and Probabilistic Mathematics), 1998.

Y. Ogata, On Lewis' simulation method for point processes, IEEE Transactions on Information Theory, vol.27, issue.1, pp.23-31, 1981.

A. Christine and . Parlour, Price dynamics in limit order markets, The Review of Financial Studies, vol.11, issue.4, pp.789-816, 1998.

M. Rambaldi, E. Bacry, and J. Muzy, Disentangling and quantifying market participant volatility contributions, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02392863

R. Riordan and A. Storkenmaier, Latency, liquidity and price discovery, Journal of Financial Markets, vol.15, issue.4, pp.416-437, 2012.

K. Rock, The specialist's order book and price anomalies, Review of Financial Studies, vol.9, pp.1-20, 1996.

M. Rosenbaum, Integrated volatility and round-o error, Bernoulli, vol.15, issue.3, pp.687-720, 2009.

I. Ro?u, A dynamic model of the limit order book, The Review of Financial Studies, vol.22, issue.11, pp.4601-4641, 2009.

P. Saliba, The information content of high frequency traders aggressive orders: recent evidences. Available at SSRN, 2019.

M. Scholtus, B. Dick-van-dijk, and . Frijns, Speed, algorithmic trading, and market quality around macroeconomic news announcements, Journal of Banking & Finance, vol.38, pp.89-105, 2014.

. Sec, Concept release on equity market structure, 2010.

J. Duane and . Seppi, Liquidity provision with limit orders and a strategic specialist, Review of Financial Studies, vol.10, issue.1, pp.103-150, 1997.

E. Smith, J. Doyne, L. Farmer, S. Gillemot, and . Krishnamurthy, Statistical theory of the continuous double auction, Quantitative AEnance, vol.3, issue.6, pp.481-514, 2003.

S. Stoikov, The micro-price: a high frequency estimator of future prices, Quantitative Finance, vol.18, issue.12, pp.1959-1966, 2018.

R. Hans and . Stoll, The supply of dealer services in securities markets, The Journal of Finance, vol.33, issue.4, pp.1133-1151, 1978.

B. Tóth, Y. Lemperiere, C. Deremble, J. De-lataillade, J. Kockelkoren et al., Anomalous price impact and the critical nature of liquidity in AEnancial markets, Physical Review X, vol.1, issue.2, p.21006, 2011.

B. Toth, I. Palit, F. Lillo, and D. Farmer, Why is equity order Øow so persistent, Journal of Economic Dynamics and Control, vol.51, pp.218-239, 2015.

. Trésor-economics, Impact of falling oil prices on the major emerging economies, Ministère des Finances et des Comptes Publics Ministère de l'Économie de l'Industrie et du Numérique, 2016.

J. Wilder and T. , On the distribution of the fractional part of a statistical variable, Matematiceskij Sbornik, vol.4, issue.3, pp.561-562, 1938.

, Board of Governors of the Federal Reserve System and Exchange Commission U.S. Commodity Futures Trading Commission. The U.S. treasury market on, 2014.

P. Wu, M. Rambaldi, J. Muzy, and E. Bacry, Queuereactive hawkes models for the order Øow, 2019.

M. Wyart, J. Bouchaud, J. Kockelkoren, M. Potters, and M. Vettorazzo, Relation between bid-ask spread, impact and volatility in orderdriven markets, Quantitative Finance, vol.8, issue.1, pp.41-57, 2008.

F. Zhang, High-frequency trading, stock volatility, and price discovery, 2010.