Efficiency of the price formation process in presence of high frequency participants: a mean field game analysis

Mathematics and Financial Economics

Volumn 10, Issue 3, 2016, Pages 223-262

  Lachapelle, Aimé ^a   Lasry, Jean Michel ^b   Lehalle, Charles Albert ^c,d   Lions, Pierre Louis ^e  

^a MFG Labs   (France)

^b Centre National de la Recherche Scientifique   (France)

^c Capital Fund Management   (France)

^d IMPERIAL COLLEGE LONDON   (United Kingdom)

^e l'alimentation et l'Environnement   (France)

Author keywords

High frequency trading; Liquidity equilibrium; Market microstructure; Mean field games; Order driven market; Orderbook modeling; Price formation process; Waiting cost

Indexed keywords

EID: 84946112935     PISSN: 18629679     EISSN: 18629660     Source Type: Journal    
DOI: 10.1007/s11579-015-0157-1     Document Type: Article

References (41)

1. Adlakha, S., Johari, R., Weintraub, G.Y.: Equilibria of dynamic games with many players: existence, approximation, and market structure. J. Econ. Theory 156, 269–316 (2013)
2. Alfonsi, A., Fruth, A., Schied, A.: Optimal execution strategies in limit order books with general shape functions. Quant. Financ. 10(2), 143–157 (2009)
3. Almgren, R., Thum, C., Hauptmann, E., Li, H.: Direct estimation of equity market impact. Risk 18, 57–62 (2005)
4. Almgren, R.F., Chriss, N.: Optimal execution of portfolio transactions. J. Risk 3(2), 5–39 (2000)
5. Bacry, E., Delattre, S., Hoffmann, M., Muzy, J.F.: Modeling microstructure noise with mutually exciting point processes. Quant. Financ. 13, 65–77 (2012)
6. Bouchard, B., Dang, N.-M., Lehalle, C.-A.: Optimal control of trading algorithms: a general impulse control approach. SIAM J. Financ. Math. 2(1), 404–438 (2011)
7. Brogaard, J., Baron, M., Kirilenko, A.: The Trading Profits of High Frequency Traders. Confronting Many Viewpoints, In Market Microstructure (2012)
8. Cardaliaguet, P., Lasry, J.-M., Lions, P.-L., Porretta, A.: Long time average of mean field games. Netw. Heterog. Media 7(2), 279–301 (2012)
9. Carmona, R., Delarue, F., Lachapelle, A.: Control of McKean–Vlasov dynamics versus mean field games. Math. Financ. Econ. 7, 131–136 (2012)
10. Carmona, R., Lacker, D.: A probabilistic weak formulation of mean field games and applications. Math. Financ. Econ. 7, 131–136 (2013)
11. Crandall, M.G., Ishii, H., Lions, P.-L.: User’s guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. 27(1), 1–67 (1992)
12. Euronext. EuroNext rules: book I. Technical report, EuroNext (2006)
13. Field, J., Large, J.: Pro-rata matching and one-tick futures markets. CFS working paper 2008,40, Frankfurt, Main (2008)
14. Foucault, T., Kadan, O., Kandel, E.: Limit order book as a market for liquidity. Rev. Financ. Stud. 18(4), 1171–1217 (2005)
15. Foucault, T., Menkveld, A.J.: Competition for order flow and smart order routing systems. J. Financ. 63(1), 119–158 (2008)
16. Foucault, T., Pagano, M., Röell, A.: Market Liquidity: Theory, Evidence, and Policy. Oxford University Press, Oxford (2013)
17. Ganchev, K., Nevmyvaka, Y., Kearns, M., Vaughan, J.W.: Censored exploration and the dark pool problem. Commun. ACM 53(5), 99–107 (2010)
18. Gareche, A., Disdier, G., Kockelkoren, J., Bouchaud, J.P.: A Fokker–Planck description for the queue dynamics of large tick stocks. Phys. Rev. E 88, 032809 (2013)
19. Gatheral, J.: No-dynamic-arbitrage and market impact. Quant. Financ. 10(7), 749–759 (2010)
20. Guéant, O., Lasry, J.-M., Lions, P.-L.: Paris-Princeton Lectures on Mathematical Finance 2010, chapter Mean Field Games and Applications. Springer, New York (2010)
21. Guéant, O., Lehalle, C.-A., Fernandez-Tapia, J.: Optimal execution with limit orders. SIAM J. Financ. Math. 13(1), 740–764 (2012)
22. Hall, A., Kofman, P., Mcculloch, J.: True Spreads Censored by Tick Size. Technical report (2005)
23. Ho, T., Stoll, H.R.: The dynamics of dealer markets under competition. J. Financ. 38(4), 1053–1074 (1983)
24. Huang, M.Y., Caines, P.E., Malhame, R.P.: Large population cost-coupled LQG problems with non-uniform individuals. IEEE Trans. Autom. Control 52(9), 1560–1571 (2007)
25. Kirilenko, A. A., Kyle, A. P., Samadi, M., Tuzun, T.: The Flash Crash: The Impact of High Frequency Trading on an Electronic Market. Social Science Research Network Working Paper Series(2010)
26. Krusell, P., Smith, A.A.: Income and wealth heterogeneity in the macroeconomy. J. Polit. Econ. 106(5), 867–896 (1998)
27. Kyle, A.P.: Continuous auctions and insider trading. Econometrica 53(6), 1315–1335 (1985)
28. Lachapelle, A., Wolfram, M.-T.: On a mean field game approach modeling congestion and aversion in pedestrian crowds. Transp. Res. Part B 15, 10 (2011)
29. Lasry, J.-M., Lions, P.-L.: Mean field games. Jpn. J. Math. 2(1), 229–260 (2007)
30. Lehalle, C.-A., Guéant, O., Razafinimanana, J.: High Frequency Simulations of an Order Book: a Two-Scales Approach. In: Abergel, F., Chakrabarti, B.K., Chakraborti, A., Mitra, M. (eds.) Econophysics of Order-Driven Markets. Springer, New Economic Windows, New York (2010)
31. Lehalle, C.-A., Laruelle, S., Burgot, R., Pelin, S., Lasnier, M.: Market Microstructure in Practice. World Scientific publishing, Singapore (2013)
32. Lions, P.-L. (2007–2012). Jeux à champ moyen et applications. Technical report, Collège de France
33. Lucas, R., Moll, B.: Knowledge growth and the allocation of time. J. Polit. Econ. 75, 352 (2013)
34. Madhavan, A.: Exchange-Traded Funds, Market Structure and the Flash Crash. Social Science Research Network Working Paper Series (2011)
35. Mendelson, H., Amihud, Y.: How (Not) to Integrate the European Capital Markets. Cambridge University Press, Cambridge (1991)
36. Menkveld, A. J.: High Frequency Trading and The New-Market Makers. Social Science Research Network Working Paper Series (2010)
37. Pagès, G., Laruelle, S., Lehalle, C.-A.: Optimal split of orders across liquidity pools: a stochatic algorithm approach. SIAM J. Financ. Math. 2, 1042–1076 (2011)
38. Pequito, S., Aguiar, A. P., Sinopoli, B., Gomes, D. A.: Nonlinear Estimation Using Mean Field Games. In: 2011 5th International Conference on Network Games, Control and Optimization (NetGCooP) (2011a)
39. Pequito, S., Aguiar, A. P., Sinopoli, B., Gomes, D. A.: Unsupervised Learning of Finite Mixture Using Mean Field Games. In: 9th Allerton Conference on Communication, Control and Computing(2011b)
40. Robert, C.Y., Rosenbaum, M.: A new approach for the dynamics of ultra-high-frequency data: the model with uncertainty zones. J. Financ. Econom. 9(2), 344–366 (2011)
41. Roşu, I.: A dynamic model of the limit order book. Rev. Financ. Stud. 22(11), 4601–4641 (2009)