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On the Existence of Linear Equilibria in Models of Market Making

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  • Mark Bagnoli
  • S. Viswanathan
  • Craig Holden

Abstract

We derive necessary and sufficient conditions for a linear equilibrium in three types of competitive market making models: Kyle type models (when market makers only observe aggregate net order flow), Glosten–Milgrom and Easley–O'Hara type models (when market makers observe and trade one order at a time), and call markets models (individual order models when market makers observe a number of orders before pricing and executing any of them). We study two cases: when privately informed (strategic) traders are symmetrically informed and when they have differential information. We derive necessary and sufficient conditions on the distributions of the random variables for a linear equilibrium. We also explore those features of the equilibrium that depend on linearity as opposed to the particular distributional assumptions and we provide a large number of examples of linear equilibria for each of the models.

Suggested Citation

  • Mark Bagnoli & S. Viswanathan & Craig Holden, 2001. "On the Existence of Linear Equilibria in Models of Market Making," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 1-31, January.
    • Handle: RePEc:bla:mathfi:v:11:y:2001:i:1:p:1-31
    DOI: 10.1111/1467-9965.00106
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    Cited by:

    1. Grégoire, Philippe & Huang, Hui, 2012. "Information disclosure with leakages," Economic Modelling, Elsevier, vol. 29(5), pages 2005-2010.
    2. Christian Ewerhart & Nuno Cassola & Steen Ejerskov & Natacha Valla, 2007. "Manipulation in Money Markets," International Journal of Central Banking, International Journal of Central Banking, vol. 3(1), pages 113-148, March.
    3. Georg Nöldeke & Thomas Tröger, 2006. "A characterization of the distributions that imply existence of linear equilibria in the Kyle-model," Annals of Finance, Springer, vol. 2(1), pages 73-85, January.
    4. Fabrizio Lillo, 2021. "Order flow and price formation," Papers 2105.00521, arXiv.org.
    5. Carré, Sylvain & Collin-Dufresne, Pierre & Gabriel, Franck, 2022. "Insider trading with penalties," Journal of Economic Theory, Elsevier, vol. 203(C).
    6. Nöldeke, Georg & Tröger, Thomas, 2004. "On the Existence of Linear Equilibria in the Rochet-Vila Model of Market Making," Bonn Econ Discussion Papers 19/2004, University of Bonn, Bonn Graduate School of Economics (BGSE).
    7. Christoph Kuhn & Matthias Riedel, 2012. "Price-Setting of Market Makers: A Filtering Problem with an Endogenous Filtration," Papers 1210.4000, arXiv.org.
    8. Biais, Bruno & Glosten, Larry & Spatt, Chester, 2005. "Market microstructure: A survey of microfoundations, empirical results, and policy implications," Journal of Financial Markets, Elsevier, vol. 8(2), pages 217-264, May.
    9. Adlai Fisher & Robert Heinkel, 2008. "Reputation and Managerial Truth‐Telling as Self‐Insurance," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 17(2), pages 489-540, June.
    10. Christian Ewerhart & Marco Serena, 2023. "On the (Im-)Possibility of Representing Probability Distributions as a Difference of I.I.D. Noise Terms," Working Papers tax-mpg-rps-2023-04, Max Planck Institute for Tax Law and Public Finance.
    11. Albert S. Kyle & Anna A. Obizhaeva, 2020. "Adverse Selection and Liquidity: From Theory to Practice," Working Papers w0268, New Economic School (NES).
    12. Deb, Pragyan & Koo, Bonsoo & Liu, Zijun, 2014. "Competition, premature trading and excess volatility," Journal of Banking & Finance, Elsevier, vol. 41(C), pages 178-193.
    13. Joao Amaro de Matos & Ana Lacerda, 2006. "Equilibrium bid-ask spread of European derivatives in dry markets," Nova SBE Working Paper Series wp480, Universidade Nova de Lisboa, Nova School of Business and Economics.

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