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High Frequency Market Making

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  • Rene Carmona
  • Kevin Webster

Abstract

Since they were authorized by the U.S. Security and Exchange Commission in 1998, electronic exchanges have boomed, and by 2010 high frequency trading accounted for over 70% of equity trades in the US. Such markets are thought to increase liquidity because of the presence of market makers, who are willing to trade as counterparties at any time, in exchange for a fee, the bid-ask spread. In this paper, we propose an equilibrium model showing how such market makers provide liquidity. The model relies on a codebook for client trades, the implied alpha. After solving the individual clients optimization problems and identifying their implied alphas, we frame the market maker stochastic optimization problem as a stochastic control problem with an infinite dimensional control variable. Assuming either identical time horizons for all the clients, or a stochastic partial differential equation model for their beliefs, we solve the market maker problem and derive tractable formulas for the optimal strategy and the resulting limit-order book dynamics.

Suggested Citation

  • Rene Carmona & Kevin Webster, 2012. "High Frequency Market Making," Papers 1210.5781, arXiv.org.
    • Handle: RePEc:arx:papers:1210.5781
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    References listed on IDEAS

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    1. Kurtz, Thomas G. & Xiong, Jie, 1999. "Particle representations for a class of nonlinear SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 103-126, September.
    2. Amihud, Yakov & Mendelson, Haim, 1986. "Asset pricing and the bid-ask spread," Journal of Financial Economics, Elsevier, vol. 17(2), pages 223-249, December.
    3. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    4. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    5. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 251-256.
    6. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    7. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    8. Rama Cont & Sasha Stoikov & Rishi Talreja, 2010. "A Stochastic Model for Order Book Dynamics," Operations Research, INFORMS, vol. 58(3), pages 549-563, June.
    9. Garman, Mark B., 1976. "Market microstructure," Journal of Financial Economics, Elsevier, vol. 3(3), pages 257-275, June.
    10. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Science & Finance (CFM) working paper archive 0203511, Science & Finance, Capital Fund Management.
    11. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
    12. Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2008. "Relation between bid-ask spread, impact and volatility in order-driven markets," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 41-57.
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    Cited by:

    1. Pietro Fodra & Huy^en Pham, 2013. "High frequency trading and asymptotics for small risk aversion in a Markov renewal model," Papers 1310.1756, arXiv.org, revised Jan 2015.
    2. Roman Gayduk & Sergey Nadtochiy, 2015. "Liquidity Effects of Trading Frequency," Papers 1508.07914, arXiv.org, revised May 2017.
    3. Jian Guo & Heung-Yeung Shum, 2024. "Large Investment Model," Papers 2408.10255, arXiv.org, revised Aug 2024.
    4. Pietro Fodra & Huyen Pham, 2013. "High frequency trading in a Markov renewal model," Working Papers hal-00867113, HAL.

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