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Optimal market making under partial information with general intensities

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  • Diego Zabaljauregui
  • Luciano Campi

Abstract

Starting from the Avellaneda-Stoikov framework, we consider a market maker who wants to optimally set bid/ask quotes over a finite time horizon, to maximize her expected utility. The intensities of the orders she receives depend not only on the spreads she quotes, but also on unobservable factors modelled by a hidden Markov chain. We tackle this stochastic control problem under partial information with a model that unifies and generalizes many existing ones under full information, combining several risk metrics and constraints, and using general decreasing intensity functionals. We use stochastic filtering, control and piecewise-deterministic Markov processes theory, to reduce the dimensionality of the problem and characterize the reduced value function as the unique continuous viscosity solution of its dynamic programming equation. We then solve the analogous full information problem and compare the results numerically through a concrete example. We show that the optimal full information spreads are biased when the exact market regime is unknown, and the market maker needs to adjust for additional regime uncertainty in terms of P&L sensitivity and observed order flow volatility. This effect becomes higher, the longer the waiting time in between orders.

Suggested Citation

  • Diego Zabaljauregui & Luciano Campi, 2019. "Optimal market making under partial information with general intensities," Papers 1902.01157, arXiv.org, revised Apr 2020.
  • Handle: RePEc:arx:papers:1902.01157
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    References listed on IDEAS

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    1. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    2. Erhan Bayraktar & Michael Ludkovski, 2014. "Liquidation In Limit Order Books With Controlled Intensity," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 627-650, October.
    3. Pietro Fodra & Mauricio Labadie, 2012. "High-frequency market-making with inventory constraints and directional bets," Papers 1206.4810, arXiv.org.
    4. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Optimal Portfolio Liquidation with Limit Orders," Papers 1106.3279, arXiv.org, revised Jul 2012.
    5. Nicole Bäuerle & Ulrich Rieder, 2009. "MDP algorithms for portfolio optimization problems in pure jump markets," Finance and Stochastics, Springer, vol. 13(4), pages 591-611, September.
    6. Ho, Thomas & Stoll, Hans R., 1981. "Optimal dealer pricing under transactions and return uncertainty," Journal of Financial Economics, Elsevier, vol. 9(1), pages 47-73, March.
    7. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    8. �lvaro Cartea & Sebastian Jaimungal, 2013. "Modelling Asset Prices for Algorithmic and High-Frequency Trading," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(6), pages 512-547, December.
    9. Pietro Fodra & Mauricio Labadie, 2012. "High-frequency market-making with inventory constraints and directional bets," Working Papers hal-00675925, HAL.
    10. K. Giesecke & H. Kakavand & M. Mousavi, 2011. "Exact Simulation of Point Processes with Stochastic Intensities," Operations Research, INFORMS, vol. 59(5), pages 1233-1245, October.
    11. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, February.
    12. Olivier Gu'eant, 2016. "Optimal market making," Papers 1605.01862, arXiv.org, revised May 2017.
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    Cited by:

    1. Marcello Monga, 2024. "Automated Market Making and Decentralized Finance," Papers 2407.16885, arXiv.org.

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