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Market Making And Portfolio Liquidation Under Uncertainty

Author

Listed:
  • KAJ NYSTRÖM

    (Department of Mathematics, Uppsala University, S-751 06 Uppsala, Sweden)

  • SIDI MOHAMED OULD ALY

    (Department of Mathematics, Uppsala University, S-751 06 Uppsala, Sweden)

  • CHANGYONG ZHANG

    (Department of Mathematics, Uppsala University, S-751 06 Uppsala, Sweden)

Abstract

Market making and optimal portfolio liquidation in the context of electronic limit order books are of considerably practical importance for high frequency (HF) market makers as well as more traditional brokerage firms supplying optimal execution services for clients. In general, the two problems are based on probabilistic models defined on certain reference probability spaces. However, due to uncertainty in model parameters or in periods of extreme market turmoil, ambiguity concerning the correct underlying probability measure may appear and an assessment of model risk, as well as the uncertainty on the choice of the model itself, becomes important, as for a market maker or a trader attempting to liquidate large positions, the uncertainty may result in unexpected consequences due to severe mispricing. This paper focuses on the market making and the optimal liquidation problems using limit orders, accounting for model risk or uncertainty. Both are formulated as stochastic optimal control problems, with the controls being the spreads, relative to a reference price, at which orders are placed. The models consider uncertainty in both the drift and volatility of the underlying reference price, for the study of the effect of the uncertainty on the behavior of the market maker, accounting also for inventory restriction, as well as on the optimal liquidation using limit orders.

Suggested Citation

  • Kaj Nyström & Sidi Mohamed Ould Aly & Changyong Zhang, 2014. "Market Making And Portfolio Liquidation Under Uncertainty," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(05), pages 1-33.
  • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:05:n:s0219024914500344
    DOI: 10.1142/S0219024914500344
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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.
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    7. Hagströmer, Björn & Nordén, Lars, 2013. "The diversity of high-frequency traders," Journal of Financial Markets, Elsevier, vol. 16(4), pages 741-770.
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    Citations

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    Cited by:

    1. Pankaj Kumar, 2021. "Deep Hawkes Process for High-Frequency Market Making," Papers 2109.15110, arXiv.org.
    2. Horst, Ulrich & Xia, Xiaonyu & Zhou, Chao, 2021. "Portfolio Liquidation under Factor Uncertainty," Rationality and Competition Discussion Paper Series 274, CRC TRR 190 Rationality and Competition.
    3. Sofiene El Aoud & Frédéric Abergel, 2015. "A stochastic control approach for options market making," Post-Print hal-01061852, HAL.
    4. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    5. Burcu Aydoğan & Ömür Uğur & Ümit Aksoy, 2023. "Optimal Limit Order Book Trading Strategies with Stochastic Volatility in the Underlying Asset," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 289-324, June.
    6. Philippe Bergault & David Evangelista & Olivier Gu'eant & Douglas Vieira, 2018. "Closed-form approximations in multi-asset market making," Papers 1810.04383, arXiv.org, revised Sep 2022.
    7. Baron Law & Frederi Viens, 2019. "Market Making under a Weakly Consistent Limit Order Book Model," Papers 1903.07222, arXiv.org, revised Jan 2020.
    8. Ulrich Horst & Xiaonyu Xia & Chao Zhou, 2019. "Portfolio liquidation under factor uncertainty," Papers 1909.00748, arXiv.org.
    9. Jonathan Ch'avez-Casillas & Jos'e E. Figueroa-L'opez & Chuyi Yu & Yi Zhang, 2024. "Adaptive Optimal Market Making Strategies with Inventory Liquidation Cos," Papers 2405.11444, arXiv.org.
    10. Joseph Jerome & Gregory Palmer & Rahul Savani, 2022. "Market Making with Scaled Beta Policies," Papers 2207.03352, arXiv.org, revised Sep 2022.

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