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Optimal liquidation with temporary and permanent price impact, an application to cryptocurrencies

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  • Hugo E. Ramirez
  • Juli'an Fernando Sanchez

Abstract

This paper studies the optimal liquidation of stocks in the presence of temporary and permanent price impacts, and we focus in the case of cryptocurrencies. We start by presenting analytical solutions to the problem with linear temporary impact, and linear and quadratic permanent impact. Then, using data from the order book of the BNB cryptocurrency, we estimate the functional form of the temporary and permanent price impact in three different scenarios: underestimation, overestimation and average estimation, finding different functional forms for each scenario. Using finite differences and optimal policy iteration, we solve the problem numerically and observe interesting changes in the optimal liquidation policy when applying calibrated linear and power forms for the temporary and permanent price impacts. Then, with these optimal policies, we identify optimal liquidation trajectories and simulate the liquidation of initial inventories to compare the performance among the optimal strategies under different parametrizations and against a naive strategy. Finally, we characterize the optimal policies based on the functional form of the inventory and find that policies generating the highest revenue are those starting with a low trading rate and increasing it as time passes.

Suggested Citation

  • Hugo E. Ramirez & Juli'an Fernando Sanchez, 2023. "Optimal liquidation with temporary and permanent price impact, an application to cryptocurrencies," Papers 2303.10043, arXiv.org.
    • Handle: RePEc:arx:papers:2303.10043
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    References listed on IDEAS

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    1. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, July.
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    3. 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.
    4. Gianbiagio Curato & Jim Gatheral & Fabrizio Lillo, 2017. "Optimal execution with non-linear transient market impact," Quantitative Finance, Taylor & Francis Journals, vol. 17(1), pages 41-54, January.
    5. Brunovský, Pavol & Černý, Aleš & Komadel, Ján, 2018. "Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1159-1171.
    6. Weston Barger & Matthew Lorig, 2018. "Optimal liquidation under stochastic price impact," Papers 1804.04170, arXiv.org.
    7. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    8. Nataliya Bershova & Dmitry Rakhlin, 2013. "The non-linear market impact of large trades: evidence from buy-side order flow," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1759-1778, November.
    9. Fabrizio Lillo & J. Doyne Farmer & Rosario N. Mantegna, 2003. "Master curve for price-impact function," Nature, Nature, vol. 421(6919), pages 129-130, January.
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    Cited by:

    1. Erdong Chen & Mengzhong Ma & Zixin Nie, 2024. "Exploring the Impact: How Decentralized Exchange Designs Shape Traders' Behavior on Perpetual Future Contracts," Papers 2402.03953, arXiv.org, revised Apr 2024.

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