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A Monte Carlo method for optimal portfolio executions

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  • Nico Achtsis
  • Dirk Nuyens

Abstract

Traders are often faced with large block orders in markets with limited liquidity and varying volatility. Executing the entire order at once usually incurs a large trading cost because of this limited liquidity. In order to minimize this cost traders split up large orders over time. Varying volatility however implies that they now take on price risk, as the underlying assets' prices can move against the traders over the execution period. This execution problem therefore requires a careful balancing between trading slow to reduce liquidity cost and trading fast to reduce the volatility cost. R. Almgren solved this problem for a market with one asset and stochastic liquidity and volatility parameters, using a mean-variance framework. This leads to a nonlinear PDE that needs to be solved numerically. We propose a different approach using (quasi-)Monte Carlo which can handle any number of assets. Furthermore, our method can be run in real-time and allows the trader to change the parameters of the underlying stochastic processes on-the-fly.

Suggested Citation

  • Nico Achtsis & Dirk Nuyens, 2013. "A Monte Carlo method for optimal portfolio executions," Papers 1312.5919, arXiv.org.
  • Handle: RePEc:arx:papers:1312.5919
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    File URL: http://arxiv.org/pdf/1312.5919
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    References listed on IDEAS

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    1. 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.
    2. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    3. Konishi, Hizuru, 2002. "Optimal slice of a VWAP trade," Journal of Financial Markets, Elsevier, vol. 5(2), pages 197-221, April.
    4. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    5. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    6. 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.
    7. 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.
    8. Zoltán Eisler & Jean-Philippe Bouchaud & Julien Kockelkoren, 2012. "The price impact of order book events: market orders, limit orders and cancellations," Quantitative Finance, Taylor & Francis Journals, vol. 12(9), pages 1395-1419, September.
    9. Alfonsi Aurélien & Alexander Schied & Alla Slynko, 2012. "Order Book Resilience, Price Manipulation, and the Positive Portfolio Problem," Post-Print hal-00941333, HAL.
    10. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, July.
    11. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
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