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Optimal Trading Execution with Nonlinear Market Impact: An Alternative Solution Method

Author

Listed:
  • Massimiliano Marzo

    (Department of Economics, Università di Bologna)

  • Daniele Ritelli

    (Department of Mathematics, Università di Bologna)

  • Paolo Zagaglia

    (Department of Economics, Università di Bologna)

Abstract

We consider the optimal trade execution strategies for a large portfolio of single stocks proposed by Almgren (2003). This framework accounts for a nonlinear impact of trades on average market prices. The results of Almgren (2003) are based on the assumption that no shares of assets per unit of time are trade at the beginning of the period. We propose a general solution method that accomodates the case of a positive stock of assets in the initial period. Our findings are twofold. First of all, we show that the problem admits a solution with no trading in the opening period only if additional parametric restrictions are imposed. Second, with positive asset holdings in the initial period, the optimal execution time depends on trading activity at the beginning of the planning period.

Suggested Citation

  • Massimiliano Marzo & Daniele Ritelli & Paolo Zagaglia, 2011. "Optimal Trading Execution with Nonlinear Market Impact: An Alternative Solution Method," Working Paper series 52_11, Rimini Centre for Economic Analysis.
    • Handle: RePEc:rim:rimwps:52_11
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    References listed on IDEAS

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    1. Holthausen, Robert W. & Leftwich, Richard W. & Mayers, David, 1990. "Large-block transactions, the speed of response, and temporary and permanent stock-price effects," Journal of Financial Economics, Elsevier, vol. 26(1), pages 71-95, July.
    2. Huang, Roger D & Stoll, Hans R, 1997. "The Components of the Bid-Ask Spread: A General Approach," The Review of Financial Studies, Society for Financial Studies, vol. 10(4), pages 995-1034.
    3. Boucekkine, R. & Ruiz-Tamarit, J.R., 2008. "Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 33-54, January.
    4. Kraus, Alan & Stoll, Hans R, 1972. "Price Impacts of Block Trading on the New York Stock Exchange," Journal of Finance, American Finance Association, vol. 27(3), pages 569-588, June.
    5. Hasbrouck, Joel & Seppi, Duane J., 2001. "Common factors in prices, order flows, and liquidity," Journal of Financial Economics, Elsevier, vol. 59(3), pages 383-411, March.
    6. Jones, Charles M. & Lipson, Marc L., 1999. "Execution Costs of Institutional Equity Orders," Journal of Financial Intermediation, Elsevier, vol. 8(3), pages 123-140, July.
    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.
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    More about this item

    Keywords

    optimal execution; market impact; ordinary differential equations;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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