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

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  • M. Marzo
  • D. Ritelli
  • P. Zagaglia

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 execution strategy of Almgren (2003) is based on the assumption that no shares per unit of time are trade at the beginning of the period. We use a general solution method that accomodates the case of positive initial trades. Our results 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 initial trading, the optimal execution time depends on trading activity in the initial period.

Suggested Citation

  • M. Marzo & D. Ritelli & P. Zagaglia, 2011. "Optimal Trading Execution with Nonlinear Market Impact: An Alternative Solution Method," Working Papers wp797, Dipartimento Scienze Economiche, Universita' di Bologna.
    • Handle: RePEc:bol:bodewp:wp797
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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.
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    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

    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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