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

Quaderni DSE Working Paper No. 797

16 Pages Posted: 25 Nov 2011

See all articles by Massimiliano Marzo

Massimiliano Marzo

Department of Management, University of Bologna

Daniele Ritelli

University of Bologna - Department of Mathematics for Economic and Social Sciences

Paolo Zagaglia

University of Bologna; Rimini Centre for Economic Analysis

Date Written: November 25, 2011

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.

Keywords: optimal execution, market impact, trading strategy

JEL Classification: G11, G12

Suggested Citation

Marzo, Massimiliano and Ritelli, Daniele and Zagaglia, Paolo, Optimal Trading Execution with Nonlinear Market Impact: An Alternative Solution Method (November 25, 2011). Quaderni DSE Working Paper No. 797. Available at SSRN: https://ssrn.com/abstract=1964660 or http://dx.doi.org/10.2139/ssrn.1964660

Massimiliano Marzo (Contact Author)

Department of Management, University of Bologna ( email )

34, Via Capo di Lucca
Bologna, Bologna 40126
Italy
0512098091 (Phone)

Daniele Ritelli

University of Bologna - Department of Mathematics for Economic and Social Sciences ( email )

Piazza Scaravilli 2
40139 Bologna
Italy

Paolo Zagaglia

University of Bologna ( email )

Via degli Ariani 1
Ravenna, 48121
Italy

Rimini Centre for Economic Analysis ( email )

Rimini
Italy

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