Optimal Trading Execution with Nonlinear Market Impact: An Alternative Solution Method
Quaderni DSE Working Paper No. 797
16 Pages Posted: 25 Nov 2011
Date Written: November 25, 2011
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
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