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Optimal Execution of Derivatives: A Taylor Expansion Approach

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Optimization, Control, and Applications of Stochastic Systems

Part of the book series: Systems & Control: Foundations & Applications ((SCFA))

Abstract

In this chapter, we derive the Markowitz-optimal trading trajectory for a trader who wishes to sell a large position of Kunits on some contingent claim. To do so, we first use a Taylor expansion of the derivative with respect to the price of the underlying asset at time zero. We then use up to the second-order approximation to solve the mean-variance optimization problem.

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Acknowledgements

The authors were partially supported by Algorithmic Trading Management LLC.

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Authors and Affiliations

  1. Statistics Department, Columbia University, New York, NY, 10027, USA

    Gerardo Hernandez-del-Valle

  2. Cornell University, Theca, NY, 14853, USA

    Yuemeng Sun

Authors
  1. Gerardo Hernandez-del-Valle
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  2. Yuemeng Sun
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Corresponding author

Correspondence to Gerardo Hernandez-del-Valle .

Editor information

Editors and Affiliations

  1. , Department of Probability and Statistics, Center for Research in Mathematics, Jalisco s/n, Guanajuato, 36000, Mexico

    Daniel Hernández-Hernández

  2. , Department of Mathematics, University of Sonora, Rosales s/n, Hermosillo, 83000, Sonora, Mexico

    J. Adolfo Minjárez-Sosa

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Hernandez-del-Valle, G., Sun, Y. (2012). Optimal Execution of Derivatives: A Taylor Expansion Approach. In: Hernández-Hernández, D., Minjárez-Sosa, J. (eds) Optimization, Control, and Applications of Stochastic Systems. Systems & Control: Foundations & Applications. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8337-5_9

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