Advertisement

Optimal Execution of Derivatives: A Taylor Expansion Approach

  • Gerardo Hernandez-del-Valle
  • Yuemeng Sun
Chapter
Part of the Systems & Control: Foundations & Applications book series (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.

Keywords

Contingent Claim Market Impact Optimal Trading Large Position Claim Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The authors were partially supported by Algorithmic Trading Management LLC.

References

  1. 1.
    A. Alfonsi, A. Fruth and A. Schied (2010). Optimal execution strategies in limit order books with general shape functions, Quantitative Finance, 10, no. 2, 143–157.MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    A. Alfonsi and A. Schied (2010). Optimal trade execution and absence of price manipulations limit order books models, SIAM J. on Financial Mathematics, 1, pp. 490–522.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    R. Almgren and N. Chriss (1999). Value under liquidation, Risk, 12, pp. 61–63.Google Scholar
  4. 4.
    R. Almgren and N. Chriss (2000). Optimal execution of portfolio transactions, J. Risk, 3 (2), pp. 5–39.Google Scholar
  5. 5.
    R. Almgren and J. Lorenz (2007). Adaptive arrival price, Trading, no. 1, pp. 59–66.Google Scholar
  6. 6.
    D. Bertsimas and D. Lo (1998). Optimal control of execution costs, Journal of Financial Markets, 1(1), pp. 1–50.CrossRefGoogle Scholar
  7. 7.
    P.A. Forsyth (2011). Hamilton Jacobi Bellman approach to optimal trade schedule, Journal of Applied Numerical Mathematics, 61(2), pp. 241–265.MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    A. Obizhaeva, and J. Wang (2006). Optimal trading strategy and supply/demand dynamics. Journal of Financial Markets, forthcoming.Google Scholar
  9. 9.
    A. Schied, T. Schöneborn and M. Tehranchi (2010). Optimal basket liquidation for CARA investors is deterministic, Applied Mathematical Finance, 17, pp. 471–489.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Statistics DepartmentColumbia UniversityNew YorkUSA
  2. 2.Cornell UniversityThecaUSA

Personalised recommendations