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Journal of Optimization Theory and Applications

, Volume 139, Issue 3, pp 515–540 | Cite as

Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing

  • B. Düring
  • A. Jüngel
  • S. Volkwein
Article

Abstract

Our goal is to identify the volatility function in Dupire’s equation from given option prices. Following an optimal control approach in a Lagrangian framework, a globalized sequential quadratic programming (SQP) algorithm combined with a primal-dual active set strategy is proposed. Existence of local optimal solutions and of Lagrange multipliers is shown. Furthermore, a sufficient second-order optimality condition is proved. Finally, some numerical results are presented underlining the good properties of the numerical scheme.

Keywords

Dupire equation Parameter identification Optimal control Optimality conditions SQP method Primal-dual active set strategy 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Institute for Analysis and Scientific ComputingVienna University of TechnologyViennaAustria
  2. 2.Institute for Mathematics and Scientific ComputingUniversity of GrazGrazAustria

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