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


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.


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


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© 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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