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Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing

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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.

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Authors and Affiliations

  1. Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 1040, Vienna, Austria

    B. Düring & A. Jüngel

  2. Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010, Graz, Austria

    S. Volkwein

Authors
  1. B. Düring
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  2. A. Jüngel
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  3. S. Volkwein
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Corresponding author

Correspondence to B. Düring.

Additional information

Communicated by H.J. Pesch.

The first and second author acknowledge partial support from the Deutsche Forschungsgemeinschaft, Grant JU 359/6 (Forschergruppe 518). The second author was supported partially by the Wissenschaftskolleg “Differential Equations”, funded by Fonds zur Förderung der wissenschaftlichen Forschung (FWF). The first author was supported in part by the FWF under the Special Research Center F003 “Optimization and Control”. This research is part of the ESF Program “Global and geometrical aspects of nonlinear partial differential equations (GLOBAL)”.

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Düring, B., Jüngel, A. & Volkwein, S. Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing. J Optim Theory Appl 139, 515–540 (2008). https://doi.org/10.1007/s10957-008-9404-4

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