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Sequential quadratic programming method for volatility estimation in option pricing

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Datum

2008

Autor:innen

Düring, Bertram
Jüngel, Ansgar

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http://nbn-resolving.de/urn:nbn:de:bsz:352-186643
DOI (zitierfähiger Link)
https://doi.org/10.1007/s10957-008-9404-4
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Mathematik und Statistik: Publikationen
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Journal of Optimization Theory and Applications. 2008, 139(3), pp. 515-540. ISSN 0022-3239. Available under: doi: 10.1007/s10957-008-9404-4

Zusammenfassung

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.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

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

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ISO 690DÜRING, Bertram, Ansgar JÜNGEL, Stefan VOLKWEIN, 2008. Sequential quadratic programming method for volatility estimation in option pricing. In: Journal of Optimization Theory and Applications. 2008, 139(3), pp. 515-540. ISSN 0022-3239. Available under: doi: 10.1007/s10957-008-9404-4
BibTex
@article{During2008Seque-18664,
  year={2008},
  doi={10.1007/s10957-008-9404-4},
  title={Sequential quadratic programming method for volatility estimation in option pricing},
  number={3},
  volume={139},
  issn={0022-3239},
  journal={Journal of Optimization Theory and Applications},
  pages={515--540},
  author={Düring, Bertram and Jüngel, Ansgar and Volkwein, Stefan}
}
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