@techreport{During2006Seque-521,
  year={2006},
  series={CoFE-Diskussionspapiere / Zentrum für Finanzen und Ökonometrie},
  title={A Sequential Quadratic Programming Method For Volatility Estimation In Option Pricing},
  number={2006/02},
  author={Düring, Bertram and Jüngel, Ansgar and Volkwein, Stefan}
}

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    <dc:contributor>Volkwein, Stefan</dc:contributor>
    <dc:creator>Düring, Bertram</dc:creator>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-22T17:44:54Z</dc:date>
    <dc:contributor>Jüngel, Ansgar</dc:contributor>
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    <dcterms:abstract xml:lang="eng">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, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian { to ensure that every SQP step is a descent direction { and implement a line search strategy. In each level of the SQP method a linear{quadratic optimal control problem with box constraints is solved by a primal{dual active set strategy. This guarantees L1 constraints for the volatility, in particular assuring its positivity. The proposed algorithm is founded on a thorough first{ and second{order optimality analysis. We prove the existence of local optimal solutions and of a Lagrange multiplier associated with the inequality constraints. Furthermore, we prove a sufficient second-order optimality condition and present some numerical results underlining the good properties of the numerical scheme.</dcterms:abstract>
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