A Sequential Quadratic Programming Method For Volatility Estimation In Option Pricing

Düring, Bertram; Jüngel, Ansgar; Volkwein, Stefan

A Sequential Quadratic Programming Method For Volatility Estimation In Option Pricing

Dateien

dp06_02.pdfGröße: 476.27 KBDownloads: 573

Datum

2006

Autor:innen

Düring, Bertram

Jüngel, Ansgar

Volkwein, Stefan

Schriftenreihe

CoFE-Diskussionspapiere / Zentrum für Finanzen und Ökonometrie

URI (zitierfähiger Link)

http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-18793

Link zur Lizenz

Urheberrechtlich geschützt

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Mathematik und Statistik

Publikationstyp

Working Paper/Technical Report

Publikationsstatus

Published

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, 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.

Fachgebiet (DDC)

330 Wirtschaft

Schlagwörter

option pricing

Zitieren

ISO 690

DÜRING, Bertram, Ansgar JÜNGEL, Stefan VOLKWEIN, 2006. A Sequential Quadratic Programming Method For Volatility Estimation In Option Pricing

BibTex

@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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Universitätsbibliographie

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