A Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing

27 Pages Posted: 14 May 2007

See all articles by Bertram Düring

Bertram Düring

University of Warwick - Mathematics Institute

Ansgar Jüngel

Fachbereich Mathematik und Informatik, University of Mainz

Stefan Volkwein

University of Graz

Date Written: March 29, 2006

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, 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 L^1 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.

Keywords: Dupire equation, parameter identification, optimal control, optimality

JEL Classification: G13, C61

Suggested Citation

Düring, Bertram and Jüngel, Ansgar and Volkwein, Stefan, A Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing (March 29, 2006). Available at SSRN: https://ssrn.com/abstract=928219 or http://dx.doi.org/10.2139/ssrn.928219

Bertram Düring (Contact Author)

University of Warwick - Mathematics Institute ( email )

Zeeman Building
Coventry, CV4 7AL
United Kingdom

Ansgar Jüngel

Fachbereich Mathematik und Informatik, University of Mainz ( email )

D-55099 Mainz
Germany

Stefan Volkwein

University of Graz ( email )

A-8010 Graz
Austria

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