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A Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing

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Author Info

  • Bertram Düring

    ()
    (University of Mainz)

  • Ansgar Jüngel

    ()
    (University of Mainz)

  • S. Volkwein

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 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.

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Bibliographic Info

Paper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 06-02.

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Length: 27 pages
Date of creation: 29 Mar 2006
Date of revision:
Handle: RePEc:knz:cofedp:0602

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Related research

Keywords: Dupire equation; parameter identification; optimal control; optimality conditions; SQP method; primal-dual active set strategy;

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  1. Marco Avellaneda & Craig Friedman & Richard Holmes & Dominick Samperi, 1997. "Calibrating volatility surfaces via relative-entropy minimization," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 37-64.
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