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Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing

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  • B. Düring

    (Vienna University of Technology)

  • A. Jüngel

    (Vienna University of Technology)

  • S. Volkwein

    (University of Graz)

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, 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.

Suggested Citation

  • B. Düring & A. Jüngel & S. Volkwein, 2008. "Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing," Journal of Optimization Theory and Applications, Springer, vol. 139(3), pages 515-540, December.
    • Handle: RePEc:spr:joptap:v:139:y:2008:i:3:d:10.1007_s10957-008-9404-4
    DOI: 10.1007/s10957-008-9404-4
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    References listed on IDEAS

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    1. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    2. Ronald Lagnado & Stanley Osher, "undated". "A Technique for Calibrating Derivative Security Pricing Models: Numerical Solution of an Inverse Problem," Computing in Economics and Finance 1997 101, Society for Computational Economics.
    3. Martin Hanke & Elisabeth Rösler, 2005. "Computation Of Local Volatilities From Regularized Dupire Equations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 207-221.
    4. Yves Achdou & Olivier Pironneau, 2002. "Volatility Smile By Multilevel Least Square," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(06), pages 619-643.
    5. 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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