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Computation Of Local Volatilities From Regularized Dupire Equations

Author

Listed:
  • MARTIN HANKE

    (Fachbereich Mathematik, Johannes Gutenberg-Universität, 55099 Mainz, Germany)

  • ELISABETH RÖSLER

    (Fachbereich Mathematik, Johannes Gutenberg-Universität, 55099 Mainz, Germany)

Abstract

We propose a new method to calibrate the local volatility function of an asset from observed option prices of the underlying. Our method is initialized with a preprocessing step in which the given data are smoothened using cubic splines before they are differentiated numerically. In a second step the Dupire equation is rewritten as a linear equation for a rational expression of the local volatility. This equation is solved with Tikhonov regularization, using some discrete gradient approximation as penalty term. We show that this procedure yields local volatilities which appear to be qualitatively correct.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:02:n:s0219024905002950
    DOI: 10.1142/S0219024905002950
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    Cited by:

    1. Kathrin Hellmuth & Christian Klingenberg, 2022. "Computing Black Scholes with Uncertain Volatility-A Machine Learning Approach," Papers 2202.07378, arXiv.org.
    2. Elyas Elyasiani & Silvia Muzzioli & Alessio Ruggieri, 2016. "Forecasting and pricing powers of option-implied tree models: Tranquil and volatile market conditions," Department of Economics 0099, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    3. 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.
    4. Abdulwahab Animoku & Ömür Uğur & Yeliz Yolcu-Okur, 2018. "Modeling and implementation of local volatility surfaces in Bayesian framework," Computational Management Science, Springer, vol. 15(2), pages 239-258, June.

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