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Calibration of local volatility using the local and implied instantaneous variance

Author

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  • Gabriel Turinici

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

We document the calibration of the local volatility in terms of local and implied instantaneous variances; we first explore the theoretical properties of the method for a particular class of volatilities. We confirm the theoretical results through a numerical procedure which uses a Gauss-Newton style approximation of the Hessian in the framework of a sequential quadratic programming (SQP) approach. The procedure performs well on benchmarks from the literature and on FOREX data.

Suggested Citation

  • Gabriel Turinici, 2009. "Calibration of local volatility using the local and implied instantaneous variance," Post-Print hal-00338114, HAL.
    • Handle: RePEc:hal:journl:hal-00338114
    Note: View the original document on HAL open archive server: https://hal.science/hal-00338114v2
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    References listed on IDEAS

    as
    1. Lishang Jiang & Qihong Chen & Lijun Wang & Jin Zhang, 2003. "A new well-posed algorithm to recover implied local volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 451-457.
    2. Thomas F. Coleman & Yuying Li & Arun Verma, 2001. "Reconstructing The Unknown Local Volatility Function," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 7, pages 192-215, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Gabriel Turinici, 2009. "Robust recovery of the risk neutral probability density from option prices," Analele Stiintifice ale Universitatii "Alexandru Ioan Cuza" din Iasi - Stiinte Economice (1954-2015), Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, vol. 56, pages 197-201, November.
    2. F. Gerlich & A. Giese & J. Maruhn & E. Sachs, 2012. "Parameter identification in financial market models with a feasible point SQP algorithm," Computational Optimization and Applications, Springer, vol. 51(3), pages 1137-1161, April.
    3. Cristian Homescu, 2011. "Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance," Papers 1107.1831, arXiv.org.

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