Calibration of local volatility using the local and implied instantaneous variance
AbstractWe 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.
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Bibliographic InfoPaper provided by HAL in its series Post-Print with number hal-00338114.
Date of creation: 09 Dec 2009
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Publication status: Published, Journal of Computational Finance, 2009, 13, 2, 1--18
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calibration; local volatility; implied volatility; Dupire formula; adjoint; instantaneous local variance; instantaneous implied variance; implied variance;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-02-22 (All new papers)
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- 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.
- Cristian Homescu, 2011. "Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance," Papers 1107.1831, arXiv.org.
- 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.
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