Calibration of Local Volatility Using the Local and Implied Instantaneous Variance

Posted: 29 Jan 2009  

Turinici M. Gabriel

CEREMADE, Université Paris Dauphine

Date Written: January 29, 2009

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.

Keywords: calibration, local volatility, implied volatility, Dupire formula, adjoint, instantaneous local variance, instantaneous implied variance, implied variance

JEL Classification: C63, C6

Suggested Citation

Gabriel, Turinici M., Calibration of Local Volatility Using the Local and Implied Instantaneous Variance (January 29, 2009). Available at SSRN: https://ssrn.com/abstract=1334870

Turinici M. Gabriel (Contact Author)

CEREMADE, Université Paris Dauphine ( email )

Place du Marechal de Lattre de Tassigny
Paris Cedex 16, 75775
France

HOME PAGE: http://www.ceremade.dauphine.Fr/~turinici

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