Calibration of Local Volatility Using the Local and Implied Instantaneous Variance
Posted: 29 Jan 2009
Date Written: January 29, 2009
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
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