Calibration of local volatility using the local and implied instantaneous variance

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.calibration; local volatility; implied volatility; Dupire formula; adjoint; instantaneous local variance;instantaneous implied variance; implied variance