Calibration of local volatility using the local and implied instantaneous variance

Gabriel Turinici

Abstract

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 approach. The procedure performs well on benchmarks from the literature and on foreign exchange data.