Local volatility calibration for convenient choices of variables
Within the framework of the calibration of the local volatility, we analyse the effect of the change of variables. Lead by theoretical results we proposed in a recent publication the use of local and implied instantaneous variances instead of the (local volatility, price) couple. The theoretical results were confirmed 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.
Illiquid FOREX options
This work, in collaboration with Marc Laillat from Thomson Reuters, concerns the pricing of illiquid FOREX cross-currency options. We propose and numerically solve the associated 2D Black-Scholes equation. As a technical point the boundary conditions are approximated through an analytical formula.
