Christian ROBERT (Université Lyon 1) « How large is the jump discontinuity in the diffusion coefficient of an Itô diffusion?”
Time: 3:30 pm – 4:30 pm
Date: 04th of March 2019
Place: Room 3105
Abstract : We consider high frequency observations from a one-dimensional diffusion process Y. We assume that the diffusion coefficient σ is continuously differentiable, but with a jump discontinuity at some levely. Such a diffusion has already been considered as a local volatility model for the underlying price of an asset, but raises several issues for pricing European options or for hedging such derivatives. We introduce kernel sign-constrained estimators of the left and right limits of σ at y, but up to constant factors. We present and discuss the asymptotic properties of these kernel estimators. We then propose a method to evaluate these constant factors by looking for bandwiths for which the kernel estimators are stable by iteration. We finally provide an estimator of the jump discontinuity size and discuss its convergence rate.