Non-parametric news impact curve: a variational approach

In this paper, we propose an innovative algorithm for modelling the news impact curve. The news impact curve provides a nonlinear relation between past returns and current volatility and thus enables to forecast volatility. Our news impact curve is the solution of a dynamic optimization problem based on variational calculus. Consequently, it is a non-parametric and smooth curve. The technique we propose is directly inspired from noise removal techniques in signal theory. To our knowledge, this is the first time that such a method is used for volatility modelling. Applications on simulated heteroskedastic processes as well as on financial data show a better accuracy in estimation and forecast for this approach than for standard parametric (symmetric or asymmetric ARCH) or non-parametric (Kernel-ARCH) econometric techniques.