Ferraty, Frédéric et Quintela-del-río, Alejandro, Conditional VAR and Expected Shortfall: A New Functional Approach, Econometric reviews , 35(2), 2016, pp. 263-292
We estimate two well-known risk measures, the value-at-risk (VAR) and the expected shortfall, conditionally to a functional variable (i.e., a random variable valued in some semi(pseudo)-metric space). We use nonparametric kernel estimation for constructing estimators of these quantities, under general dependence conditions. Theoretical properties are stated whereas practical aspects are illustrated on simulated data: nonlinear functional and GARCH(1,1) models. Some ideas on bandwidth selection using bootstrap are introduced. Finally, an empirical example is given through data of the S&P 500 time series.