Qualitative and quantitative properties of the Cornish-Fisher-Expansion in the context of Delta-Gamma-Normal approaches to the computation of Value at Risk are presented. Some qualitative deficiencies of the Cornish-Fisher-Expansion - the monotonicity of the distribution function as well as...

We establish a relation between stochastic volatility models and the class of generalized hyperbolic distributions. These distributions have been found to fit exceptionally well to the empirical distribution of stock returns. We review the background of hyperbolic distributions and prove...

We propose a new method of tail analysis for data featuring a high degree of leptokurtosis. Heavy tails can typically be found in financial series, like for example, the stock returns or durations between arrivals of trades. In our framework, the shape of tails can be assessed by fitting some...

We consider density pointwise estimation and look for best attainable asymptotic rates of convergence. The problem is adaptive, which means that the regularity parameter, β, describing the class of densities, varies in a set B. We shall consider, successively, two classes of densities, issued...

We consider chi-squared type tests for testing the hypothesis H 0 that a density f of observations X1,..., Xn lies in a parametric class of densities F. We consider a version of chi-squared type test using kernel estimates for the density. The main result is, following Liero, Läuter and Konakov...

For the problems of nonparametric estimation of nonincreasing and symmetric unimodal density functions with bounded supports we determine the projections of estimates onto the convex families of possible parent densities with respect to the weighted integrated squared error. We also describe the...