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 consider a diffusion model of small variable type with positive drift density varying in a nonparametric set. We investigate Gaussian and Poisson approximations to this model. In the sense of asymptotic equivalence of experiments, it is shown that observation of the diffusion process until...

This paper studies the smooth transition regression model where regressors are I(1) and errors are I(0). The regressors and errors are assumed to be dependent both serially and contemporaneously. Using the triangular array asymptotics, the nonlinear least squares estimator is shown to be...

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...

In a complete financial market every contingent claim can be hedged perfectly. In an incomplete market it is possible to stay on the safe side by superhedging. But such strategies may require a large amount of initial capital. Here we study the question what an investor can do who is unwilling...

Stochastic Volatility (SV) models are widely used in financial applications. To decide whether standard parametric restrictions are justified for a given dataset, a statistical test is required. In this paper, we develop such a test based on the linear state space representation. We provide a...