Let (Mn,Qn)n∈N be an i.i.d. sequence in R2. Much attention has been paid to causal strictly stationary solutions of the random recurrence equation Xn=MnXn−1+Qn, n∈N, i.e. to strictly stationary solutions of this equation when X0 is assumed to be independent of (Mn,Qn)n∈N. Goldie and...

We characterize convergence of a sequence of d-dimensional random vectors by convergence of the one-dimensional margins and of the copula. The result is applied to the approximation of portofolio modelled by t-copulas with large degrees of freedom, and to the convergence of certain dependence...

Empirical volatility changes in time and exhibits tails, which are heavier than normal. Moreover, empirical volatility has - sometimes quite substantial - upwards jumps and clusters on high levels. We investigate classical and nonclassical stochastic volatility models with respect to their...

We use a discrete time analysis, giving necessary and sufficient conditions for the almost sure convergence of ARCH(1) and GARCH(1,1) discrete time models, to suggest an extension of the (G)ARCH concept to continuous time processes. Our COGARCH (continuous time GARCH) model, based on a single...

We compare the probabilistic properties of the non-Gaussian Ornstein-Uhlenbeck based stochastic volatility model of Barndorff-Nielsen and Shephard (2001) with those of the COGARCH process. The latter is a continuous time GARCH process introduced by the authors (2004). Many features are shown to...