Ornstein–Uhlenbeck models are continuous-time processes which have broad applications in finance as, e.g., volatility processes in stochastic volatility models or spread models in spread options and pairs trading. The paper presents a least squares estimator for the model parameter in a...

In this paper we study the extremal behavior of a stationary continuous-time moving average process for , where f is a deterministic function and L is a Lévy process whose increments, represented by L(1), are subexponential and in the maximum domain of attraction of the Gumbel distribution. We...

The paper presents a cointegration model in continuous time, where the linear combinations of the integrated processes are modeled by a multivariate Ornstein–Uhlenbeck process. The integrated processes are defined as vector-valued Lévy processes with an additional noise term. Hence, if we...

In this paper we consider a continuous-time autoregressive moving average (CARMA) process (Yt)t∈R driven by a symmetric α-stable Lévy process with α∈(0,2] sampled at a high-frequency time-grid {0,Δn,2Δn,…,nΔn}, where the observation grid gets finer and the last observation tends to...