In this study, we investigate the performance of different parametric models with stable and
tempered stable distributions for capturing the tail behaviour of log-returns (financial asset …

Constructing Lévy-driven Ornstein–Uhlenbeck processes is a task closely related to the
notion of self-decomposability. In particular, their transition laws are linked to the properties …

In this paper novel simulation methods are provided for the generalised inverse Gaussian
(GIG) Lévy process. Such processes are intractable for simulation except in certain special …

We introduce a methodology for the simulation and parameter estimation of multivariate
tempered stable distributions with an emphasis on the bivariate case. Our approach is …

Generalised hyperbolic (GH) processes are a class of stochastic processes that are used to
model the dynamics of a wide range of complex systems that exhibit heavy-tailed behavior …

We derive methods for risk-neutral pricing of multi-asset options, when log-returns jointly
follow a multivariate tempered stable distribution. These lead to processes that are more …

Abstract We study the Ornstein-Uhlenbeck process having a symmetric normal tempered
stable stationary law and represent its transition distribution in terms of the sum of …

We give an explicit representation for the transition law of a tempered stable Ornstein–
Uhlenbeck process and use it to develop a rejection sampling algorithm for exact simulation …

This paper analyzes various classes of processes associated with the tempered positive
Linnik (TPL) distribution. We provide several subordinated representations of TPL Lévy …

We discuss simulation schemes for continuous-time autoregressive moving average
(CARMA) processes driven by tempered stable L\'evy noises. CARMA processes are the …