A GENERAL ORNSTEIN–UHLENBECK STOCHASTIC VOLATILITY MODEL WITH LÉVY JUMPS

Abstract

We present a general class of stochastic volatility models with jumps where the stochastic variance process follows a Lévy-driven Ornstein–Uhlenbeck (OU) process and the jumps in the log-price process follow a Lévy process. This financial market model is a true extension of the Barndorff-Nielsen–Shephard (BNS) model class and can establish a weak link between log-price jumps and volatility jumps. Furthermore, we investigate the weak-link [Formula: see text]-OU-BNS model as a special case, where we calculate the characteristic function of the logarithmic price in closed form. The classical [Formula: see text]-OU-BNS model can be obtained as a limit of weak-link [Formula: see text]-OU-BNS models in the Skorokhod topology. We highlight that the weak-link property may be a useful model extension in the case of pricing barrier options.