Valuation in a simplifiedBarndorff-Nielsen Shepard Model

Asset process driven by non-normal Lévy processes have become popular in the last few years. To be mentioned are models, where the asset processes are pure Lévy processes. Such models date back the work of Mandelbrot (1967). But also more complex models as for example stochastic volatility model of Barndorff-Nielsen and Shephard (2001) have been developed. This class of models, hereafter termed BN-S models, is constructed via a mean reverting, stationary process of the Ornstein Uhlenbeck type driven by a subordinator, à Lévy process with no Gaussian component and positive increments.[...] This model allows to deal with the so called leverage type problem, i.e. for equities a fall in the price is associated with an increase in future volatility.[...]