The use of time-inhomogeneous additive models in option pricing has gained attention in recent years due to their potential to adequately price options across both strike and maturity with relatively few parameters. In this thesis two such classes of models based on the selfsimilar additive processes of Sato are developed.
One class of models consists of the risk-neutral exponentials of a selfsimilar additive process, while the other consists of the risk-neutral exponentials of a Brownian motion time-changed by an independent, increasing, selfsimilar additive process. Examples from each class are constructed in which the time one distributions are Variance Gamma or Normal Inverse Gaussian distributed. Pricing errors are assessed for the case of Standard and Poor's 500 index options from the year 2005. Both sets of time-inhomogeneous additive models show dramatic improvement in pricing error over their associated Lévy processes. Furthermore, with regard to the
average of the pricing errors over the quote dates studied, the selfsimilar Normal Inverse Gaussian model yields a mean pricing error significantly less than that implied by the bid-ask spreads of the options, and also significantly less than that given by its associated, less parsimonious, Lévy stochastic volatility model.
