Title: Estimation and goodness-of-fit testing of Levy processes: The variance gamma process Authors:  Gerrit Grobler - North-West University (South Africa) [presenting]
Simos Meintanis - University of Athens (Greece)
Emanuele Taufer - University of Trento (Italy)
Denis Belomestny - Duisburg-Essen University (Germany)
Abstract: The price of financial securities, such as an exchange rate or a stock, is typically modelled as a continuous time stochastic process. Due to empirical evidence of infrequent large movements of security prices, processes that allow for jumps are increasingly popular models to use. A family of continuous time stochastic processes that allow for jumps are exponential Levy processes that generalize the classical geometric Brownian motion process. However, choosing a specific model from the large family of Levy processes requires model validation. A goodness-of-fit test of the variance gamma process that utilizes the analytical tractability of its characteristic function is presented. Since the estimation of this model is required to apply the test, estimation methods based on a likelihood approach as well as on the characteristic function will be discussed. In addition, the newly developed goodness-of-fit test will be applied to a variety of historically observed security prices.