On estimation of diffusion processes driven by alpha-stable Levy-motions

by Miklos Veber (Budapest)

In this presentation we investigate how to give estimations for the parameters of stochastic differential equations describing stock prices.

It has become clear by now, that the chaotic features of stock prices can not be modelled appropriately by the standard Brownian-motion. Alpha-stable Levy-processes, which do not have their second moments and therefore hit extremal values with higher probabilities than the standard Brownian-motion, seem to be more appropriate candidates for this purpose.

Processes described by linear stochastic differential equations which are driven by these alpha-stable processes approximate real stock prices more adequately than the formerly applied standard geometric Brownian- motion.

Now our task as well as the main goal of the presentation is to give an appropriate estimation of the parameters for which we use the maximum likelihood method.