Estimation the vasicek interest rate model driven by fractional Lévy processes with application

In this article, we present that fractional Lévy processes which is very an important field in both probability theory and its application in recent years. The fractional Brownian motion is suggested as the fractional Lévy processes in this article. We will make parameters estimate of the Vasicek process driven by fractional Brownian motion, that represented the short memory parameter (0 < H < ½) and the long memory parameter (½ < H < 1). So, Our aim is to study the behavior of stochastitc Vasicek Interest driven by fractional Brownian motion. We use maximum likelihood to estimate the drift, diffusion and Hurst parameters and generally the fractional Lévy processes. We illustrate our methods, and show the behavior of stochastic parameters using simulation and real data (ISX60). (paper)