The classical financial models are based on the standard Brownian diffusion-type
processes. However, in the exhibition of some real market data (like interest or
exchange rates) we observe characteristic periods of constant values. Moreover, in
the case of financial data, the assumption of normality is often unsatisfied. In such
cases the popular Vasicek model, that is a mathematical system describing the
evolution of interest rates based on the OrnsteinUhlenbeck process, seems not to be
applicable. Therefore, we propose an alternative approach based on a combination of
the popular OrnsteinUhlenbeck process with a stable distribution and subdiffusion
systems that demonstrate such characteristic behavior. The probability density
function of the proposed process can be described by a Fokker-Planck type equation
and therefore it can be examined as an extension of the basic OrnsteinUhlenbeck
model. In this paper, we propose the parameters estimation method and calibrate the
subordinated Vasicek model to the interest rate data.
