Calibration of the Subdiffusive Arithmetic Brownian Motion with Tempered Stable Waiting-Times

Article

Abstract

In the classical analysis many models used to real data description are based on the standard Brownian diffusion-type processes. However, some real data exhibit characteristic periods of constant values. In such cases the popular systems seem not to be applicable. Therefore we propose an alternative approach, based on the combination of the popular Brownian motion with drift (called also the arithmetic Brownian motion) and tempered stable subordinator. The probability density function of the proposed model can be described by a Fokker-Planck type equation and therefore it has many similar properties as the popular Brownian motion with drift. In this paper we propose the estimation procedure for the considered tempered stable subdiffusive arithmetic Brownian motion and calibrate the analyzed process to the real financial data.

Keywords

Subdiffusion Tempered stable distribution Calibration 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer Science, Hugo Steinhaus CenterWrocław University of TechnologyWrocławPoland

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