Subordinated alpha-stable Ornstein-Uhlenbeck process as a tool for financial data description
The classical financial models are based on the standard Brownian diffusion-type processes. However, in 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 Ornstein-Uhlenbeck process, seems not to be applicable. Therefore we propose an alternative approach based on a combination of the popular Ornstein-Uhlenbeck 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 Ornstein-Uhlenbeck model. In this paper we propose the parameters' estimation method and calibrate the subordinated Vasicek model to the interest rate data.
|Date of creation:||2011|
|Publication status:||Published in Physica A 390 (2011) 4379–4387.|
|Contact details of provider:|| Postal: Wybrzeze Wyspianskiego 27, 50-370 Wroclaw|
Web page: http://prac.im.pwr.wroc.pl/~hugo
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- Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
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- Borak, Szymon & Misiorek, Adam & Weron, Rafal, 2010. "Models for Heavy-tailed Asset Returns," MPRA Paper 25494, University Library of Munich, Germany.
- Szymon Borak & Adam Misiorek & Rafal Weron, 2010. "Models for Heavy-tailed Asset Returns," HSC Research Reports HSC/10/01, Hugo Steinhaus Center, Wroclaw University of Technology.
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