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Subordinated α-stable Ornstein–Uhlenbeck process as a tool for financial data description


  • Janczura, Joanna
  • Orzeł, Sebastian
  • Wyłomańska, Agnieszka


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 Vasiček 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 Vasiček model to the interest rate data.

Suggested Citation

  • Janczura, Joanna & Orzeł, Sebastian & Wyłomańska, Agnieszka, 2011. "Subordinated α-stable Ornstein–Uhlenbeck process as a tool for financial data description," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4379-4387.
  • Handle: RePEc:eee:phsmap:v:390:y:2011:i:23:p:4379-4387 DOI: 10.1016/j.physa.2011.07.007

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    References listed on IDEAS

    1. 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, June.
    2. Krzysztof Burnecki & Joanna Janczura & Rafal Weron, 2010. "Building Loss Models," HSC Research Reports HSC/10/03, Hugo Steinhaus Center, Wroclaw University of Technology.
    3. Szymon Borak & Adam Misiorek & Rafał Weron, 2010. "Models for Heavy-tailed Asset Returns," SFB 649 Discussion Papers SFB649DP2010-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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    Cited by:

    1. Foad Shokrollahi, 2016. "Subdiffusive fractional Brownian motion regime for pricing currency options under transaction costs," Papers 1612.06665,, revised Aug 2017.
    2. Gu, Hui & Liang, Jin-Rong & Zhang, Yun-Xiu, 2012. "Time-changed geometric fractional Brownian motion and option pricing with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3971-3977.


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