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

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  • Joanna Janczura
  • Sebastian Orzel
  • Agnieszka Wylomanska

Abstract

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.

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File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_11_03.pdf
File Function: Original version, 2011
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Bibliographic Info

Paper provided by Hugo Steinhaus Center, Wroclaw University of Technology in its series HSC Research Reports with number HSC/11/03.

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Length: 13 pages
Date of creation: 2011
Date of revision:
Publication status: Published in Physica A 390 (2011) 4379–4387.
Handle: RePEc:wuu:wpaper:hsc1103

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Keywords: Vasicek model; Ornstein-Uhlenbeck process; Alpha-stable distribution; Subdiffusion; Estimation; Calibration; Interest rates;

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References

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  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.
  2. Burnecki, Krzysztof & Janczura, Joanna & Weron, Rafal, 2010. "Building Loss Models," MPRA Paper 25492, University Library of Munich, Germany.
  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.
  4. Young Kim & Svetlozar Rachev & Michele Bianchi & Frank Fabozzi, 2009. "Computing VAR and AVaR in Infinitely Divisible Distributions," Yale School of Management Working Papers amz2569, Yale School of Management.
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