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Calibration of the subdiffusive arithmetic Brownian motion with tempered stable waiting-times

Author

Listed:
  • Sebastian, Orzeł
  • Agnieszka, Wyłomańska

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 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 arithmetic Brownian motion. 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.

Suggested Citation

  • Sebastian, Orzeł & Agnieszka, Wyłomańska, 2010. "Calibration of the subdiffusive arithmetic Brownian motion with tempered stable waiting-times," MPRA Paper 28593, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:28593
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    References listed on IDEAS

    as
    1. Sebastian Orzel & Aleksander Weron, 2009. "Calibration of the subdiffusive Black–Scholes model," HSC Research Reports HSC/09/02, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    2. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook0501, December.
    3. Borak, Szymon & Härdle, Wolfgang Karl & Weron, Rafał, 2005. "Stable distributions," SFB 649 Discussion Papers 2005-008, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    4. Marcin Magdziarz & Sebastian Orzel & Aleksander Weron, 2011. "Option pricing in subdiffusive Bachelier model," HSC Research Reports HSC/11/05, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    5. Sokolov, I.M & Chechkin, A.V & Klafter, J, 2004. "Fractional diffusion equation for a power-law-truncated Lévy process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 245-251.
    6. Rosinski, Jan, 2007. "Tempering stable processes," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 677-707, June.
    7. Janczura, Joanna & Wyłomańska, Agnieszka, 2009. "Subdynamics of financial data from fractional Fokker-Planck equation," MPRA Paper 30649, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Subdiffusion; Tempered stable distribution; Calibration;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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