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Subdynamics of financial data from fractional Fokker-Planck equation

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  • Janczura, Joanna
  • Wyłomańska, Agnieszka

Abstract

In exhibition of many real market data we observe characteristic traps. This behavior is especially noticeable for processes corresponding to stock prices. Till now, such economic systems were analyzed in the following manner: before the further investigation trap-data were removed or omitted and then the conventional methods used. Unfortunately, for many observations this approach seems not to be reasonable therefore we propose an alternative approach based on the subdiffusion models that demonstrate such characteristic behavior and their corresponding probability density function (pdf) is described by the fractional Fokker-Planck equation. In this paper we model market data using subdiffusion with a constant force. We demonstrate properties of the considered systems and propose estimation methods.

Suggested Citation

  • Janczura, Joanna & Wyłomańska, Agnieszka, 2009. "Subdynamics of financial data from fractional Fokker-Planck equation," MPRA Paper 30649, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:30649
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    File URL: https://mpra.ub.uni-muenchen.de/30649/1/MPRA_paper_30649.pdf
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    References listed on IDEAS

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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.
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    Cited by:

    1. Foad Shokrollahi & Marcin Marcin Magdziarz, 2020. "Equity warrant pricing under subdiffusive fractional Brownian motion of the short rate," Papers 2007.12228, arXiv.org, revised Nov 2020.
    2. 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.
    3. Dupret, Jean-Loup & Hainaut, Donatien, 2022. "A subdiffusive stochastic volatility jump model," LIDAM Discussion Papers ISBA 2022001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Kumar, A. & Wyłomańska, A. & Połoczański, R. & Sundar, S., 2017. "Fractional Brownian motion time-changed by gamma and inverse gamma process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 648-667.
    5. Xie, Jiaquan & Yao, Zhibin & Gui, Hailian & Zhao, Fuqiang & Li, Dongyang, 2018. "A two-dimensional Chebyshev wavelets approach for solving the Fokker-Planck equations of time and space fractional derivatives type with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 197-208.
    6. 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.
    7. Jabłońska-Sabuka, Matylda & Teuerle, Marek & Wyłomańska, Agnieszka, 2017. "Bivariate sub-Gaussian model for stock index returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 628-637.
    8. Jelena Ryvkina, 2015. "Fractional Brownian Motion with Variable Hurst Parameter: Definition and Properties," Journal of Theoretical Probability, Springer, vol. 28(3), pages 866-891, September.
    9. Anh, V.V. & Leonenko, N.N. & Sikorskii, A., 2017. "Stochastic representation of fractional Bessel-Riesz motion," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 135-139.
    10. Foad Shokrollahi, 2016. "Subdiffusive fractional Brownian motion regime for pricing currency options under transaction costs," Papers 1612.06665, arXiv.org, revised Aug 2017.
    11. Nikolai Leonenko & Ely Merzbach, 2015. "Fractional Poisson Fields," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 155-168, March.

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    More about this item

    Keywords

    subdiffusion; constant periods; fractional Fokker-Planck equation; stock prices;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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