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Bypassing the truncation problem of truncated Lévy flights

Author

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  • Matsushita, Raul
  • Da Silva, Sergio
  • Da Fonseca, Regina
  • Nagata, Mateus

Abstract

We suggest a solution to the problem of truncation of truncated Lévy flights by deductively finding a power law between the truncation length and its standard deviation. We offer a generalization where the pdf of returns is left unknown, and its distributional moments are allowed to vary in time. Our model fits well with a financial dataset, which exhibits extreme moves.

Suggested Citation

  • Matsushita, Raul & Da Silva, Sergio & Da Fonseca, Regina & Nagata, Mateus, 2020. "Bypassing the truncation problem of truncated Lévy flights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    • Handle: RePEc:eee:phsmap:v:559:y:2020:i:c:s0378437120305392
    DOI: 10.1016/j.physa.2020.125035
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    References listed on IDEAS

    as
    1. Matsushita, Raul & Rathie, Pushpa & Da Silva, Sergio, 2003. "Exponentially damped Lévy flights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 326(3), pages 544-555.
    2. Adrian Dragulescu & Victor Yakovenko, 2002. "Probability distribution of returns in the Heston model with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 443-453.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. Mazzeu, Joao & Otuki, Thiago & Da Silva, Sergio, 2011. "The canonical econophysics approach to the flash crash of May 6, 2010," MPRA Paper 29138, University Library of Munich, Germany.
    5. Mantegna, Rosario N. & Stanley, H.Eugene, 1998. "Modeling of financial data: Comparison of the truncated Lévy flight and the ARCH(1) and GARCH(1,1) processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 254(1), pages 77-84.
    6. repec:ebl:ecbull:v:7:y:2002:i:3:p:1-12 is not listed on IDEAS
    7. Sergio Da Silva & Raul Matsushita & Iram Gleria, 2002. "Scaling power laws in the Sao Paulo Stock Exchange," Economics Bulletin, AccessEcon, vol. 7(3), pages 1-12.
    8. Gupta, Hari M. & Campanha, José R., 1999. "The gradually truncated Lévy flight for systems with power-law distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 268(1), pages 231-239.
    9. Parameswaran Gopikrishnan & Martin Meyer & Luis A Nunes Amaral & H Eugene Stanley, 1998. "Inverse Cubic Law for the Probability Distribution of Stock Price Variations," Papers cond-mat/9803374, arXiv.org, revised May 1998.
    10. P. Gopikrishnan & M. Meyer & L.A.N. Amaral & H.E. Stanley, 1998. "Inverse cubic law for the distribution of stock price variations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 3(2), pages 139-140, July.
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    1. Matsushita, Raul & Brandão, Helena & Nobre, Iuri & Da Silva, Sergio, 2024. "Differential entropy estimation with a Paretian kernel: Tail heaviness and smoothing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 646(C).

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