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A theory of fluctuations in stock prices

Author

Listed:
  • Alejandro-Quiñones, Ángel L.
  • Bassler, Kevin E.
  • Field, Michael
  • McCauley, Joseph L.
  • Nicol, Matthew
  • Timofeyev, Ilya
  • Török, Andrew
  • Gunaratne, Gemunu H.

Abstract

The distribution of price returns is studied for a class of market models with Markovian dynamics. The models have a non-constant diffusion coefficient that depends on the value of the return. An analytical expression for the distribution of returns is obtained, and shown to match the results of computer simulations for two simple cases. Those two cases are shown to have exponential and “fat-tailed” power-law decaying distributions, respectively.

Suggested Citation

  • Alejandro-Quiñones, Ángel L. & Bassler, Kevin E. & Field, Michael & McCauley, Joseph L. & Nicol, Matthew & Timofeyev, Ilya & Török, Andrew & Gunaratne, Gemunu H., 2006. "A theory of fluctuations in stock prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 383-392.
    • Handle: RePEc:eee:phsmap:v:363:y:2006:i:2:p:383-392
    DOI: 10.1016/j.physa.2005.08.037
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    References listed on IDEAS

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    1. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    2. Rama Cont & Marc Potters & Jean-Philippe Bouchaud, 1997. "Scaling in stock market data: stable laws and beyond," Science & Finance (CFM) working paper archive 9705087, Science & Finance, Capital Fund Management.
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    Citations

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    Cited by:

    1. Giacomo Bormetti & Sofia Cazzaniga, 2014. "Multiplicative noise, fast convolution and pricing," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 481-494, March.
    2. Giacomo Bormetti & Sofia Cazzaniga, 2011. "Multiplicative noise, fast convolution, and pricing," Papers 1107.1451, arXiv.org.
    3. Marcin Wk{a}torek & Jaros{l}aw Kwapie'n & Stanis{l}aw Dro.zd.z, 2021. "Financial Return Distributions: Past, Present, and COVID-19," Papers 2107.06659, arXiv.org.
    4. Olkhov, Victor, 2018. "Expectations, Price Fluctuations and Lorenz Attractor," MPRA Paper 89105, University Library of Munich, Germany.
    5. Bucsa, G. & Jovanovic, F. & Schinckus, C., 2011. "A unified model for price return distributions used in econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3435-3443.
    6. Bassler, Kevin E. & McCauley, Joseph L. & Gunaratne, Gemunu H., 2006. "Nonstationary increments, scaling distributions, and variable diffusion processes in financial markets," MPRA Paper 2126, University Library of Munich, Germany.
    7. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    8. Hua, Jia-Chen & Chen, Lijian & Falcon, Liberty & McCauley, Joseph L. & Gunaratne, Gemunu H., 2015. "Variable diffusion in stock market fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 221-233.

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