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Long Range Interaction Generating Fat-Tails in Finance

Listed author(s):
  • Marco Airoldi


  • Vito Antonelli

    (Universita' degli Studi di Milano & INFN Milano)

  • Bruno Bassetti

    (Universita' degli Studi di Milano & INFN Milano)

  • Andrea Martinelli

    (Banca Intesa)

  • Marco Picariello

    (Universita' degli Studi di Milano & INFN Milano)

It's commonly known that the correlation between stocks increases during market turbulent periods. In this work we propose a modellization of this feature, viewed as a collective effect, rearranging a toy-model first proposed in 2001. Equities are modelled as quasi random walk variables, where the non-Brownian components of stocks movement are linked to the market trend via a long range interaction function. Our model generates fat tails for stock probability distributions and implied volatility surfaces analogous to real data, suggesting an unitary picture of long range interaction, fat tails and volatility smiles.

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Paper provided by EconWPA in its series GE, Growth, Math methods with number 0404006.

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Length: 13 pages
Date of creation: 27 Apr 2004
Date of revision: 27 Apr 2004
Handle: RePEc:wpa:wuwpge:0404006
Note: Type of Document - tar.gz; pages: 13. 13 pages, latex, 7 figures
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  8. Zhi-Feng Huang & Sorin Solomon, 2001. "Finite market size as a source of extreme wealth inequality and market instability," Papers cond-mat/0103170,
  9. J-P. Bouchaud & I. Giardina & M. Mzard, 2001. "On a universal mechanism for long-range volatility correlations," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 212-216.
  10. Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
  11. Lisa Borland, 2002. "A Theory of Non_Gaussian Option Pricing," Papers cond-mat/0205078,, revised Dec 2002.
  12. Kaizoji, Taisei & Bornholdt, Stefan & Fujiwara, Yoshi, 2002. "Dynamics of price and trading volume in a spin model of stock markets with heterogeneous agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 441-452.
  13. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
  14. Huang, Zhi-Feng & Solomon, Sorin, 2001. "Finite market size as a source of extreme wealth inequality and market instability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 294(3), pages 503-513.
  15. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
  16. P. Cizeau & M. Potters & J-P. Bouchaud, 2001. "Correlation structure of extreme stock returns," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 217-222.
  17. Marco Airoldi, 2001. "Correlation Structure and Fat Tails in Finance: a New Mechanism," Papers cond-mat/0107593,
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