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Long Range Interaction Generating Fat-Tails in Finance

  • Marco Airoldi

    (MedioBanca)

  • 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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File URL: http://econwpa.repec.org/eps/ge/papers/0404/0404006.ps.gz
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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
Contact details of provider: Web page: http://econwpa.repec.org

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  1. Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
  2. Bak, P. & Paczuski, M. & Shubik, M., 1997. "Price variations in a stock market with many agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 430-453.
  3. Focardi, Sergio & Cincotti, Silvano & Marchesi, Michele, 2002. "Self-organization and market crashes," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 241-267, October.
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  6. 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.
  7. Pierre Cizeau & Marc Potters & Jean-Philippe Bouchaud, 2000. "Correlation structure of extreme stock returns," Science & Finance (CFM) working paper archive 0006034, Science & Finance, Capital Fund Management.
  8. 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.
  9. Damiano Brigo & Fabio Mercurio & Giulio Sartorelli, 2003. "Alternative asset-price dynamics and volatility smile," Quantitative Finance, Taylor & Francis Journals, vol. 3(3), pages 173-183.
  10. Fabrizio Lillo & Rosario N. Mantegna, 2000. "Variety and Volatility in Financial Markets," Papers cond-mat/0006065, arXiv.org.
  11. Jean-Philippe Bouchaud & Giulia Iori & Didier Sornette, 1995. "Real-world options: smile and residual risk," Science & Finance (CFM) working paper archive 500039, Science & Finance, Capital Fund Management.
  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. Lisa Borland, 2002. "A theory of non-Gaussian option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 415-431.
  14. Lisa Borland, 2002. "A Theory of Non_Gaussian Option Pricing," Papers cond-mat/0205078, arXiv.org, revised Dec 2002.
  15. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  16. Marco Airoldi, 2001. "Correlation Structure and Fat Tails in Finance: a New Mechanism," Papers cond-mat/0107593, arXiv.org.
  17. 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.
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