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Long Range Interaction Generating Fat-Tails in Finance

Author

Listed:
  • 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)

Abstract

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.

Suggested Citation

  • Marco Airoldi & Vito Antonelli & Bruno Bassetti & Andrea Martinelli & Marco Picariello, 2004. "Long Range Interaction Generating Fat-Tails in Finance," GE, Growth, Math methods 0404006, University Library of Munich, Germany, revised 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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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Mathematical models; quantitative finance; interactions and correlations;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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