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Elements for a theory of financial risks

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  • Jean-Philippe Bouchaud

    (Science & Finance, Capital Fund Management
    CEA Saclay;)

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    Abstract

    Estimating and controlling large risks has become one of the main concern of financial institutions. This requires the development of adequate statistical models and theoretical tools (which go beyond the traditionnal theories based on Gaussian statistics), and their practical implementation. Here we describe three interrelated aspects of this program: we first give a brief survey of the peculiar statistical properties of the empirical price fluctuations. We then review how an option pricing theory consistent with these statistical features can be constructed, and compared with real market prices for options. We finally argue that a true `microscopic' theory of price fluctuations (rather than a statistical model) would be most valuable for risk assessment. A simple Langevin-like equation is proposed, as a possible step in this direction.

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    Bibliographic Info

    Paper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 500042.

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    Date of creation: Jun 1998
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    Publication status: Forthcoming in `Order, Chance and Risk', Les Houches (March 1998), to be published by Springer/EDP Sciences
    Handle: RePEc:sfi:sfiwpa:500042

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    References

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    1. P. Bak & M. Paczuski & Martin Shubik, 1996. "Price Variations in a Stock Market with Many Agents," Cowles Foundation Discussion Papers 1132, Cowles Foundation for Research in Economics, Yale University.
    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. Jean-Philippe Bouchaud & Rama Cont, 1998. "A Langevin approach to stock market fluctuations and crashes," Science & Finance (CFM) working paper archive 500027, Science & Finance, Capital Fund Management.
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    Cited by:
    1. Jean-Philippe Bouchaud & Marc Potters, 1998. "Back to basics: historical option pricing revisited," Science & Finance (CFM) working paper archive 500036, Science & Finance, Capital Fund Management.
    2. Z. Eisler & J. Kertész, 2006. "Size matters: some stylized facts of the stock market revisited," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 51(1), pages 145-154, 05.
    3. M. Sysi-Aho & A. Chakraborti & K. Kaski, 2003. "Intelligent minority game with genetic crossover strategies," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 34(3), pages 373-377, August.
    4. M. Boguñá & J. Masoliver, 2004. "Conditional dynamics driving financial markets," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 40(3), pages 347-352, August.
    5. A. Svorenčík & F. Slanina, 2007. "Interacting gaps model, dynamics of order book, and stock-market fluctuations," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 57(4), pages 453-462, 06.
    6. F. Slanina, 2008. "Critical comparison of several order-book models for stock-market fluctuations," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 61(2), pages 225-240, 01.
    7. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
    8. G. Bonanno & D. Valenti & B. Spagnolo, 2006. "Role of noise in a market model with stochastic volatility," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 53(3), pages 405-409, October.

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