A Langevin approach to stock market fluctuations and crashes

Jean-Philippe Bouchaud and Rama Cont
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Jean-Philippe Bouchaud: Science & Finance, Capital Fund Management
Rama Cont: Science & Finance, Capital Fund Management

No 500027, Science & Finance (CFM) working paper archive from Science & Finance, Capital Fund Management

Abstract: We propose a non linear Langevin equation as a model for stock market fluctuations and crashes. This equation is based on an identification of the different processes influencing the demand and supply, and their mathematical transcription. We emphasize the importance of feedback effects of price variations onto themselves. Risk aversion, in particular, leads to an up-down symmetry breaking term which is responsible for crashes, where `panic' is self reinforcing. It is also responsible for the sudden collapse of speculative bubbles. Interestingly, these crashes appear as rare, `activated' events, and have an exponentially small probability of occurence. We predict that the shape of the falldown of the price during a crash should be logarithmic. The normal regime, where the stock price exhibits behavior similar to that of a random walk, however reveals non trivial correlations on different time scales, in particular on the time scale over which operators perceive a change of trend.

JEL-codes: G10 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-fin and nep-fmk
Date: 1998-01
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Published in European Journal of Physics B 6, 543-550 (1998)

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Persistent link: http://EconPapers.repec.org/RePEc:sfi:sfiwpa:500027

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