Flash Crashes: The Role of Information Processing Based Subordination and the Cauchy Distribution in Market Instability

Edgar Parker


While a wide variety of hypotheses have been offered to explain the anomalous market phenomena known as a “Flash Crash”, there is as of yet no consensus among financial experts as to the sources of these sudden market collapses.  In contrast to the behavior expected from standard financial theory, both the equity and bond markets have been thrown into freefall in the absence of any significant news event.  The author posits that a combination of probability and information theory, and diffusion dynamics offers a relatively simple explanation of the causes of some of these dramatic events.  This new avenue of research also suggests new policies or measures to lower the probability of occurrence and to mitigate the effects of these extreme events.

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Bachelier, L. (1900). The theory of speculation, Annales Scientifiques de l’E´cole Normale Supe´rieure Se´r. 3(17), 21–86.

Bohacek, S., & Rozovskii, B. A. (2004). Diffusion model of roundtrip time. Computational Statistics and Data Analysis 45, 25-50.

Christian, S. (2005). Applications of physics to finance and economics: Returns, trading activity and income, Phd Thesis, Department of Physics, University of Maryland.

Clark, P. K. (1973). A subordinated stochastic process model with finite variance for speculative prices. Econometrica 41, 135-155.

Einstein, A. (1905). On the movement of small particles suspended in a stationary liquid demanded by the kinetic molecular theory of heat, Annalen. der Physik, 4. Folge, 17, 549-560.

Farmer, J. D., Gillemot, L., Lillo, F., Mike, S., & Sen, A. (2004). What really causes large price changes, Quantitative Finance 4(4), 383-397.

Huth, N., & Abergel, F. (2012). The times change: Multivariate subordination. Empirical facts, Quantitative Finance, 12(1) 1-10.

Klages, R. (2010). Reviews of Nonlinear Dynamics and Complexity Volume 3, Heinz Georg Schuster (Ed.). Weinheim, Germany: Wiley-VCH Verlag GmbH & Co. KGaA.

Lux, T., & Marchesi, M. (1999). Scaling and criticality in a stochastic multi-agent model of a financial market, Nature, 397, 498–500.

Mandelbrot, B. (2006). The misbehavior of markets: A fractal view of risk, ruin, and reward. New York, NY: Basic Books.

Mandelbrot, B., & Taylor, H. M. (1967). On the distribution of stock price differences, Operations Research Vol. 15(6) 1057-1062.

Parker, E. (2013). Efficient markets meet the shannon limit (The shannon limit, relative channel capacity, and price uncertainty). [Kindle DX version]. Retrieved from Amazon.com or http://dx.doi.org/10.2139/ssrn.2516557 .

Parker, E. (2015). Entropy production and technological progress: The yin and yang of economics and finance. [Kindle DX version]. Retrieved from Amazon.com or http://dx.doi.org/10.2139/ssrn.2684841 .

Plerou, V., Gopikrishnan, P., Amaral, L. A. N., Gabaix, X., & Stanley, H. E. (2000). Economic fluctuations and anomalous diffusion. Physical Review E 62(3), 3023-3026.

Ross, S. A. (1989). The no-arbitrage martingale approach to timing and resolution irrelevancy. The Journal of Finance, 44, 1-17.


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This work is licensed under a Creative Commons Attribution 4.0 International License.