# Probability of large movements in financial markets

01 Dec 2009-Physica A-statistical Mechanics and Its Applications (North-Holland)-Vol. 388, Iss: 23, pp 4838-4844

TL;DR: Based on empirical financial time series, it is shown that the “silence-breaking” probability follows a super-universal power law: the probability of observing a large movement is inversely proportional to the length of the on-going low-variability period.

Abstract: Based on empirical financial time series, we show that the “silence-breaking” probability follows a super-universal power law: the probability of observing a large movement is inversely proportional to the length of the on-going low-variability period . Such a scaling law has been previously predicted theoretically [R. Kitt, J. Kalda, Physica A 353 (2005) 480], assuming that the length-distribution of the low-variability periods follows a multi-scaling power law.

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01 Dec 2006

TL;DR: It is found that the distribution of the recurrence times strongly depends on the previous recurrence time tau0, such that small and largeRecurrence times tend to cluster in time, and the risk of encountering the next event within a certain time span after the last event depends significantly on the past.

Abstract: We study the statistics of the recurrence times tau between earthquakes above a certain magnitude M in six (one global and five regional) earthquake catalogs. We find that the distribution of the recurrence times strongly depends on the previous recurrence time tau0, such that small and large recurrence times tend to cluster in time. This dependence on the past is reflected in both the conditional mean recurrence time and the conditional mean residual time until the next earthquake, which increase monotonically with tau0. As a consequence, the risk of encountering the next event within a certain time span after the last event depends significantly on the past, an effect that has to be taken into account in any effective earthquake prognosis.

8 citations

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TL;DR: In this paper, an adaptive stochastic model is introduced to simulate the behavior of real asset markets, which adapts itself by changing its parameters automatically on the basis of the recent historical data.

Abstract: An adaptive stochastic model is introduced to simulate the behavior of real asset markets. The model adapts itself by changing its parameters automatically on the basis of the recent historical data. The basic idea underlying the model is that a random variable uniformly distributed within an interval with variable extremes can replicate the histograms of asset returns. These extremes are calculated according to the arrival of new market information. This adaptive model is applied to the daily returns of three well-known indices: Ibex35, Dow Jones and Nikkei, for three complete years. The model reproduces the histograms of the studied indices as well as their autocorrelation structures. It produces the same fat tails and the same power laws, with exactly the same exponents, as in the real indices. In addition, the model shows a great adaptation capability, anticipating the volatility evolution and showing the same volatility clusters observed in the assets. This approach provides a novel way to model asset markets with internal dynamics which changes quickly with time, making it impossible to define a fixed model to fit the empirical observations.

5 citations

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01 Jan 2013TL;DR: In this paper, the authors use the abundance of high frequency data to estimate scaling law models and then apply appropriately scaled measures to provide long-term market risk forecasts, making use of the scale invariance property of the scaling law.

Abstract: This chapter uses the abundance of high frequency data to estimate scaling law models and then apply appropriately scaled measures to provide long-term market risk forecasts. The objective is to analyse extreme price movements from tick-by-tick real-time data to trace the footprints of traders that eventually form the overall movement of market prices (price coastline) and potential bubbles. The framework is applied to empirical limit order book data from the London Stock Exchange. The sample period ranges from June 2007 to June 2008 and covers the start of the subprime crisis that later escalated into the economic crisis. After extracting the scaling exponent and checking its robustness with bootstrap simulations, the authors investigate longer term price movements in more detail, making use of the scale invariance property of the scaling law. In particular, they provide financial risk forecasts for a testing period and compare these with the popular Value-at-Risk and expected tail loss measures, showing the outperformance of the scaling law approach. Finally, a set of simulations are run to explore which scaling exponent is more likely to trigger market turbulence.

2 citations

##### References

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01 Jan 1982

TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.

Abstract: "...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature

24,199 citations

### "Probability of large movements in f..." refers background in this paper

...Indeed, the presen e of apower-law means that there are some representatives of a population, whi hare very di erent from the typi al members of that population....

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01 Jan 19495,898 citations

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01 Jan 2000TL;DR: Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.

Abstract: This book concerns the use of concepts from statistical physics in the description of financial systems. The authors illustrate the scaling concepts used in probability theory, critical phenomena, and fully developed turbulent fluids. These concepts are then applied to financial time series. The authors also present a stochastic model that displays several of the statistical properties observed in empirical data. Statistical physics concepts such as stochastic dynamics, short- and long-range correlations, self-similarity and scaling permit an understanding of the global behaviour of economic systems without first having to work out a detailed microscopic description of the system. Physicists will find the application of statistical physics concepts to economic systems interesting. Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.

2,826 citations

### "Probability of large movements in f..." refers background in this paper

...This is ompletelydi erent from the biologi al evolution: e.g. the weight of a single living ∗Corresponding author....

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TL;DR: A simple and robust model of biological evolution of an ecology of interacting species that self-organizes into a critical steady state with intermittent coevolutionary avalanches of all sizes and exhibits ``punctuated equilibrium'' behavior.

Abstract: A simple and robust model of biological evolution of an ecology of interacting species is introduced The model self-organizes into a critical steady state with intermittent coevolutionary avalanches of all sizes; ie, it exhibits ``punctuated equilibrium'' behavior This collaborative evolution is much faster than non-cooperative scenarios since no large and coordinated, and hence prohibitively unlikely, mutations are involved

1,329 citations