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
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
01 Jan 2013
TL;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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TL;DR: In this article, the analysis of volatility return intervals, defined as the time between two volatilities larger than a given threshold, can help to get a better understanding of the behavior of financial time series.
Abstract: We discuss recent results concerning statistical regularities in the return intervals of volatility in financial markets In particular, we show how the analysis of volatility return intervals, defined as the time between two volatilities larger than a given threshold, can help to get a better understanding of the behavior of financial time series We find scaling in the distribution of return intervals for thresholds ranging over a factor of 25, from 06 to 15 standard deviations, and also for various time windows from one minute up to 390 min (an entire trading day) Moreover, these results are universal for different stocks, commodities, interest rates as well as currencies We also analyze the memory in the return intervals which relates to the memory in the volatility and find two scaling regimes, � � ∗ with α2 =0 92 ± 004; these exponent values are similar to results of Liu et al for the volatility As an application, we use the scaling and memory properties of the return intervals to suggest a possibly useful method for estimating risk
50 citations
TL;DR: It is shown explicitly that the interoccurrence times between large daily returns follow the same behavior, in a nearly quantitative manner, that is a general consequence of the nonlinear memory inherent in the multifractal data sets.
Abstract: We study the statistics of the interoccurrence times between events above some threshold Q in two kinds of multifractal data sets (multiplicative random cascades and multifractal random walks) with vanishing linear correlations. We show that in both data sets the relevant quantities (probability density functions and the autocorrelation function of the interoccurrence times, as well as the conditional return period) are governed by power laws with exponents that depend explicitly on the considered threshold. By studying a large number of representative financial records (market indices, stock prices, exchange rates, and commodities), we show explicitly that the interoccurrence times between large daily returns follow the same behavior, in a nearly quantitative manner. We conclude that this kind of behavior is a general consequence of the nonlinear memory inherent in the multifractal data sets.
40 citations
TL;DR: In this article, the authors investigate scaling and memory effects in return intervals between price volatilities above a certain threshold q for the Japanese stock market using daily and intraday data sets.
Abstract: We investigate scaling and memory effects in return intervals between price volatilities above a certain threshold q for the Japanese stock market using daily and intraday data sets. We find that the distribution of return intervals can be approximated by a scaling function that depends only on the ratio between the return interval τ and its mean 〈τ〉. We also find memory effects such that a large (or small) return interval follows a large (or small) interval by investigating the conditional distribution and mean return interval. The results are similar to previous studies of other markets and indicate that similar statistical features appear in different financial markets. We also compare our results between the period before and after the big crash at the end of 1989. We find that scaling and memory effects of the return intervals show similar features although the statistical properties of the returns are different.
33 citations
TL;DR: Forward and backward time-directed avalanches are defined for a broad class of self-organized critical models including invasion percolation, interface depinning, and a simple model of evolution.
Abstract: We define forward and backward time-directed avalanches for a broad class of self-organized critical models including invasion percolation, interface depinning, and a simple model of evolution. Although the geometrical properties of the avalanches do not change under time reversal, their stationary state statistical distribution does. The overall distribution of forward avalanches [ital P]([ital s])[similar to][ital s][sup [minus]2] is superuniversal in this class of models. The power-law exponent [pi] for the distribution of distances between subsequent active sites is derived from the properties of backward avalanches.
33 citations
TL;DR: In this article, the S&P 500 index data for the 13-year period, from January 1, 1984 to December 31, 1996, with one data point every 10 min, was analyzed and the distribution and clustering of volatility return intervals, which are defined as the time intervals between successive volatilities above a certain threshold.
Abstract: We analyze the S&P 500 index data for the 13-year period, from January 1, 1984 to December 31, 1996, with one data point every 10 min For this database, we study the distribution and clustering of volatility return intervals, which are defined as the time intervals between successive volatilities above a certain threshold q We find that the long memory in the volatility leads to a clustering of above-median as well as below-median return intervals In addition, it turns out that the short return intervals form larger clusters compared to the long return intervals When comparing the empirical results to the ARMA-FIGARCH and fBm models for volatility, we find that the fBm model predicts scaling better than the ARMA-FIGARCH model, which is consistent with the argument that both ARMA-FIGARCH and fBm capture the long-term dependence in return intervals to a certain extent, but only fBm accounts for the scaling We perform the Student's t-test to compare the empirical data with the shuffled records, ARMA-FIGARCH and fBm We analyze separately the clusters of above-median return intervals and the clusters of below-median return intervals for different thresholds q We find that the empirical data are statistically different from the shuffled data for all thresholds q Our results also suggest that the ARMA-FIGARCH model is statistically different from the S&P 500 for intermediate q for both above-median and below-median clusters, while fBm is statistically different from S&P 500 for small and large q for above-median clusters and for small q for below-median clusters Neither model can fully explain the entire regime of q studied
26 citations