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: This article investigated 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 and found that the distribution of return intervals can be approximated by a scaling function that depends only on the ratio between the return interval $\tau$ and its mean $ $.
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 $\tau$ and its mean $ $. 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.
24 citations
Book•
01 Jan 2006
TL;DR: In this paper, an agent-based model of financial returns in a limit order market stock price process and the long-range percolation is used to predict stock price changes.
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New Ideas Personal versus economic freedom Complexity in an Interacting System of Production Four Ingredients for New Approaches to Macroeconomic Modeling Competition phase space: theory and practice Analysis of Retail Spatial Market System by the Constructive Simulation Method Quantum-Monadology Approach to Economic Systems Visualization of microstructures of economic flows and adaptive control
23 citations
TL;DR: In this paper, the authors studied the long-term dynamics of the short-time variability level of human heart rate, an aspect which is not addressed by the traditional methods of nonlinear time-series analysis.
Abstract: We study the long-term dynamics of the short-time variability level of human heart rate, an aspect which is not addressed by the traditional methods of non-linear time-series analysis. The length-distribution of low-variability periods in human heartbeat dynamics typically follows a multi-scaling power law. The values of the scaling exponents are personal characteristics and depend on the daily habits of the subjects. Though, the distribution function of the low-variability periods as a whole discriminates efficiently between several heart pathologies.
14 citations
TL;DR: In this paper, the scaling properties of the time series of asset prices and trading volumes of stock markets are analyzed, and it is shown that trading volume data obey multi-scaling length-distribution of low-variability periods.
Abstract: The scaling properties of the time series of asset prices and trading volumes of stock markets are analysed. It is shown that similar to the asset prices, the trading volume data obey multi-scaling length-distribution of low-variability periods. In the case of asset prices, such scaling behaviour can be used for risk forecasts: the probability of observing next day a large price movement is (super-universally) inversely proportional to the length of the ongoing low-variability period. Finally, a method is devised for a multi-factor scaling analysis. We apply the simplest, two-factor model to equity index and trading volume time series.
9 citations
TL;DR: In this paper, a scaling analysis of low-variability periods in time series is proposed to reveal more details about time series than the traditional multi-affine analysis, and the results show a good scaling behavior for different model parameters.
Abstract: Properties of low-variability periods in the time series are analysed. The theoretical approach is used to show the relationship between the multi-scaling of low-variability periods and multi-affinity of the time series. It is shown that this technically simple method is capable of revealing more details about time series than the traditional multi-affine analysis. We have applied this scaling analysis to financial time series: a number of daily currency and stock index time series. The results show a good scaling behaviour for different model parameters. The analysis of high-frequency USD-EUR exchange rate data confirmed the theoretical expectations.
4 citations