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 model is based on the hypothesis that large movements in stock market activity arise from the trades of large participants, and explains certain striking empirical regularities that describe the relationship between large fluctuations in prices, trading volume and the number of trades.
Abstract: Insights into the dynamics of a complex system are often gained by focusing on large fluctuations. For the financial system, huge databases now exist that facilitate the analysis of large fluctuations and the characterization of their statistical behaviour. Power laws appear to describe histograms of relevant financial fluctuations, such as fluctuations in stock price, trading volume and the number of trades. Surprisingly, the exponents that characterize these power laws are similar for different types and sizes of markets, for different market trends and even for different countries--suggesting that a generic theoretical basis may underlie these phenomena. Here we propose a model, based on a plausible set of assumptions, which provides an explanation for these empirical power laws. Our model is based on the hypothesis that large movements in stock market activity arise from the trades of large participants. Starting from an empirical characterization of the size distribution of those large market participants (mutual funds), we show that the power laws observed in financial data arise when the trading behaviour is performed in an optimal way. Our model additionally explains certain striking empirical regularities that describe the relationship between large fluctuations in prices, trading volume and the number of trades.
1,261 citations
TL;DR: Mandelbrot's original field of applied research was in econometrics and financial models, applying ideas of scaling and self-similarity to arrays of data generated by financial analyses as discussed by the authors.
Abstract: Mandelbrot is world famous for his creation of the new mathematics of fractal geometry. Yet few people know that his original field of applied research was in econometrics and financial models, applying ideas of scaling and self-similarity to arrays of data generated by financial analyses. This book brings together his original papers as well as many original chapters specifically written for this book.
563 citations
"Probability of large movements in f..." refers background in this paper
...Indeed, various power-laws have been observed in financial time series since 1960-es, by B. Mandelbrot (cf. [5, 6 ] and references therein)....
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Book•
11 May 2001
TL;DR: In this paper, the authors describe parallels between statistical physics and finance, both long established and new research results on capital markets, and show how computer simulations of markets provide insights into price fluctuations and how crashes are modelled in ways analogous to phase transitions.
Abstract: PHYSICS TODAYThis introductory treatment describes parallels between statistical physics and finance, both long established and new research results on capital markets. Forming the core of Voit's treatment are the concepts of random walks, scaling of data, and risk control. Voit discusses the underlying assumptions using empirical financial data and analogies to physical models such as fluid flows and turbulence. He formulates theories of derivative pricing and risk control, and shows how computer simulations of markets provide insights into price fluctuations and how crashes are modelled in ways analogous to phase transitions. This corrected edition has been updated with several new and significant developments, e.g. the dynamics of volatility smiles and implied volatility surfaces, path integral approaches to option pricing, a new simulation scheme for options, multifractals, the application of nonextensive statistical mechanics to financial markets, and the minority game.
398 citations
"Probability of large movements in f..." refers background in this paper
...[8,9,10,11], effectively creating a new branch of statistical physics — the econophysics....
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Book•
18 Sep 1997
TL;DR: In this paper, Cootner, Parzen and Morris presented a case against the lognormal distribution and proposed a L-stable model for the distribution of income, which is based on the L-stability and multiplicative variation of income.
Abstract: List of Chapters.- El Introduction (1996).- E2 Discontinuity and scaling: scope and likely limitations (1996).- E3 New methods in statistical economics (M 1963e).- E4 Sources of inspiration and historical background (1996).- E5 States of randomness from mild to wild, and concentration in the short, medium and long run (1996).- E6 Self-similarity and panorama of self-affinity (1996).- E7 Rank-size plots, Zipf's law, and scaling (1996).- E8 Proportional growth with or without diffusion, and other explanations of scaling (1996). * Appendices (M 1964o, M 1974d).- E9 A case against the lognormal distribution (1996).- E10 L-stable model for the distribution of income (M 1960i). * Appendices (M 1963i, M 1963j).- E11 L-stability and multiplicative variation of income (M 1961e).- E12 Scaling distributions and income maximization (M 1962q).- E13 Industrial concentration and scaling (1996).- E14 The variation of certain speculative prices (M 1963b). * Appendices (Fama & Blume 1966, M 1972b, M 1982c).- E15 The variation of the price of cotton, wheat, and railroad stocks, and of some financial rates (M 1967j).- E16 Mandelbrot on price variation (Fama 1963).- E17 Comments by P. H. Cootner, E. Parzen & W. S. Morris (1960s), and responses (1996).- E18 Computation of the L-stable distributions (1996).- E19 Nonlinear forecasts, rational bubbles, and martingales (M 1966b).- E20 Limitations of efficiency and martingales (M 1971e).- E21 Self-affine variation in fractal time (M & Taylor 1967, M 1973c).- Cumulative Bibliography.
356 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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