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1.
Clustering of volatility as a multiscale phenomenon 总被引:3,自引:0,他引:3
M. Pasquini M. Serva 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,16(1):195-201
The dynamics of prices in financial markets has been studied intensively both experimentally (data analysis) and theoretically
(models). Nevertheless, a complete stochastic characterization of volatility is still lacking. What is well known is that
absolute returns have memory on a long time range, this phenomenon is known as clustering of volatility. In this paper we
show that volatility correlations are power-laws with a non-unique scaling exponent. This kind of multiscale phenomenology
has some analogies with fully developed turbulence and disordered systems and it is now pointed out for financial series.
Starting from historical returns series, we have also derived the volatility distribution, and the results are in agreement
with a log-normal shape. In our study, we consider the New York Stock Exchange (NYSE), daily composite index closes (January
1966 to June 1998) and the US Dollar/Deutsche Mark (USD-DM) noon buying rates certified by the Federal Reserve Bank of New
York (October 1989 to September 1998).
Received 1 February 2000 相似文献
2.
I.M. Jánosi 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,17(2):333-339
The statistical properties of the total yield are analyzed for an assembly of gamblers in an erratic period on the Budapest
stock exchange. Random trading results in a log-normal limit distribution of a surprisingly large width, while the simplest
profit realizing strategy narrows down the peak around a positive average value. The effect of transaction costs, the statistics
of extremes, and patterns of successful trading are also investigated. In spite of the very simple approach, we present strong
indications that large trading activity (e.g. day trading) is a rather risky way of capital investment. A comparison with the yield distribution of 32 public investment
funds in the given period does not reflect the presence of a sophisticated investment strategy in the background.
Received 5 May 2000 相似文献
3.
P.S. Grassia 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,17(2):347-362
An asset whose price exhibits geometric Brownian motion is analysed. The basic Brownian motion model is modified to account
for the effects of market delay and investor feedback. A Langevin equation model is appropriate. When the feedback coupling
is sufficiently strong, the market dynamics switches from a slow random walk behaviour to a rapid unstable behaviour with
a fast time scale characteristic of the market delay. The unstable runaway behaviour is subsequently quenched by investors
deserting a collapsing market or saturating a booming one. This quenching effect is sufficient to ensure long term bounding
of the asset price. A form of market sabotage is demonstrated in which investors can push the market from a stable to an unstable
regime.
Received 24 February 2000 相似文献
4.
A. Johansen D. Sornette 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,17(2):319-328
The Nasdaq Composite fell another % on Friday the 14'th of April 2000 signaling the end of a remarkable speculative high-tech bubble starting in spring 1997.
The closing of the Nasdaq Composite at 3321 corresponds to a total loss of over 35% since its all-time high of 5133 on the
10'th of March 2000. Similarities to the speculative bubble preceding the infamous crash of October 1929 are quite striking:
the belief in what was coined a “New Economy” both in 1929 and presently made share-prices of companies with three digits
price-earning ratios soar. Furthermore, we show that the largest draw downs of the Nasdaq are outliers with a confidence level
better than 99% and that these two speculative bubbles, as well as others, both nicely fit into the quantitative framework
proposed by the authors in a series of recent papers.
Received 3 May 2000 相似文献
5.
Hierarchical structure in financial markets 总被引:12,自引:0,他引:12
R. N. Mantegna 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,11(1):193-197
I find a hierarchical arrangement of stocks traded in a financial market by investigating the daily time series of the logarithm
of stock price. The topological space is a subdominant ultrametric space associated with a graph connecting the stocks of
the portfolio analyzed. The graph is obtained starting from the matrix of correlation coefficient computed between all pairs
of stocks of the portfolio by considering the synchronous time evolution of the difference of the logarithm of daily stock
price. The hierarchical tree of the subdominant ultrametric space associated with the graph provides a meaningful economic
taxonomy.
Received 24 March 1999 and Received in final form 28 June 1999 相似文献
6.
T. Huillet A. Porzio M. Ben Alaya 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,17(1):147-158
This work emphasizes the special role played by max-semistable and log-max-semistable distributions as relevant statistical models of various observable and “internal” variables in Physics. Some of their remarkable
properties (chiefly self-similarity) are displayed in some detail. One of their characteristic features is a log-periodic variation of the scale parameter which
appears in the stable extreme value distributions.
Received 29 November 1999 and Received in final form 24 March 2000 相似文献
7.
A generalized spin model of financial markets 总被引:1,自引:0,他引:1
D. Chowdhury D. Stauffer 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,8(3):477-482
We reformulate the Cont-Bouchaud model of financial markets in terms of classical “super-spins” where the spin value is a
measure of the number of individual traders represented by a portfolio manager of an investment agency. We then extend this
simplified model by switching on interactions among the super-spins to model the tendency of agencies getting influenced by the opinion of other managers. We also introduce
a fictitious temperature (to model other random influences), and time-dependent local fields to model a slowly changing optimistic
or pessimistic bias of traders. We point out close similarities between the price variations in our model with N super-spins and total displacements in an N-step Levy flight. We demonstrate the phenomena of natural and artificially created bubbles and subsequent crashes as well
as the occurrence of “fat tails” in the distributions of stock price variations.
Received 13 October 1998 相似文献
8.
Apparent multifractality in financial time series 总被引:4,自引:0,他引:4
J.-P. Bouchaud M. Potters M. Meyer 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,13(3):595-599
We present a exactly soluble model for financial time series that mimics the long range volatility correlations known to be
present in financial data. Although our model is asymptotically `monofractal' by construction, it shows apparent multiscaling
as a result of a slow crossover phenomenon on finite time scales. Our results suggest that it might be hard to distinguish
apparent and true multifractal behavior in financial data. Our model also leads to a new family of stable laws for sums of
correlated random variables.
Received 30 June 1999 相似文献
9.
N. Vandewalle Ph. Boveroux F. Brisbois 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,15(3):547-549
In order to emphasize cross-correlations for fluctuations in major market places, series of up and down spins are built from
financial data. Patterns frequencies are measured, and statistical tests performed. Strong cross-correlations are emphasized,
proving that market moves are collective behaviors.
Received 15 January 2000 相似文献
10.
11.
Numerical data for the distribution of citations are examined for: (i) papers published in 1981 in journals which are catalogued
by the Institute for Scientific Information (783,339 papers) and (ii) 20 years of publications in Physical Review D, vols.
11-50 (24,296 papers). A Zipf plot of the number of citations to a given paper versus its citation rank appears to be consistent with a power-law dependence for leading rank papers, with exponent close to -1/2.
This, in turn, suggests that the number of papers with x citations, N(x), has a large-x power law decay , with .
Received: 12 May 1998 / Accepted: 12 May 1998 相似文献
12.
D. Sornette D. Zajdenweber 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,8(4):653-664
At what level should government or companies support research? This complex multi-faceted question encompasses such qualitative
bonus as satisfying natural human curiosity, the quest for knowledge and the impact on education and culture, but one of its
most scrutinized component reduces to the assessment of economic performance and wealth creation derived from research. Many
studies report evidences of positive economic benefits derived from basic research [#!Martin!#,#!NAS!#]. In certain areas
such as biotechnology, semi-conductor physics, optical communications [#!Ehrenreich!#], the impact of basic research is direct
while, in other disciplines, the path from discovery to applications is full of surprises. As a consequence, there are persistent
uncertainties in the quantification of the exact economic returns of public expenditure on basic research. This gives little
help to policy makers trying to determine what should be the level of funding. Here, we suggest that these uncertainties have
a fundamental origin to be found in the interplay between the intrinsic “fat tail” power law nature of the distribution of
economic returns, characterized by a mathematically diverging variance, and the stochastic character of discovery rates. In
the regime where the cumulative economic wealth derived from research is expected to exhibit a long-term positive trend, we
show that strong fluctuations blur out significantly the short-time scales: a few major unpredictable innovations may provide
a finite fraction of the total creation of wealth. In such a scenario, any attempt to assess the economic impact of research
over a finite time horizon encompassing only a small number of major discoveries is bound to be highly unreliable. New tools,
developed in the theory of self-similar and complex systems [#!Dubrulleetal!#] to tackle similar extreme fluctuations in Nature
[#!Mandelbrot!#], can be adapted to measure the economic benefits of research, which is intimately associated to this large
variability.
Received 26 October 1998 and
Received in final form 27 October 1998 相似文献
13.
F. Lillo R.N. Mantegna 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,15(4):603-606
We select the n stocks traded in the New York Stock Exchange and we form a statistical ensemble of daily stock returns for each of the k trading days of our database from the stock price time series. We study the ensemble return distribution for each trading
day and we find that the symmetry properties of the ensemble return distribution drastically change in crash and rally days
of the market. In crash and rally days, the distribution becomes asymmetric. In particular for crashes the positive tail is
steeper than the negative one whereas the reverse is observed in rally days.
Received 25 February 2000 相似文献
14.
J.V. Andersen S. Gluzman D. Sornette 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,14(3):579-601
Starting from the characterization of the past time evolution of market prices in terms of two fundamental indicators, price
velocity and price acceleration, we construct a general classification of the possible patterns characterizing the deviation
or defects from the random walk market state and its time-translational invariant properties. The classification relies on
two dimensionless parameters, the Froude number characterizing the relative strength of the acceleration with respect to the
velocity and the time horizon forecast dimensionalized to the training period. Trend-following and contrarian patterns are
found to coexist and depend on the dimensionless time horizon. The classification is based on the symmetry requirements of
invariance with respect to change of price units and of functional scale-invariance in the space of scenarii. This “renormalized
scenario” approach is fundamentally probabilistic in nature and exemplifies the view that multiple competing scenarii have
to be taken into account for the same past history. Empirical tests are performed on about nine to thirty years of daily returns
of twelve data sets comprising some major indices (Dow Jones, SP500, Nasdaq, DAX, FTSE, Nikkei), some major bonds (JGB, TYX)
and some major currencies against the US dollar (GBP, CHF, DEM, JPY). Our “renormalized scenario” exhibits statistically significant
predictive power in essentially all market phases. In contrast, a trend following strategy and following strategy perform well only on different and specific market phases. The value of the “renormalized scenario” approach
lies in the fact that it always selects the best of the two, based on a calculation of the stability of their predicted market
trajectories.
Received 3 October 1999 相似文献
15.
Are citations of scientific papers a case of nonextensivity? 总被引:1,自引:0,他引:1
C. Tsallis M.P. de Albuquerque 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,13(4):777-780
The distribution N(x) of citations of scientific papers has recently been illustrated (on ISI and PRE data sets) and analyzed by Redner (Eur.
Phys. J. B 4, 131 (1998)). To fit the data, a stretched exponential () has been used with only partial success. The success is not complete because the data exhibit, for large citation count
x, a power law (roughly for the ISI data), which, clearly, the stretched exponential does not reproduce. This fact is then attributed to a possibly
different nature of rarely cited and largely cited papers. We show here that, within a nonextensive thermostatistical formalism,
the same data can be quite satisfactorily fitted with a single curve (namely, [0pt] for the available values of x. This is consistent with the connection recently established by Denisov (Phys. Lett. A 235, 447 (1997)) between this nonextensive formalism and the Zipf-Mandelbrot law. What the present analysis ultimately suggests
is that, in contrast to Redner's conclusion, the phenomenon might essentially be one and the same along the entire range of the citation number x.
Received 13 April 1999 相似文献
16.
J. Laherrère D. Sornette 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,2(4):525-539
To account quantitatively for many reported “natural” fat tail distributions in Nature and Economy, we propose the stretched
exponential family as a complement to the often used power law distributions. It has many advantages, among which to be economical
with only two adjustable parameters with clear physical interpretation. Furthermore, it derives from a simple and generic
mechanism in terms of multiplicative processes. We show that stretched exponentials describe very well the distributions of
radio and light emissions from galaxies, of US GOM OCS oilfield reserve sizes, of World, US and French agglomeration sizes,
of country population sizes, of daily Forex US-Mark and Franc-Mark price variations, of Vostok (near the south pole) temperature
variations over the last 400 000 years, of the Raup-Sepkoski's kill curve and of citations of the most cited physicists in
the world. We also discuss its potential for the distribution of earthquake sizes and fault displacements. We suggest physical
interpretations of the parameters and provide a short toolkit of the statistical properties of the stretched exponentials.
We also provide a comparison with other distributions, such as the shifted linear fractal, the log-normal and the recently
introduced parabolic fractal distributions.
Received: 20 January 1998 / Received in final form: 27 January 1998 / Accepted: 6 February 1998 相似文献
17.
18.
Self-organized model for information spread in financial markets 总被引:1,自引:0,他引:1
Zhi-Feng Huang 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,16(2):379-385
A self-organized model with social percolation process is proposed to describe the propagations of information for different
trading ways across a social system and the automatic formation of various groups within market traders. Based on the market
structure of this model, some stylized observations of real market can be reproduced, including the slow decay of volatility
correlations, and the fat tail distribution of price returns which is found to cross over to an exponential-type asymptotic
decay in different dimensional systems.
Received 15 March 2000 相似文献
19.
D. Sornette 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,3(1):125-137
We propose a formulation of the term structure of interest rates in which the forward curve is seen as the deformation of
a string. We derive the general condition that the partial differential equations governing the motion of such string must
obey in order to account for the condition of absence of arbitrage opportunities. This condition takes a form similar to a
fluctuation-dissipation theorem, albeit on the same quantity (the forward rate), linking the bias to the covariance of variation
fluctuations. We provide the general structure of the models that obey this constraint in the framework of stochastic partial
(possibly non-linear) differential equations. We derive the general solution for the pricing and hedging of interest rate
derivatives within this framework, albeit for the linear case (we also provide in the appendix a simple and intuitive derivation
of the standard European option problem). We also show how the “string” formulation simplifies into a standard N-factor model under a Galerkin approximation.
Received: 30 January 1998 / Revised: 12 February 1998 / Accepted: 16 February 1998 相似文献
20.
A. Arnéodo J.-F. Muzy D. Sornette 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,2(2):277-282
We use wavelets to decompose the volatility (standard deviation) of intraday (S&P500) return data across scales. We show that
when investigating two-point correlation functions of the volatility logarithms across different time scales, one reveals
the existence of a causal information cascade from large scales (i.e. small frequencies) to fine scales. We quantify and visualize the information flux across scales. We provide a possible interpretation
of our findings in terms of market dynamics.
Received: 9 January 1998 / Received in final form and accepted: 13
January 1998 相似文献