Scaling in currency exchange

Galluccio, Stefano; Caldarelli, Guido; Marsili, Matteo; Zhang, Yicheng

doi:10.1016/s0378-4371(97)00316-6

Cited by 95 publications

(83 citation statements)

References 18 publications

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“…To validate the assumption of daily repetition of the stochastic process, we implement a corresponding analysis of fluctuations throughout a trading week (8). Fig.…”

Section: Resultsmentioning

confidence: 99%

Nonstationary increments, scaling distributions, and variable diffusion processes in financial markets

Bassler

McCauley

Gunaratne

2007

Proc. Natl. Acad. Sci. U.S.A.

139

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Fat-tailed distributions have been reported in fluctuations of financial markets for more than a decade. Sliding interval techniques used in these studies implicitly assume that the underlying stochastic process has stationary increments. Through an analysis of intraday increments, we explicitly show that this assumption is invalid for the Euro-Dollar exchange rate. We find several time intervals during the day where the standard deviation of increments exhibits power law behavior in time. Stochastic dynamics during these intervals is shown to be given by diffusion processes with a diffusion coefficient that depends on time and the exchange rate. We introduce methods to evaluate the dynamical scaling index and the scaling function empirically. In general, the scaling index is significantly smaller than previously reported values close to 0.5. We show how the latter as well as apparent fat-tailed distributions can occur only as artifacts of the sliding interval analysis.fat tails ͉ Fokker-Planck equation ͉ Langevin simulations A rguably the most important problem in quantitative finance is to understand the nature of stochastic processes that underlie market dynamics. One aspect of the solution to this problem involves determining characteristics of the distribution of fluctuations in returns. Empirical studies conducted over the last decade have reported that they are non-Gaussian, scale in time, and have power law (or fat) tails (1-6). However, by combining increments at multiple times in their statistical analyses (sliding interval techniques), these studies implicitly assume that the stochastic process has stationary increments. For financial markets, it is not clear whether this assumption is valid. For example, it is possible that trading activity at the beginning of a trading day may differ from that at the end of the day. How is it possible to test whether intraday fluctuations are timeindependent? If they are time-dependent, how can statistical analyses be conducted? Will results from previous studies be invalidated?Our analysis is conducted on intraday Euro-Dollar exchange rates (traded 24 h per day) during 1999-2004 recorded in 1-min intervals. It is based on the assumption that intraday variations in the market follow the same underlying stochastic process every day. Then, a statistical analysis for fluctuations at a given time of the day can be conducted by using data from multiple trading days within the sample.We find from this analysis the following. (i) The stochastic process is time-dependent and there are several intervals during the day where the standard deviation of increments exhibits power law behavior. Stochastic dynamics during these intervals is given by variable diffusion processes (2). (ii) Dynamical scaling indices and empirical scaling functions within these scaling intervals are different from previously reported results. We show how the latter can result from the application of sliding interval methods to a time-dependent stochastic process. (iii) Autocorrelation functions for var...

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“…To validate the assumption of daily repetition of the stochastic process, we implement a corresponding analysis of fluctuations throughout a trading week (8). Fig.…”

Section: Resultsmentioning

confidence: 99%

Nonstationary increments, scaling distributions, and variable diffusion processes in financial markets

Bassler

McCauley

Gunaratne

2007

Proc. Natl. Acad. Sci. U.S.A.

139

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“…West et al [1997], Barabási and Albert [1999], Newman [2005]). In finance, there is one scaling law that has been widely reported (Müller et al [1990], Mantegna and Stanley [1995], Galluccio et al [1997], Guillaume et al [1997], Ballocchi et al [1999], , Corsi et al [2001], Di Matteo et al [2005]): the size of the average absolute price change (return) is scale-invariant to the time interval of its occurrence. This scaling law has been applied to risk management and volatility modelling (see Ghashghaie et al [1996], Gabaix et al [2003], Sornette [2000], Di Matteo [2007]) even though there has been no consensus amongst researchers for why the scaling law exists (e.g., Bouchaud [2001], Barndorff-Nielsen and Prause [2001], Farmer and Lillo [2004], Lux [2006], Joulin et al [2008]).…”

Section: Introductionmentioning

confidence: 99%

Patterns in high-frequency FX data: discovery of 12 empirical scaling laws

Glattfelder¹,

Dupuis

Olsen

2011

Quantitative Finance

144

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We have discovered 12 independent new empirical scaling laws in foreign exchange data-series that hold for close to three orders of magnitude and across 13 currency exchange rates. Our statistical analysis crucially depends on an event-based approach that measures the relationship between different types of events. The scaling laws give an accurate estimation of the length of the price-curve coastline, which turns out to be surprisingly long. The new laws substantially extend the catalogue of stylised facts and sharply constrain the space of possible theoretical explanations of the market mechanisms.

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“…Looking at the scaling law characterizing physical systems where large numbers of units interact [4][5][6][7], anyway, one observes that there is no need to introduce different classes of agents. Since the details of the circumstances governing the expectations and decisions of all the individuals are unknown to the modeler, the behavior of a large number of heterogeneous agents may best be formalized using a probabilistic setting.…”

Section: Introductionmentioning

confidence: 99%

On financial markets trading

Matassini

Franci

2001

Physica A: Statistical Mechanics and its Applications

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Abstract.Starting from the observation of the real trading activity, we propose a model of a stockmarket simulating all the typical phases taking place in a stock exchange. We show that there is no need of several classes of agents once one has introduced realistic constraints in order to confine money, time, gain and loss within an appropriate range. The main ingredients are local and global coupling, randomness, Zipf distribution of resources and price formation when inserting an order. The simulation starts with the initial public offer and comprises the broadcasting of news/advertisements and the building of the book, where all the selling and buying orders are stored. The model is able to reproduce fat tails and clustered volatility, the two most significant characteristics of a real stockmarket, being driven by very intuitive parameters.

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Scaling in currency exchange

Cited by 95 publications

References 18 publications

Nonstationary increments, scaling distributions, and variable diffusion processes in financial markets

Nonstationary increments, scaling distributions, and variable diffusion processes in financial markets

Patterns in high-frequency FX data: discovery of 12 empirical scaling laws

On financial markets trading

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