From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets

Guillaume, Dominique; Dacorogna, Michel M.; Dave, Rakhal; Müller, Ulrich; Olsen, Richard B.; Pictet, Olivier V.

doi:10.1007/s007800050018

Cited by 403 publications

(266 citation statements)

References 59 publications

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“…This value is significantly larger that the value in the range 3 − 5 often reported in the literature [9][10][11][12][13] for assets others than exchange rates. One possible explanation is that exchange rates are known to exhibit thinner tails that stocks.…”

Section: Numerical Evaluationcontrasting

confidence: 53%

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Fokker–Planck equation of distributions of financial returns and power laws

Sornette

2001

Physica A: Statistical Mechanics and its Applications

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Our purpose is to relate the Fokker-Planck formalism proposed by [Friedrich et al., Phys. Rev. Lett. 84, 5224 (2000)] for the distribution of stock market returns to the empirically well-established power law distribution with an exponent in the range 3 − 5.We show how to use Friedrich et al.'s formalism to predict that the distribution of returns is indeed asymptotically a power law with an exponent µ that can be determined from the Kramers-Moyal coefficients determined by Friedrich et al. However, with their values determined for the U.S. dollar-German mark exchange rates, the exponent µ predicted from their theory is found around 12, in disagreement with the often-quoted value between 3 and 5. This could be explained by the fact that the large asymptotic value of 12 does not apply to real data that lie still far from the stationary state of the Fokker-Planck description.Another possibility is that power laws are inadequate. The mechanism for the power law is based on the presence of multiplicative noise across time-scales, which is different from the multiplicative noise at fixed time-scales implicit in the ARCH models developed in the Finance literature.

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Section: Numerical Evaluationcontrasting

confidence: 53%

“…• multiplicative noise models with reinjections [6][7][8] which provide a mechanism for power law distributions [9][10][11][12][13]; we note that such models are equivalent to ARCH models via a nonlinear change of variable [14,15,8];…”

Section: Summary Of Competing Models For Return Distributionsmentioning

confidence: 99%

Fokker–Planck equation of distributions of financial returns and power laws

Sornette

2001

Physica A: Statistical Mechanics and its Applications

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“…Later, in 1997, a second scaling law was reported by Guillaume et al [1997], relating the number N(∆χ dc ) of so-called directional changes to the the directional-change sizes ∆χ dc N(∆χ dc ) = ∆χ dc C N,dc…”

Section: The New Scaling Lawsmentioning

confidence: 99%

“…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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“…The distributional and dynamic properties of volatility appear especially important for risk-management purposes, since different specifications will yield to various pricing structures (Guillaume et al, 1997). The investigation of such properties has been revivified by the recent literature on realized volatility, which relies on the use of intraday data.…”

Section: Introductionmentioning

confidence: 99%

On the realized volatility of the ECX CO2 emissions 2008 futures contract: distribution, dynamics and forecasting

Chevallier

Sévi

2009

Ann Finance

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Abstract:The recent implementation of the EU Emissions Trading Scheme (EU ETS) in January 2005 created new financial risks for emitting firms. To deal with these risks, options are traded since October 2006. Because the EU ETS is a new market, the relevant underlying model for option pricing is still a controversial issue. This article improves our understanding of this issue by characterizing the conditional and unconditional distributions of the realized volatility for the 2008 futures contract in the European Climate Exchange (ECX), which is valid during Phase II (2008)(2009)(2010)(2011)(2012) of the EU ETS. The realized volatility measures from naive, kernel-based and subsampling estimators are used to obtain inferences about the distributional and dynamic properties of the ECX emissions futures volatility. The distribution of the daily realized volatility in logarithmic form is shown to be close to normal. The mixture-of-distributions hypothesis is strongly rejected, as the returns standardized using daily measures of volatility clearly departs from normality. A simplified HAR-RV model (Corsi, 2009) with only a weekly component, which reproduces long memory properties of the series, is then used to model the volatility dynamics. Finally, the predictive accuracy of the HAR-RV model is tested against GARCH specifications using one-step-ahead forecasts, which confirms the HAR-RV superior ability. Our conclusions indicate that (i) the standard Brownian motion is not an adequate tool for option pricing in the EU ETS, and (ii) a jump component should be included in the stochastic process to price options, thus providing more efficient tools for risk-management activities.JEL Classification: C5, G1, Q4.

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From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets

Cited by 403 publications

References 59 publications

Fokker–Planck equation of distributions of financial returns and power laws

Fokker–Planck equation of distributions of financial returns and power laws

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

On the realized volatility of the ECX CO2 emissions 2008 futures contract: distribution, dynamics and forecasting

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