scholarly journals New statistic for financial return distributions: Power-law or exponential?

2006 ◽  
Vol 366 ◽  
pp. 387-400 ◽  
Author(s):  
V. Pisarenko ◽  
D. Sornette
Keyword(s):  
Power Law ◽  
Financial Return ◽  
Return Distributions

scholarly journals Financial Return Distributions: Past, Present, and COVID-19

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 884
Author(s):  
Marcin Wątorek ◽  
Jarosław Kwapień ◽  
Stanisław Drożdż
Keyword(s):  
Normal Distribution ◽  
Power Law ◽  
Universal Constant ◽  
Market Dynamics ◽  
Financial Return ◽  
Currency Exchange ◽  
Time Flow ◽  
Two Factors ◽  
Return Distributions ◽  
Real Market

We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017–2020, we model tails of the return distributions at different time scales by using power-law, stretched exponential, and q-Gaussian functions. We focus on the fitted function parameters and how they change over the years by comparing our results with those from earlier studies and find that, on the time horizons of up to a few minutes, the so-called “inverse-cubic power-law” still constitutes an appropriate global reference. However, we no longer observe the hypothesized universal constant acceleration of the market time flow that was manifested before in an ever faster convergence of empirical return distributions towards the normal distribution. Our results do not exclude such a scenario but, rather, suggest that some other short-term processes related to a current market situation alter market dynamics and may mask this scenario. Real market dynamics is associated with a continuous alternation of different regimes with different statistical properties. An example is the COVID-19 pandemic outburst, which had an enormous yet short-time impact on financial markets. We also point out that two factors—speed of the market time flow and the asset cross-correlation magnitude—while related (the larger the speed, the larger the cross-correlations on a given time scale), act in opposite directions with regard to the return distribution tails, which can affect the expected distribution convergence to the normal distribution.

Influences of Trading Volume on Financial Return Distributions: A Reassessment and a Step Further

2012 ◽  
Author(s):  
Hung Xuan Do ◽  
Robert Darren Brooks ◽  
Sirimon Treepongkaruna ◽  
Eliza Wu
Keyword(s):  
Trading Volume ◽  
Financial Return ◽  
Return Distributions

scholarly journals The HS-SAS and GSH-SAS Distribution as Model for Unconditional and Conditional Return Distributions

2016 ◽  
Vol 42 (1) ◽  
Author(s):  
Matthias Fischer ◽  
Klaus Herrmann
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Quantile Function ◽  
Form Solution ◽  
Cumulative Distribution ◽  
Generalized Hyperbolic Distribution ◽  
Financial Return ◽  
Hyperbolic Distribution ◽  
Return Distributions ◽  
New Distribution

We introduce two new skewed and leptokurtic distributions derived from the hyperbolic secant distribution and from Vaughan (2002)’s generalized hyperbolic distribution by use of the sinh-arcsinh transformation introduced in Jones and Pewsey (2009). Properties of these new distribution are given. Their flexibility for modeling financial return data is comparable to that of their most advanced peers. Contrary to the latter for both distributions a closed-form solution for the density, cumulative distribution and quantile function can be given.

scholarly journals How does trading volume affect financial return distributions?

2014 ◽  
Vol 35 ◽  
pp. 190-206 ◽  
Author(s):  
Hung Xuan Do ◽  
Robert Brooks ◽  
Sirimon Treepongkaruna ◽  
Eliza Wu
Keyword(s):  
Trading Volume ◽  
Financial Return ◽  
Return Distributions

Analysis of power law assumptions for short-period comets and Kuiper bodies

1999 ◽  
Vol 173 ◽  
pp. 289-293 ◽  
Author(s):  
J.R. Donnison ◽  
L.I. Pettit
Keyword(s):  
Power Law ◽  
Pareto Distribution ◽  
Limited Data ◽  
Short Period ◽  
Probability Plots ◽  
Exponential Probability

AbstractA Pareto distribution was used to model the magnitude data for short-period comets up to 1988. It was found using exponential probability plots that the brightness did not vary with period and that the cut-off point previously adopted can be supported statistically. Examination of the diameters of Trans-Neptunian bodies showed that a power law does not adequately fit the limited data available.

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