On Stock-Price Fluctuations in the Periods of Booms and Stagnations
The statistical properties of the fluctuations of financial prices have been widely researched since Mandelbrot  and Fama  presented an evidence that return distributions can be well described by a symmetric Levy stable law with tail index close to 1.7. Many empirical studies have shown that the tails of the distributions of returns and volatility follow approximately a power law with estimates of the tail index falling in the range 2 to 4 for large value of returns and volatility. (See, for examples, de Vries ; Pagan ; Longin , Lux ; Guillaume et al. ; Muller et al. ; Gopikrishnan et al. , Gopikrishnan et al. , Plerou et al. , Liu et al. ). However, there is also evidence against power-law tails. For instance, Barndorff-Nielsen , and Eberlein et al.  have respectively fitted the distributions of returns using normal inverse Gaussian, and hyperbolic distribution. Laherrere and Sornette  have suggested to describe the distributions of returns by the stretched-exponential distribution. Dragulescu and Yakovenko  have shown that the distributions of returns have been approximated by exponential distributions. More recently, Malevergne, Pisarenko and Sornette  have suggested that the tails ultimately decay slower than any stretched exponential distribution but probably faster than power laws with reasonable exponents as a result from various statistical tests of returns.
KeywordsStock Market Exponential Distribution Return Distribution Tail Index Noise Trader
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- 1.Mandelbrot B (1963) Journal of Business 36:392–417Google Scholar
- 3.de Vries CG (1994) in The Handbook of International Macroeconomics, F. van der Ploeg (ed.) pp.348–389 BlackwellGoogle Scholar
- 5.Longin FM (1996) Journal of Business 96:383–408Google Scholar
- 8.Muller UA, Dacarogna MM, Picktet OV (1998) in R.J. Adler, R.E. Feldman, M.S. Taqqu, Birkhauser, Boston (eds.), A Practical Guide to Heavy Tails, pp.55–78Google Scholar