Generalized entropy approach to stable Lèvy distributions with financial application

Employing the generalized entropy introduced by Tsallis, we propose a new method to estimate the scaling index of the stable Lèvy distribution. We investigate the scaling behavior of the daily Nikkei average sampled from January 1991 to December 2000 for the time intervals up to 75 days from two aspects, self-similarity of the distribution and long-range dependence in the autocorrelation function. It is found that the theoretically estimated scaling index μ*=1.59 and Hurst exponent H*=0.629 agree well with μ=1.50 and H=0.617 obtained from the measured data, respectively, suggesting the usefulness and fitness of the present method.