Universal L\'evy's stable law of stock market and its characterization

TL;DR

This paper demonstrates that stock market price fluctuations follow Lévý's stable distribution, with stable parameters indicating a universal pattern in long-term data, but showing instability and correlation in short-term analysis.

Contribution

It provides empirical evidence that stock market fluctuations conform to Lévý's stable law and characterizes their stability and instability across different time scales.

Findings

Stable parameters are consistent across four stock markets in long-term data.

Stock prices and parameters fluctuate with correlation in short-term analysis.

Stock markets exhibit stability in long-term but instability in short-term.

Abstract

Price fluctuations in financial markets can be characterized by L\'evy's stable distribution, which is supported by the generalized central limit system. When the stable parameters were estimated from four different stock markets in long term, they similarly indicated an unique value. On the other hand, when analyzed in short term, parameters and the stock prices fluctuated with correlation, which shows that the stock markets are instable.