Multi-Fractal Spectral Analysis of the 1987 Stock Market Crash

Abstract

The multifractal model of asset returns captures the volatility persistence of many financial time series. Its multifractal spectrum computed from wavelet modulus maxima lines provides the spectrum of irregularities in the distribution of market returns over time and thereby of the kind of uncertainty or "randomness" in a particular market. Changes in this multifractal spectrum display distinctive patterns around substantial market crashes or "drawdowns." In other words, the kinds of singularities and the kinds of irregularity change in a distinct fashion in the periods immediately preceding and following major market drawdowns. This paper focuses on these identifiable multifractal spectral patterns surrounding the stock market crash of 1987. Although we are not able to find a uniquely identifiable irregularity pattern within the same market preceding different crashes at different times, we do find the same uniquely identifiable pattern in various stock markets experiencing the same crash at the same time. Moreover, our results suggest that all such crashes are preceded by a gradual increase in the weighted average of the values of the Lipschitz regularity exponents, under low dispersion of the multifractal spectrum. At a crash, this weighted average irregularity value drops to a much lower value, while the dispersion of the spectrum of Lipschitz exponents jumps up to a much higher level after the crash. Our most striking result, however, is that the multifractal spectra of stock market returns are not stationary. Also, while the stock market returns show a global Hurst exponent of slight persistence 0.5 < H < 0.7, these spectra tend to be skwed towards anti-persistence in the returns.

Evidence of Multifractality from Emerging European Stock Markets

“…This paper proposes itself to answer to several questions, namely whether the daily returns in the selected CEE stock market indices are characterized by multifractality, how much using a surrogate data series, shuffled ones, leads to changes in the results. Not at last, we also investigate whether the crisis period has lead to different strenghts of multifractal spectrum, as suggested in an earlier work on the 1987 financial crisis by [14] .…”

Fraktalna analiza finansowych szeregów czasowych z wykorzystaniem wymiaru fraktalnego oraz punktowych wykładników Höldera

“…Another group of studies focused on the analysis of variation of Hurst exponent over time, showing the possible impact of capital flow and trading volume on the decrease of Hurst exponent values (Cajueiro, Tabak, 2004), the influence that the end of Bretton Woods System had on efficiency of US stock markets (Alvarez-Ramirez, Alvarez, Rodriguez, Fernandez-Anaya, 2008), or the relationship between local Hurst exponent and stock market crashes with example of the Warsaw Stock Exchange Index (Grech, Pamuła, 2008). Due to certain limitations of classical R/S analysis approach and Hurst exponent itself, some of the authors explored Hölderian pointwise regularity of some major stock market indices (Bianchi, Pantanella, 2010) and usage of multifractal spectra analysis in order to discover patterns of change in price series before the 1987 market crash and other significant market drawdowns (Los, Yalamova, 2004).…”

Notice of Retraction: Multifractal analysis of the 2007 stock market crash

“…So the traditional method may be not suitable to analysis financial crash, while the multifractal model of asset returns can describe important empirical regularities observed in financial time series, including fat distribution tails (which is equal to non-normal occurrence of extreme events) and the abnormally occurring outliers observed in fmancial time series [3].…”