The frequent financial critical states that occur in our world, during many centu-ries have attracted scientists from different areas. The impact of similar fluctua-tions continues to have a huge impact on the world economy, causing instability in it concerning normal and natural disturbances [1]. The anticipation, prediction, and identification of such phenomena remain a huge challenge. The crisis starting in 1997, strongly affected on the worldwide economy, raised fears among people about its future. The International Monitory Fund (IMF) after the experienced Asian Crisis pointed out that such phenomena will occur again in the nearest future [2]. To be able to prevent such critical events, we focus our research on the chaotic properties of the stock market indices. During the discussion of the recent papers that have been devoted to the chaotic behavior and complexity in the financial system, we find that the Largest Lyapunov exponent and the spectrum of Lyapunov exponents can be evaluated to determine whether the system is com-pletely deterministic, or chaotic. Accordingly, we give a theoretical background on the method for Lyapunov exponents estimation, specifically, we followed the methods proposed by J. P. Eckmann and Sano-Sawada to compute the spectrum of Lyapunov exponents. With Rosenstein’s algorithm, we compute only the Largest (Maximal) Lyapunov exponents from an experimental time series. And we consider one of the measures from recurrence quantification analysis that in a similar way as the Largest Lyapunov exponent detects highly non-monotonic behavior. Along with the theoretical material, we present the empirical results which evidence that chaos theory and theory of complexity have a powerful toolkit for construction of indicators-precursors of crisis events in financial markets.