Predicting major downturns in financial markets is a popular topic among researchers. Improving the models used for this could benefit individuals, investment banks and financial institutions. The latest developments in econophysics provide additional forecasting tools that may aid this endeavor. This paper introduces an innovative method to identify early warnings for major declines in the Standard & Poor’s 500 (S&P 500) index. This method performs a nonlinear analysis of the logarithmic returns of the index and then uses the moving Lyapunov exponent as a dynamic indicator of stability. The results show that the fluctuating behavior of the moving Lyapunov exponent forms spikes, which may act as warning signals since they precede all significant events that have caused major drops in the S&P 500 index over the past 20 years, including the dot-com bubble, the Great Recession and the Covid-19 pandemic.