<p>Permutation entropy analysis is a time series analysis tool to measure complexity and is used in this paper to investigate three important characteristics of financial markets, namely the stochastic characteristic of a financial market, changes in market dynamics prior to financial crashes and market efficiency. These characteristics are analysed in two stock markets: the Johannesburg Stock Exchange (JSE) Top 40 - a market from a developing country, and the Nasdaq-100 - a market from a developed country, over a period of 20 years. Using the complexity-entropy causality plane, it is confirmed that the JSE Top 40 and the Nasdaq-100 are driven by underlying stochastic processes, as opposed to chaotic processes. It is also observed that both markets experienced a steady decrease in permutation entropy leading up to some major financial crises. Hence, permutation entropy may be used as a predictive tool for market crashes. In addition, permutation entropy shows no clear distinction between the market efficiency of the JSE Top 40 and Nasdaq-100, despite the former belonging to a developing country and the latter belonging to a developed country. This suggests that the JSE has a solid structure in terms of a competitive environment, regulations and infrastructure. These results demonstrate the ability of permutation entropy to analyse various aspects of financial markets.</p>