Overvaluation—not volatility—is the main danger in stock markets

Real-world stock markets are volatile and express such traits as overvaluation, psychological moods, cycles and crashes. This paper develops and explores a model which has these properties. The model is aggregated, continuous and non-linear. It is developed in stages. In the initial stage it is applied to the price dynamics of one type of stock only. Later on it is applied to a weighted price index of different stocks, to try to capture the dynamics of a stock exchange as a whole. The purpose of the model is to gain insight both into short-term dynamics and stability properties, and the dynamics of long-range cycles and crashes. Based on the model, the transaction tax reform proposal to stabilise stock markets is discussed. Another and new stabilising idea is presented—substituting a stock with a type of bond.