Coevolution of stock prices and their perceived fundamental value

We develop a simple nonlinear stock market model in which speculators switch between technical and fundamental trading rules depending on market conditions. Additionally, we assume that agents are unaware of the true current fundamental value and, thus, use a weighted average of the current price and the known long-run fundamental value as an estimate of the fundamental price. Using analytical and numerical methods, we demonstrate that an increase in the reaction parameter of technical traders may cause boom-bust dynamics. Moreover, we show that a heightened belief among agents that the fundamental value is more sensitive to deviations of the current price from its long-run fundamental value can cause the price to become trapped above or below this long-run value, oscillate within a higher price range, and prolong the duration of a bubble. In two model extensions, we assume that agents compute the current fundamental value based on the deviation between the average price and the known long-run fundamental value, using a moving average of the past k prices and an exponential moving average, respectively. These robustness checks show that, in these cases, price and perceived fundamental value fluctuate less statically around the long-run fundamental value.