Urban housing markets, along with markets of other assets, universally exhibit periods of strong price increases followed by sharp corrections. The mechanisms generating such non-linearities are not yet well understood. We develop an agentbased model populated by a large number of heterogeneous households. The agents' behavioral rules are consistent with the concept of bounded rationality. The model is calibrated using several large and distributed datasets of the Greater Sydney region (demographic, economic and financial) across three specific and diverse periods since 2006. The model is not only capable of explaining price dynamics during these periods, but also reproduces the novel behavior actually observed immediately prior to the market peak in 2017, namely a sharp increase in the variability of prices. This novel behavior is related to a combination of trend-following aptitude of the household agents (herding) and their collective propensity to borrow. Trend-following behavior is found to be essential in replicating market dynamics.