We introduce a class of agent-based market models founded upon simple descriptions of investor psychology. Agents are subject to various psychological tensions induced by market conditions and endowed with a minimal 'personality'. This personality consists of a threshold level for each of the tensions being modeled, and the agent reacts whenever a tension threshold is reached. This paper considers an elementary model including just two such tensions. The first is 'cowardice', which is the stress caused by remaining in a minority position with respect to overall market sentiment and leads to herding-type behavior. The second is 'inaction', which is the increasing desire to act or re-evaluate one's investment position. There is no inductive learning by agents and they are only coupled via the global market price and overall market sentiment. Even incorporating just these two psychological tensions, important stylized facts of real market data, including fat-tails, excess kurtosis, uncorrelated price returns and clustered volatility over the timescale of a few days are reproduced. By then introducing an additional parameter that amplifies the effect of externally generated market noise during times of extreme market sentiment, long-time volatility correlations can also be recovered.