Discussion Paper, Center for Mathematical Studies in Economics and Management Science 1549
We study the effect of frequent trading opportunities and categorization on pricing of a risky asset. Frequent opportunities to trade lead to large distortions in prices if some agents forecast future prices using a simplified model of the world that fails to distinguish between some states. In the limit as the period length vanishes, these distortions take a particular form: the price must be the same in any two states that a positive mass of agents categorize together. Price distortions therefore tend to be large when different agents categorize states in different ways. We characterize the limiting prices in terms of rational expectations prices associated with a coarsened process. Similar results hold if, instead of using a simplified model of the world, some agents overestimate the likelihood of small probability events, as in prospect theory.