Shorting in Speculative Markets

Abstract

In models of trading with heterogeneous beliefs following Harrison-Kreps, short selling is prohibited and agents face constant marginal costs-of-carry. The resale option guarantees that prices exceed buy-and-hold prices and the difference is identified as a bubble. We propose a model where risk-neutral agents face asymmetric increasing marginal costs on long and short positions. Here, agents also value an option to delay, and a Hamilton-Jacobi-Bellman equation quantifies the influence of costs on prices. An unexpected decrease in shorting costs may deflate a bubble, linking financial innovations that facilitated shorting of mortgage-backed securities to the collapse of prices.