When are Limit Orders Linear?

Abstract

We show how core assumptions on risk preferences and risk distributions in the microstructure literature shape its conclusions for investment demand curves in equilibrium. In particular, we show that the assumptions of CARA preferences and joint normality of exogenous risk factors and payoffs imply equilibrium demand curves to be linear and thus unique. Our setting is strategic trading under both information symmetry and asymmetry. The literature thus far either accepts linearity by ad hoc assumption or attempts to show it by circular argument. In either case, it fails to connect explicitly demand linearity to core assumptions. This is significant against mounting evidence showing investment demand curves to be nonlinear in reality. The results in this paper thus show rigorously that linear equilibriums in the huge existing literature are in fact unique and that additional apparently ad hoc assumptions such as ‘symmetry’ that are often made are in fact redundant. They thus impose no added restrictions. Ultimately, we point to what models’ assumptions need to change to better represent and explain observed behavior.

Keywords: market microstructure, uniqueness, market power, Kyle model, market impact

JEL Classification: C62, D82, G14