Equilibrium asset price ranges

The purpose of this paper is to ascertain what statements can be made about price ranges in equilibrium. This paper shows that equilibrium conditions impose restrictions on ranges of price processes. Specifically, it shows that the upper and the lower barriers on the price of a risky asset at any given time are themselves bounded by the discounted upper and lower barriers, respectively, on the price at any later time. It is also shown that, as a result, in the presence of a positive riskless yield, a constant finite barrier on the price of a risky asset is inconsistent with equilibrium, with an analogous result for the lower barrier. It is shown, on the other hand, that if there is a finite upper barrier on prices, then the barrier must grow at least as fast as the interest rate. The paper stresses that these restrictions must be obeyed when modeling asset prices.