Relative Asset Price Bubbles

Abstract

In models of financial bubbles, the price of a stock is a priori typically unbounded, and this plays a fundamental role in the analysis of finite horizon local martingale bubbles. It would seem that price bubbles do not apply to bounded risky asset prices, such as bond prices. To avoid this limitation, to characterize, and to identify bond price mispricings consistent with No Free Lunch with Vanishing Risk, we develop the concept of a relative asset price bubble. This notion uses a risky asset's price as the numeraire instead of the money market account's value. This change of numeraire generates some interesting mathematical complexities because some important numeraires, including risky bonds, can vanish with positive probability over the model's horizon.