Abstract

This paper studies asset price bubbles in a continuous time model using the local martingale framework. Providing careful definitions of the asset’s market and fundamental price, we characterize all possible price bubbles in an incomplete market satisfying the ”no free lunch with vanishing risk” and ”no dominance” assumptions. We propose a new theory for bubble birth which involves a nontrivial modification of the classical framework. We show that the two leading models for bubbles as either charges or as strict local martingales, respectively, are equivalent. Finally, we investigate the pricing of derivative securities in the presence of asset price bubbles, and we show that: (i) European put options can have no bubbles, (ii) European call options and discounted forward prices can have bubbles, but the magnitude of their bubbles must equal the magnitude of the asset’s price bubble, (iii) with no dividends, American call prices must always equal an otherwise identical European call’s price, regardless of bubbles, (iv) European put-call parity in market prices must always hold, regardless of bubbles, and (v) futures price bubbles can exist and they are independent of bubbles in the underlying asset’s price. These results imply that in a market satisfying NFLVR and no dominance, in the presence of an asset price bubble, risk neutral valuation can not be used to match call option prices. We propose, but do not implement, some new tests for the existence of asset price bubbles using derivative securities.

Citations