Asset Price Bubbles in Incomplete Markets

45 Pages Posted: 3 Oct 2007

See all articles by Robert A. Jarrow

Robert A. Jarrow

Cornell University - Samuel Curtis Johnson Graduate School of Management

Philip Protter

Purdue University

Kazuhiro Shimbo

Cornell University

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 (NFLVR)" and "no dominance" assumptions. We show that the two leading models for bubbles as either charges or as strict local martingales, respectively, are equivalent. We propose a new theory for bubble birth which involves a nontrivial modification of the classical martingale pricing framework. This modification involves the market exhibiting different local martingale measures across time - a possibility not previously explored within the classical theory. 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 have bubbles whose magnitudes are related to the asset's price bubble, (iii) with no dividends, American call options may be exercised early, (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 the underlying asset's price bubble. Many of these results stand in contrast to those of the classical theory. We propose, but do not implement, some new tests for the existence of asset price bubbles using derivative securities.

Suggested Citation

Jarrow, Robert A. and Protter, Philip and Shimbo, Kazuhiro, Asset Price Bubbles in Incomplete Markets. Johnson School Research Paper Series No. 03-07. Available at SSRN: https://ssrn.com/abstract=1019013 or http://dx.doi.org/10.2139/ssrn.1019013

Robert A. Jarrow (Contact Author)

Cornell University - Samuel Curtis Johnson Graduate School of Management ( email )

Department of Finance
Ithaca, NY 14853
United States
607-255-4729 (Phone)
607-254-4590 (Fax)

Philip Protter

Purdue University ( email )

1395 Mathematical Sciences Building Dept. of Mathematics & Statistics
West Lafayette, IN 47907
United States

Kazuhiro Shimbo

Cornell University ( email )

Ithaca, NY 14853
United States

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
746
Abstract Views
3,416
rank
35,422
PlumX Metrics