A liquidity-based model for asset price bubbles

Abstract

We provide a new liquidity-based model for financial asset price bubbles that explains bubble formation and bubble bursting. The martingale approach to modeling price bubbles assumes that the asset's market price process is exogenous and the fundamental price, the expected future cash flows under a martingale measure, is endogenous. In contrast, we define the asset's fundamental price process exogenously and asset price bubbles are endogenously determined by market trading activity. This enables us to generate a model that explains both bubble formation and bubble bursting. In our model, the quantity impact of trading activity on the fundamental price process—liquidity risk—is what generates price bubbles. We study the conditions under which asset price bubbles are consistent with no arbitrage opportunities and we relate our definition of the fundamental price process to the classical definition.

Keywords:

• Anomalies in prices
• Liquidity modeling
• Continuous time models
• Incomplete markets
• Bubbles
• Limit order books

JEL Classification::

• D5
• D50
• D52
• G1
• G12

Acknowledgement

Philip Protter is supported, in part, by NSF grant DMS-0906995.

Notes

† Given this is an arbitrage-free model, we concentrate on the properties of the price process itself, and not the strategic behavior of the large trader.