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A Liquidity Based Model for Asset Price Bubbles

Quantitative Finance, Forthcoming

Johnson School Research Paper Series No. 14-2010

23 Pages Posted: 2 Mar 2010 Last revised: 8 Sep 2011

Philip Protter

Columbia University

Robert A. Jarrow

Cornell University - Samuel Curtis Johnson Graduate School of Management

Alexandre F. Roch

University of Quebec at Montreal (UQAM) - Faculty of Management (ESG)

Date Written: February 1, 2011

Abstract

We provide a new liquidity based model for financial asset price bubbles that explains bubble formation and bubble bursting. The martingale approach (Cox and Hobson (2005), Jarrow et al. (2007)) 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 which 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 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.

Suggested Citation

Protter, Philip and Jarrow, Robert A. and Roch, Alexandre F., A Liquidity Based Model for Asset Price Bubbles (February 1, 2011). Quantitative Finance, Forthcoming; Johnson School Research Paper Series No. 14-2010. Available at SSRN: https://ssrn.com/abstract=1561574

Philip Protter

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

Robert A. Jarrow

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)

Alexandre F. Roch (Contact Author)

University of Quebec at Montreal (UQAM) - Faculty of Management (ESG) ( email )

Case postale 8888
Succursale Centre-ville
Montreal, Quebec H3C 3P8
Canada

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