A Liquidity Based Model for Asset Price Bubbles

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