How to Detect an Asset Bubble

After the 2007 credit crisis, financial bubbles have once again emerged as a topic of current concern. An open problem is to determine in real time whether or not a given asset’s price process exhibits a bubble. Due to recent progress in the characterization of asset price bubbles using the arbitrage-free martingale pricing technology, we are able to propose a new methodology for answering this question based on the asset’s price volatility. We limit ourselves to the special case of a risky asset’s price being modeled by a Brownian driven stochastic differential equation. Such models are ubiquitous both in theory and in practice. Our methods use sophisticated volatility estimation techniques combined with the method of reproducing kernel Hilbert spaces. We illustrate these techniques using several stocks from the alleged internet dot-com episode of 1998 2001, where price bubbles were widely thought to have existed. Our results support these beliefs.