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.