Testing for Asset Price Bubbles: An Invariance Theorem

Abstract

This paper provides an invariance theorem that facilitates testing for the existence of an asset price bubble in a market where the price evolves as a Markov diffusion process. The test involves only the properties of the price process’ quadratic variation under the statistical probability. It does not require an estimate of either the equivalent local martingale measure or the asset’s drift. Various examples are provided that illustrate applications of the invariance theorem to stochastic volatility price processes in incomplete markets.