Fearless versus Fearful Speculative Financial Bubbles

TL;DR

This paper introduces a new model-based methodology to classify speculative financial bubbles, distinguishing between those with increasing volatility and those without, based on their price and volatility behaviors.

Contribution

It develops a novel testing approach using a rational expectation model to identify and categorize different types of speculative bubbles in financial time series.

Findings

5 out of 9 analyzed series are 'fearful singular bubbles' with super-exponential growth and rising volatility.

4 bubbles, including Nasdaq and Hang Seng crashes, show no significant volatility increase.

Proposes two distinct groups of bubbles: with and without increasing volatility.

Abstract

Using a recently introduced rational expectation model of bubbles, based on the interplay between stochasticity and positive feedbacks of prices on returns and volatility, we develop a new methodology to test how this model classifies 9 time series that have been previously considered as bubbles ending in crashes. The model predicts the existence of two anomalous behaviors occurring simultaneously: (i) super-exponential price growth and (ii) volatility growth, that we refer to as the ``fearful singular bubble'' regime. Out of the 9 time series, we find that 5 pass our tests and can be characterized as ``fearful singular bubbles.'' The 4 other cases are the information technology Nasdaq bubble and three bubbles of the Hang Seng index ending in crashes in 1987, 1994 and 1997. According to our analysis, these four bubbles have developed with essentially no significant increase of their volatility. This paper thus proposes that speculative bubbles ending in crashes form two groups hitherto unrecognized, namely those accompanied by increasing volatility (reflecting increasing risk perception) and those without change of volatility (reflecting an absence of risk perception).