On Rational Bubbles and Fat Tails

SFB 303 Working Paper No. B-458

19 Pages Posted: 28 Jul 2000

See all articles by Thomas Lux

Thomas Lux

University of Kiel - Institute of Economics; University of Bonn - Economic Science Area

Didier Sornette

Risks-X, Southern University of Science and Technology (SUSTech); Swiss Finance Institute; ETH Zürich - Department of Management, Technology, and Economics (D-MTEC); Tokyo Institute of Technology

Date Written: October 1999

Abstract

This paper addresses the statistical properties of time series driven by rational bubbles a la Blanchard and Watson (1982). Using insights on the behavior of multiplicative stochastic processes, we demonstrate that the tails of the unconditional distribution emerging from such bubble processes follow power-laws (exhibit hyperbolic decline). More precisely, we find that rational bubbles predict a fat power tail for both the bubble component and price differences with an exponent m smaller than 1. The distribution of returns is dominated by the same power-law over an extended range of large returns. Although power-law tails are a pervasive feature of empirical data, these numerical predictions are in disagreement with the usual empirical estimates. It, therefore, appears that exogenous rational bubbles are hardly reconcilable with some of the stylized facts of financial data at a very elementary level.

Keywords: rational bubbles, random difference equations, multiplicative processes, rational bubbles, random difference equations, multiplicative processes, fat tails.

JEL Classification: G12, D84, C32

Suggested Citation

Lux, Thomas and Sornette, Didier, On Rational Bubbles and Fat Tails (October 1999). SFB 303 Working Paper No. B-458, Available at SSRN: https://ssrn.com/abstract=190253 or http://dx.doi.org/10.2139/ssrn.190253

Thomas Lux (Contact Author)

University of Kiel - Institute of Economics ( email )

Olshausenstr. 40
D-24118 Kiel, 24098
Germany

University of Bonn - Economic Science Area ( email )

Adenauerallee 24-42
D-53113 Bonn
Germany
+49-228-73-9519 (Phone)
+49-228-73-7953 (Fax)

Didier Sornette

Risks-X, Southern University of Science and Technology (SUSTech) ( email )

1088 Xueyuan Avenue
Shenzhen, Guangdong 518055
China

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC) ( email )

Scheuchzerstrasse 7
Zurich, ZURICH CH-8092
Switzerland
41446328917 (Phone)
41446321914 (Fax)

HOME PAGE: http://www.er.ethz.ch/

Tokyo Institute of Technology ( email )

2-12-1 O-okayama, Meguro-ku
Tokyo 152-8550, 52-8552
Japan

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
874
Abstract Views
6,872
Rank
50,730
PlumX Metrics