A Consistent Model of 'Explosive' Financial Bubbles with Mean-Reversing Residuals

35 Pages Posted: 12 Jul 2009

See all articles by Li Lin

Li Lin

China Academy of Financial Research (CAFR); ETH Zurich; Beihang University (BUAA)

Ruoen Ren

Beihang University (BUAA)

Didier Sornette

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC); Swiss Finance Institute

Multiple version iconThere are 2 versions of this paper

Date Written: May 1, 2009

Abstract

We present a self-consistent model for explosive financial bubbles, which combines a mean-reverting volatility process and a stochastic conditional return which reflects nonlinear positive feedbacks and continuous updates of the investors’ beliefs and sentiments. The conditional expected returns exhibit faster-than-exponential acceleration decorated by accelerating oscillations, called “log-periodic power law.” Tests on residuals show a remarkable low rate (0.2%) of false positives when applied to a GARCH benchmark. When tested on the S&P500 US index from Jan. 3, 1950 to Nov. 21, 2008, the model correctly identifies the bubbles ending in Oct. 1987, in Oct. 1997, in Aug. 1998 and the ITC bubble ending on the first quarter of 2000. Different unit-root tests confirm the high relevance of the model specification. Our model also provides a diagnostic for the duration of bubbles: applied to the period before Oct. 1987 crash, there is clear evidence that the bubble started at least 4 years earlier. We confirm the validity and universality of the volatility-confined LPPL model on seven other major bubbles that have occurred in the World in the last two decades. Using Bayesian inference, we find a very strong statistical preference for our model compared with a standard benchmark, in contradiction with Chang and Feigenbaum [2006] which used a unit-root model for residuals.

Keywords: Rational bubbles, mean reversal, positive feedbacks, finite-time singularity, superexponential growth, Bayesian analysis, log-periodic power law

JEL Classification: G01, G17, C11

Suggested Citation

Lin, Li and Ren, Ruoen and Sornette, Didier, A Consistent Model of 'Explosive' Financial Bubbles with Mean-Reversing Residuals (May 1, 2009). Swiss Finance Institute Research Paper No. 09-14. Available at SSRN: https://ssrn.com/abstract=1407574 or http://dx.doi.org/10.2139/ssrn.1407574

Li Lin

China Academy of Financial Research (CAFR) ( email )

1954 Huashan Road
Shanghai P.R.China, 200030
China

ETH Zurich ( email )

Zürichbergstrasse 18
Zurich, 8092
Switzerland

Beihang University (BUAA) ( email )

37 Xue Yuan Road
Beijing 100191
China

Ruoen Ren

Beihang University (BUAA)

37 Xue Yuan Road
Beijing 100083
China

Didier Sornette (Contact Author)

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/

Swiss Finance Institute

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

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