A Simple Mechanism for Financial Bubbles: Time-Varying Momentum Horizon

39 Pages Posted: 21 Oct 2016 Last revised: 18 Jun 2018

See all articles by Li Lin

Li Lin

East China University of Science and Technology (ECUST)

Michael Schatz

affiliation not provided to SSRN

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: June 10, 2018

Abstract

Building on the notion that bubbles are transient self-fulfilling prophecies created by positive feedback mechanisms, we construct the simplest continuous price process whose expected returns and volatility are functions of momentum only. The momentum itself is measured by a simple continuous moving average of past prices over a given time horizon. We introduce a simple dynamics of the time horizon used by the repre- sentative investor, which is motivated by the race of trend-following agents to forerun their competitors. We provide the full set of solutions, which includes an explosive regime where the price and momentum explodes stochastically in finite time to infinity, transient price dynamics escaping to infinity and recurrent behaviors, where the momentum remains either strictly positive or undergoes instantaneous reflections at the origin. The proposed price generating process produces price dynamics that are in agreement with the main qualitative properties of empirical financial time series. Moreover, it produces realistic regime shifts between non-bubble and bubble regimes. We construct a quasi-likelihood methodology to calibrate the model to empirical financial time series, which is applied to an Internet index and a “brick-and-mortar” index, over the period of the dot-com bubble and its subsequent crash, from Jan. 1998 to Dec. 2002. The Wilks test of nested hypotheses shows a very strong skill in diagnosing the bubble of the Internet index and in disqualifying a bubble in the “brick-and-mortar” index.

Keywords: financial bubbles, momentum, positive feedback, time-horizon, quasi-likelihood, finite-time-singularity

JEL Classification: C52, G01, G17

Suggested Citation

Lin, Li and Schatz, Michael and Sornette, Didier, A Simple Mechanism for Financial Bubbles: Time-Varying Momentum Horizon (June 10, 2018). Swiss Finance Institute Research Paper No. 16-61, Available at SSRN: https://ssrn.com/abstract=2854063 or http://dx.doi.org/10.2139/ssrn.2854063

Li Lin

East China University of Science and Technology (ECUST) ( email )

Shanghai
China

Michael Schatz

affiliation not provided to SSRN

Didier Sornette (Contact Author)

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

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