The volatility-confined LPPL model: A consistent model of ‘explosive’ financial bubbles with mean-reverting residuals |
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| Institution: | 1. School of Business, China East University of Science and Technology, 200237 Shanghai, China;2. Chair of Entrepreneurial Risks, Department of Management, Technology and Economics, ETH Zurich, Kreuplatz 5, CH-8032 Zurich, Switzerland;3. School of Economics and Management, Beihang University, 100191 Beijing, China;4. Swiss Finance Institute, Switzerland;5. University of Geneva, 40 blvd. Du Pont d''Arve, CH 1211 Geneva 4, Switzerland;1. The York Management School, University of York, Freboys Lane, York YO10 5GD, England;2. ICMA Centre, Henley Business School, University of Reading, Whiteknights, Reading RG6 6BA, England;1. University of Illinois, United States;2. Yale University, United States;3. University of Auckland, New Zealand;4. Singapore Management University, Singapore;5. University of Southampton, United Kingdom;1. School of Economics, University of Nottingham, UK;2. Newcastle University Business School, UK;3. Essex Business School, University of Essex, UK;1. ETH Zürich, Department of Management, Technology and Economics, Scheuchzerstrasse 7, Zürich 8092, Switzerland;2. Institute of Risk Analysis, Prediction and Management, Academy for Advanced Interdisciplinary Studies, Southern University of Science and Technology, Shenzhen 518055, China;3. Tokyo Tech World Research Hub Initiative (WRHI), Institute of Innovative Research, Tokyo Institute of Technology, Tokyo, Japan |
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| Abstract: | Using the concept of the stochastic discount factor with critical behavior, 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” (LPPL). 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, and 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 the 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. |
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