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The volatility-confined LPPL model: A consistent model of ‘explosive’ financial bubbles with mean-reverting residuals

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  • Lin, L.
  • Ren, R.E.
  • Sornette, D.

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 4years 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.

Suggested Citation

  • Lin, L. & Ren, R.E. & Sornette, D., 2014. "The volatility-confined LPPL model: A consistent model of ‘explosive’ financial bubbles with mean-reverting residuals," International Review of Financial Analysis, Elsevier, vol. 33(C), pages 210-225.
  • Handle: RePEc:eee:finana:v:33:y:2014:i:c:p:210-225
    DOI: 10.1016/j.irfa.2014.02.012
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    References listed on IDEAS

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    More about this item

    Keywords

    Rational bubbles; Mean reversal; Positive feedbacks; Finite-time singularity; Super-exponential growth; Bayesian analysis; Log-periodic power law; Stochastic discount factor;
    All these keywords.

    JEL classification:

    • G01 - Financial Economics - - General - - - Financial Crises
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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